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Relation between input and output states for a beam splitter
Abstract
The state of the optical field at the output of a beam splitter is expressed directly in terms of the state at the input via the diagonal coherent state representation. The conclusion is illustrated for a two-photon Fock state, and it is shown that an output having some features of the two-photon singlet state can be produced.
... When two photons impinge on a beam splitter, they behave in an interesting way. This two-photon interference effect is known generally as Hong-Ou-Mandel interference (or HOM interference for short), and is named after Chung Ki Hong, Zhe Yu Ou, and Leonard Mandel, who both theoretically discussed and then experimentally verified the effect in 1987 [1][2][3][4]. HOM interference shows up in many places, both in fundamental studies of quantum mechanics and in practical implementations of quantum technologies. At its heart, HOM interference is quite simple to understand. ...
... If the beam splitter is lossless and balanced, then the coincidence probability--that is, the probability for photons to be simultaneously detected at both outputs of the beam splitter--is 1/2. On the other hand, if the two photons are indistinguishable there is destructive interference between events (2) and (3), and the coincidence probability is identically zero [5]. ...
... The polarization example is simple to grasp, but the nature of the interference between events (2) and (3) is not bound to discrete degrees of freedom like polarization. In fact, HOM interference was first proposed with a two-photon source where the distinguishability between photons was tuned via an effective time delay and was used as a way to measure the coherence time of single photons on sub-picosecond time scales (the benefit that HOM interference provides over the usual second-order interference experiments is twofold: (1) the method works even if photons are incoherent with each other; and (2) the path length differences between photons need not be kept constant to a fraction of the photon's wavelength [1]). ...
Hong–Ou–Mandel interference is most dramatic when the photons involved are perfectly indistinguishable. Departures from this ideal scenario, however, are also interesting and useful to consider. In this tutorial, we analyze scenarios where the degree of the photons’ distinguishability depends on their spectral and temporal “overlap”. We first consider photons that are both spectrally pure and spectrally separable. We then generalize this to include spectrally entangled (but still spectrally pure) photons and spectrally mixed (but still spectrally separable) photons. This tutorial equips researchers with tools for a deeper understanding of this interesting phenomenon and its various applications.
... Photons manifest unique quantum properties that might appear odd and counter intuitive from a classical standpoint. A paradigmatic example of this unusual behavior is given by the interference of two identical photons after impinging separately at the two faces of a balanced beam splitter, as the two photons always end up together in one of the two output arms of the beam splitter [1][2][3][4][5][6][7][8]. This tendency of the photons to "bunch" together arises from the lack of information on which path the two photons undertake when interfering at the beam splitter. ...
... In particular, the employment of notions borrowed from estimation theory and the subsequent study of the Fisher information [13,14]-a way to quantify the ultimate amount of information that can be obtained about an unknown parameter with a given estimation scheme-have recently allowed for a further boost in the levels of precision achievable [9][10][11]15]. On the other hand, these analyses also show that the sensitivity of schemes based purely on the observation of the coincidence and bunching statistic is highly dependent on how much the two photons differ from each other in the parameter to estimate, such as their relative time delay [1][2][3][4][5][6][7][8][9]. In particular, such two-photon interference techniques become insensitive to photonic time delays beyond the temporal bandwidth of the photons [1][2][3][4][5][6][7][8][9] A different approach with respect to standard twophoton interference takes advantage of current detectors capable of resolving inner-mode variables of the photons, such as their time of arrival [15][16][17][18][19][20] or their frequencies [21][22][23]. ...
... On the other hand, these analyses also show that the sensitivity of schemes based purely on the observation of the coincidence and bunching statistic is highly dependent on how much the two photons differ from each other in the parameter to estimate, such as their relative time delay [1][2][3][4][5][6][7][8][9]. In particular, such two-photon interference techniques become insensitive to photonic time delays beyond the temporal bandwidth of the photons [1][2][3][4][5][6][7][8][9] A different approach with respect to standard twophoton interference takes advantage of current detectors capable of resolving inner-mode variables of the photons, such as their time of arrival [15][16][17][18][19][20] or their frequencies [21][22][23]. Indeed, one can exploit the quantum beating, i.e., the oscillations in the count of coincidence and bunching events of two photons as a function of the detection times or the detected frequencies, to infer the value of the frequency shift or the time delay of the two photons, respectively [16,17,24,25]. ...
We demonstrate the ultimate sensitivity allowed by quantum physics in the estimation of the time delay between two photons by measuring their interference at a beam splitter through frequency-resolving sampling measurements. This sensitivity can be increased quadratically by decreasing the photonic temporal bandwidth even at values smaller than the time delay when standard two-photon interferometers become inoperable and without adapting the path of the reference photon, nor the need of time-resolving detectors with an unfeasible high resolution. Applications can range from the more feasible imaging of nanostructures, including biological samples, and nanomaterial surfaces to quantum enhanced estimation based on frequency-resolved boson sampling in optical networks.
... In 1987, Prasad, Scully, and Martienssen published a theoretical paper [1] describing the unitary transformation relating input and output modes of a beam splitter. In the same year [2], Ou, Hong and Mandel deduced the expression of the field at BS output in terms of the input state through diagonal coherent state representation, noting that "with respect to any measurements involving simultaneous photon detections at output ports, the state behaves in the same way as the well-known singlet state for two orthogonally polarized photons". A few months later [3], the same authors experimentally demonstrated the interference of two identical photons on a BS obtaining the characteristic 'dip' in coincidence detection at the BS output. ...
... This is the case, at least, for areas far from the points of discontinuity of the map in Equation (2). In a setup employing a fiber-coupled BS, however, the previous equation does not necessarily hold true and should be replaced. ...
... The result is shown in Figure 4. The comparison shown in Figure 4 proves that the system employing fiber-coupled components is capable of saturating the Cramér-Rao bound for mismatch angles θ i far from the points of non-derivability in Equation (2). Due to both the piecewise definition of the functionθ i , and the intrinsically Poissionan nature of photons generation and detection (where coherent sources are employed), the number of experimental angles θ i misclassified as either Θ or Θ + 90 • increases the closer θ i is to Θ or to Θ ± 90 • , respectively. ...
The use of statistical estimation theory to boost the metrological performance of the measurement apparatus is becoming increasingly popular in a wide range of applications. Recently, such an approach has been adopted in Hong Ou Mandel interferometry, setting a new record in time delay and polarization measurement. Here, we extend these pioneering experiments in the telecom range to unlock the full potential of the information-based approach combined with a versatile spectral range, aiming for its adoption in fiber-coupled devices of up to hundreds of kilometers long as bobines or optical networks. Our measurement saturates the Cramér-Rao bound and in a long lasting experiment returns an Allan deviation of the polarization angle of 0.002 degs in 1 h of integration time.
... As a result, the dispersion law in yz surfaces of macropores change to z direction along macropores. The vertically polarized light along macropores (z direction) and horizontally polarized light (x direction) permit the explanation of results as two-photon interference (the Hong-Ou-Mandel effect) [20]. In this case, macropore is a beam splitter (BS) with maximum and minimum coincidences for measurements with parallel and perpendicularly polarizations, respectively. ...
... Moreover, by changing the thickness of the nanocoatings, it is possible to achieve a match in the frequency of interference modes with frequencies of surface bond oscillations on boundaries Si-SiO 2 and SiO 2 +РЕІ-ncCdS (slotted modes [19]). When the frequencies of local oscillations of surface bonds and slotted modes matched, then the light absorption increases up to 10 5 times on the frequencies of slit oscillations of surface bonds [20]. For macroporous silicon, 2D resonances of Wannier-Stark electro-optical effect in yz plane correspond to constructive interference of the two-photon states (bosonic behavior, 2D polaritons), and two-polar resonances in ±z direction are determined by 1D polaritons (destructive interference of the two-photon states, fermionic behavior) [2]. ...
... Measurements the giant two-polar oscillations with very small half-width 0.5 cm -1 in IR absorption spectra of polyvinyl chloride include negative IR absorption band at -690 cm -1 (Amide V) [14] and intensive positive peaks at 1430 between 1400-1500 cm -1 . Thus, vertically polarized light along carbon nanotubes and horizontally polarized light for D and 2D bands resulted in beams splitting and two-photon interference and quantum Hong-Ou-Mandel effect [20]. ...
The possibilities to enhance the properties of nanostructured surfaces are evaluated on “polymer-multiwall carbon nanotube” composites. Influence of sp3 hybridization bonds is investigated in composites derived from polypropylene, polyamide-6, polyamide-12 and polyvinyl chloride after adding CNTs to polymers. IR absorption of “polymer-CNTs” films exceeds that of polymer by 10-103 times in the entire measured spectral range. In addition, two-polar IR absorption are measured on composites with negative components at spectral positions of “D-band” and “2D-band” of sp3 hybridization. In this case, the greater oscillation amplitudes of C-C, CH2 and CH3 bonds correspond to a higher absorption at the vibration frequencies γω(CН) and γω(CH2). Two-polar oscillations of absorption with a negative component in the spectral band ranges “D” and “2D” of sp3 hybridization in nanotubes have been measured for the composites. Frequencies of 2D-band correspond to the second order frequencies of D-band. The intensity of 2D band increases with an increase in the concentration of defects. The absorption of light increases when the frequencies of local oscillations of surface bonds in carbon nanotubes correspond to the frequencies of slotted modes along the boundary of the “nanotube polymer” (surface polaritons). Two-polar oscillations have an ultra-small half width 0.4–0.6 cm–1, which indicates a strong interaction of surface polaritons with photons. Vertically polarized light along carbon nanotubes and horizontally polarized light of D and 2D bands resulted in light beams splitting, two-photon interference and realization of the quantum Hong-Ou-Mandel effect.
... From a broader perspective, the indistinguishability concept is related to a given set of quantum measurements [12]. In fact, indistinguishability plays a fundamental role in raising quantum processes, such as many-body interference [11,13], entanglement generation [9, 10, 14-17], quantum teleportation [17], quantum metrology [18,19], quantum coherence [20][21][22], quantumness protection [12,23,24], quantum key distribution [25,26], and the high state complexity exploited by Boson Sampling algorithms [27,28]. ...
... Indistinguishability of quantum identical particles [9,10] has also revealed as a useful nonclassical resource. From an operational point of view, particles are so-called indistinguishable if they are in the same mode with respect to a characterization via two-particle interference [11]. From a broader perspective, the indistinguishability concept is related to a given set of quantum measurements [12]. ...
... From a broader perspective, the indistinguishability concept is related to a given set of quantum measurements [12]. In fact, indistinguishability plays a fundamental role in raising quantum processes, such as many-body interference [11,13], entanglement generation [9,10,[14][15][16][17], quantum teleportation [17], quantum metrology [18,19], quantum coherence [20][21][22], quantumness protection [12,23,24], quantum key distribution [25,26], and the high state complexity exploited by Boson Sampling algorithms [27,28]. ...
The presence of disorder and inhomogeneities in quantum networks has often been unexpectedly beneficial for both quantum and classical resources. Here, we experimentally realize a controllable inhomogenous Quantum Walk dynamics, which can be exploited to investigate the effect of coherent disorder on the quantum correlations between two indistinguishable photons. Through the imposition of suitable disorder configurations, we observe two photon states which exhibit an enhancement in the quantum correlations between two modes of the network, compared to the case of an ordered Quantum Walk. Different configurations of disorder can steer the system towards different realizations of such an enhancement, thus allowing spatial and temporal manipulation of quantum correlations.
... It is also convenient to define with (^ †,^ †) the vector of input creation operators of photons entering through port ( , ) (see Figure 1) and with (^ †,^ †) the vector of input creation operators of photons exiting through port ( , ) -as for now we do not specify additional mode indices in the creation operators. Conservation of photon number implies that the BS is described by a transformation of the form [24][25][26]: ...
... with | | 2 + | | 2 = 1. The factors and are associated with the reflectivity and the transmissivity of the device (this can be indeed confirmed by calculating the action of the BS on an ideal laser beam, modelled as a coherent state [25]). For incident fields described by paraxial spatial modes, the coefficients and are approximately independent of the incident mode except for the OAM modes, since the index ℓ changes sign under reflection. ...
The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons -- those with complex spatial profiles -- under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions, which is a crucial contribution for its application in computational and artificial-intelligence-driven discovery of new quantum experiments exploiting the power of photons with complex spatial modes.
... When the beamsplitter has equal transmission and reflection probabilities (i.e. it is a 50:50 beamsplitter) and the two photons enter by two separate ports but are otherwise indistinguishable, then the probability of them exiting via separate ports drops to zero. Having seen this result early in 1987, Rodney slowly realized its significance over the course of the year and decided to publish after hearing of related theory results from the Martienson [2] and Mandel groups [3]. Then on a visit to the Rochester laboratory of Leonard Mandel in the summer of 1987, he guessed that an experiment might be in progress. ...
... For instance, in the case of Schor's algorithm for factorizing large products of primes [47], this is the period of a function which then constrains the search space to one solvable by a polynomial function. It is the clear sighted fundamental expositions of the simplest of these interferences by Rodney Loudon [1] and his contemporaries [2,3] that underpins all of this extraordinary progress. ...
This paper presents a short history of the discovery by Rodney Loudon and Heidi Fearn of the counter-intuitive destructive interference effect occurring when two indistinguishable photons meet at a beamsplitter. This effect, commonly known as the Hong Ou Mandel effect, underpins much of present day photonic quantum information processing. Here I try to review its development from inception to present day proposals of million qubit photonic quantum computers.
This article is part of the theme issue ‘The quantum theory of Light’.
... It will be helpful to understand how different the interference patterns are for symmetrical and asymmetrical beam splitters. There were studies about the properties of both symmetrical and asymmetrical beam splitters in quantum theory [17][18][19]. However, systematical study about the second-order interference of two independent light beams at an asymmetrical BS is still missing. ...
... The reflectivity and transmittivity of ABS are R and T , respectively. The sum of R and T is 1 for a lossless BS [17][18][19]. The probability for the photon detected by D 1 coming from S a is ...
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when asymmetrical beam splitter is employed.
... Since the total photon number is conserved, the involved photonic states include {|00⟩, |01⟩, |10⟩, |02⟩, |11⟩, |20⟩}. The beam-splitters (BS) used to separate and mix microwave light [51] can be described by an unitary matrix ...
... This can be done as follows. First, the 50/50 BS makes |11⟩ → (|02⟩ + |20⟩)/ √ 2 because of HOM interference [51]. Then, two NS gates are used to introduce a π-phase shift: |02⟩ + |20⟩ → −|02⟩ − |20⟩. ...
We propose a scheme for realizing a deterministic two-photon C-Z gate based on variants of the two-photon quantum Rabi model, which is feasible within the framework of circuit QED. We begin by utilizing the two-photon interaction to implement the nonlinear sign (NS) gate, and subsequently, we construct the C-Z gate following the KLM scheme. We consider three different regimes: the strong coupling regime, the perturbative ultrastrong coupling regime, and the large detuning regime. Our results indicate that the C-Z gate operates fast with high fidelity and is robust against decoherence, thereby offering a suitable approach for achieving deterministic two-photon quantum gates via light-matter interactions.
... A conventional beam splitter (CBS), which separates input light and transports its modes into two output ports, constitutes one of the key components in optical interferometers [1,2]. Following the development of its quantum theory [3][4][5], the CBS has found widespread applications such as linear optical quantum computing [6][7][8], quantum imaging [9][10][11][12], and quantum sensing [13][14][15]. Usually, the CBS responds symmetrically to inputs from both sides, and its reflection and transmission coefficients determined by single-photon scattering processes remain fixed. ...
... The CBS is fully characterized by its reflection and transmission coefficients. These coefficients of our QBS are determined by single-photon scattering processes and can be measured via the output signal resulting from a weak continuous- 7/6 7/6 8(7, 5) : (7,5) FIG. 2. The reflectance R(θ, ϕ) ≡ |r r→l (p)| 2 (a) and transmittance T (θ, ϕ) ≡ |t r→r (p)| 2 (b) as functions of θ = k 0 d and ϕ. Here, we consider the resonant input case with p = 0. ...
We propose a quantum beam splitter (QBS) with tunable reflection and transmission coefficients. More importantly, our device based on a Hermitian parity-time () symmetric system enables the generation and manipulation of asymmetric quantum coherence of the output photons. For the interference of two weak coherent-state inputs, our QBS can produce anti-bunched photons from one output port and bunched photons from the other, showcasing high parity asymmetry and strong coherence control capabilities. Beyond the Hong-Ou-Mandel effect, perfect photon blockade with vanishing is achievable in two-photon interference. These striking effects of the QBS fundamentally arise from the parity-symmetry-breaking interaction and the quantum interference between the photon scattering channels. Our results could inspire novel applications and the development of innovative photonic devices for the manipulation of weak quantum light.
... Instead the two photons always end up in the same output arm of the beam-splitter [1][2][3][4][5][6][7][8]. This tendency of the photons to 'bunch' together is a prerogative of all quanta of bosonic fields (e.g. the electromagnetic field), and arises from the lack of information on which path the two photons undertake when interfering at the beam splitter. ...
... To analyse the optimal precision achievable when estimating the time delay ∆t between two interfering photons when frequency-resolving detectors are employed in the two-photon interference setup in Figure 1, we evaluate the smallest possible variance of any unbiased estimator ∆t, given by the Cramér-Rao bound [13,14] Var[ ∆t] ≥ 1 N F (∆t) (5) when N repetitions of the measurement are performed. Here, F (∆t) is the Fisher Information [13,14] ...
The quantum interference occurring between two indistinguishable photons impinging on the two input faces of a beam-splitter can be exploited for a range of applications, from quantum optical coherence tomography, to quantum metrology including time intervals measurements. In the latter, recent advances managed to reach a resolution in the estimation of the delay between the two photons of the order of attoseconds, i.e. in the nanometer scale. Unfortunately, these techniques are highly affected in the estimation precision by any experimental distinguishability between the photons at the detectors. Here, we perform an analysis of the precision achievable in the estimation of the delay between two independent photons interfering at a beam-splitter when frequency-resolved measurements are employed. Remarkably, we show that the observation of the spectra of the photons at the output ports when coincidence and bunching events are recorded, largely enhance the precision of the estimation for any degree of distinguishability between the photons at the detectors. In particular, we find that such scheme is effective also for temporal delays much larger than the coherence time of each photons, a regime in which standard two-photon interferometers or spectral analyses at the single-photon level, do not provide any information. Furthermore, we show that by increasing the bandwidth of the photons it is possible to further increase quadratically the precision in the estimation, differently from non-resolved two-photon interference where the precision degrades for large bandwidth values. Therefore, such estimation scheme with frequency-resolving detectors allows to substantially enhance the precision of measurements of time delays. Relevant applications can range form the characterization of two-dimensional nanomaterials to the analysis of biological samples, including DNA and cell membranes.
... Indistinguishability of quantum identical particles [9,10] has also been revealed as a useful nonclassical resource. From an operational point of view, particles are so-called indistinguishable if they are in the same mode with respect to a characterization via two-particle interference [11]. From a broader perspective, the indistinguishability concept is related to a given set of quantum measurements [12]. ...
... From a broader perspective, the indistinguishability concept is related to a given set of quantum measurements [12]. In fact, indistinguishability plays a fundamental role in raising quantum processes, such as many-body interference [11,13], entanglement generation [9,10,[14][15][16][17], quantum teleportation [17], quantum metrology [18,19], quantum coherence [20][21][22], quantumness protection [12,23,24], quantum key distribution [25,26], and the high state complexity exploited by boson sampling algorithms [27,28]. ...
The presence of disorder and inhomogeneities in quantum networks has often been unexpectedly beneficial for both quantum and classical resources. Here we experimentally realize a controllable inhomogenous quantum walk (QW) dynamics, which can be exploited to investigate the effect of coherent disorder on the quantum correlations between two indistinguishable photons. Through the imposition of suitable disorder configurations, we observe two-photon states that exhibit an enhancement in the quantum correlations between two selected modes of the network, compared to the case of an ordered QW. Different configurations of disorder can steer the system toward different realizations of such an enhancement, thus allowing spatial and temporal manipulation of quantum correlations between remote modes of QW networks.
... Shape of oscillations [12] corresponds to the interference of polaritons as the eigenstates of the system "nanocoatingsilicon matrix -waveguide modes" (Fig. 6). In our case, an additional degree of freedom due to creation of vertically polarized light in z direction and horizontally polarized light in x direction (Fig. 5 a) permit to interpret the obtained result as two-photon interference -Hong-Ou-Mandel effect [23]. In this case, macropore is a beam splitter (BS) with maximum and minimum coincidences for measurements with parallel and perpendicularly polarizations, respectively. ...
... The quantum statistics of atoms is observed typically in the behavior of an ensemble via macroscopic observables, in addition, quantum statistics modifies the behavior of even two particles. The basis of the two-photon interaction provides the mixing between the two input modes via the action of the beam splitter (BS) [23] with the diagonal coherent state representation; in particular, they give the explicit example of what happens when two photons, one horizontally and one vertically polarized, are incident from different input ports. In this case, one observe constructive interference of the two-photon states corresponding to photons exiting through the same output ports (bosonic behavior), and destructive interference of the two-photon states corresponding to photons exiting opposite output ports (fermionic behavior). ...
In this paper, we used high-resolution IR absorption spectra to investigate 1D and 2D polaritons in periodical 2D macroporous silicon structures with nano-coatings of SiO2 and CdS, ZnO nanoparticles. The application of high-resolution IR absorption spectroscopy resulted in detection of dipole-active TO vibrations, photon splitting and giant two-polar absorption oscillations with amplitudes of ±107arb.un. As a result, the dispersion law in yz surfaces of macropores change to z direction along macropores. It means additional degree of freedom as vertically polarized light in z direction and horizontally polarized light in x direction resulted in beams splitting and two-photon interference - Hong-Ou-Mandel effect. In our case, 2D resonances of Wannier-Stark electro-optical effect in yz plane correspond to constructive interference of the two-photon states (bosonic behavior), and two-polar resonances in ±z direction are determined by destructive interference of the two-photon states (fermionic behavior). Two-polar oscillations of 1D -polaritons have the ultra-small half-width 0.4–0.6 сm–1 and minimal Rabi frequency of samples 1.0 сm–1 equaled to the resolution of spectral measurements. Furthermore, two-photon interference and 1D polaritons are perspective for high-coherent optical quantum computers on macroporous silicon with nano-coatings and, in addition, for lasers and new metamaterials.
... In a conventional Hong-Ou-Mandel (HOM) interferometer [1][2][3] photo-counting coincidences are detected at the output ports of a 50:50 beam splitter that coherently mixes two multi-frequency optical waves coming from two separate spatial modes. The sensitivity of the registered signal is directly related with the indistinguishability of the interacting light fields [4][5][6][7][8][9] making it a useful tool in a variety of information and measurement processing. ...
... andâ 1 (ω) = e iωτ ξ * 1 (ω)(ĉ 1 (ω) +ĉ 2 (ω))/ √ 2 + ... , ...
A modification of the standard Hong-Ou-Mandel interferometer is proposed that allows one to recover two independent parameters (delays) via the coincidences counts measured at the output of the setup. In the ideal case where such delays are sufficiently stable with respect to the mean wavelength of the pump source, properly symmetrized input bi-photon states allow one to pinpoint their values through the identification of a zero in the coincidence counts rate, a feature that cannot be simulated by semiclassical inputs. In the presence of fluctuating parameters the zero in the coincidences is washed away: still the bi-photon state permits to recover the values of parameters with a visibility which is higher than the one allowed by semiclassical sources. The detrimental role of loss and dispersion is also analyzed and an application in the context of quantum positioning is presented.
... with d = γoγm 4 + g 2 ⟨n⟩. By accounting for the expression of By accounting for (23), it results that matrix L determining the input-output relations between the microwave and optical fields corresponds to the matrix of a lossless beam splitter with a transmission coefficient T and a reflection coefficient R [74], [75], i.e.: ...
Superconducting and photonic technologies are envisioned to play a key role in the Quantum Internet. However the hybridization of these technologies requires functional quantum transducers for converting superconducting qubits, exploited in quantum computation, into “flying” qubits, able to propagate through the network (and vice-versa). In this paper, quantum transduction is theoretically investigated for a key functionality of the Quantum Internet, namely, multipartite entanglement distribution. Different communication models for quantum transduction are provided, in order to make the entanglement distribution possible. The proposed models departs from the large heterogeneity of hardware solutions available in literature, abstracting from the particulars of the specific solutions with a communication engineering perspective. Then, a performance analysis of the proposed models is conducted through key communication metrics, such as quantum capacity and entanglement generation probability. The analysis reveals that – although the considered communication metrics depend on transduction hardware parameters for all the proposed models – the particulars of the considered transduction paradigm play a relevant role in the overall entanglement distribution performance.
... Among them, the design of beam splitter, which splits incident wave into multiple parts with the same or different intensities, is quite demanding, it has potential applications in optical circuits and communications [1]. In the past, many researchers have considered the behavior of the quantum-mechanical beam splitter [11][12][13][14][15][16][17][18][19]. While the 1 × 2 optical splitters are used routinely (say for instance, Y-and T-branch junctions) [20], the rapidly growing need for space-division multiplexing in optical transmission [21], computing [22] and sensing networks [23] translates into the need for multi-port splitters [24]. ...
In this work, we introduce a quantum-mechanical shortcut-to-adiabatic passage (STAP) into the design of multiple beam splitter. The device consists of one input and N output waveguide (WG) channels, which are connected via a mediator WG. After reducing such (N + 2)-WG structure into a controllable 3-WG counterpart by Morris-Shore transformation, we point out that the structure is available for all possible three-level STAP methods. By implementing one of them which does not require additional couplings, we can achieve the multiple beam splitting with arbitrary ratios among the N outputs. What is more, the device length is significantly shortened. Except for this, it is quite unique that the design exhibits a one-way energy transport. The underlying physics is presented. These features may have profound impacts on exploring quantum technologies for promoting advanced optical devices.
... Let us first consider the case of a lossless beam splitter and (quasi-)monochromatic light of (mid-)frequency ω (Fig. 1). It is well known [8][9][10][11][12][13] that a lossless beam splitter transforms the operators of the incoming modeŝ a 1 (ω) andâ 2 (ω) to the operators of the outgoing modeŝ b 1 (ω) andb 2 (ω) according to ...
The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied, with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices, the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement. In particular, they do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure.
... As will be explicitely shown in the main text, event C is compatible with the microscopic conservation of energy, thus, it does not by no means correspond to some kind of dissipation. Concerning the analysis of the beam splitter problem in terms of quantized amplitudes we refer the reader to the works [41][42][43][44]. We also note that the source is not considered as a part of the measuring apparatus. ...
Correlations of detection events in two detectors are studied in case of linear excitation of the measuring apparatus. On the basis of classical probability theory and fundamental conservation laws, a general formula is derived for the two-point correlation functions for both bosons and fermions. The results obtained coincide with that derivable from quantum theory which uses quantized field amplitudes. By applying both the particle and the wave picture at the same time, the phenomena of photon bunching and antibunching, photon anticorrelation and fermion antibunching, measured in beam experiments, are interpreted in the frame of an intuitively clear description.
... Notice that the curves in Fig.2(a) From Eq.(3), we find when we adjust the pulse width or amplitude of the Stokes field so that θ = π, the oscillation stops at the maximum conversion between atom and light. Notice that the input-output relation in Eq.(3) is exactly the relation for a lossless beam splitter [21,22]: the write field here is equivalent to one of the input fields of the beam splitter and the atomic spin wave is the other field. Thus the outputs are coherent mixtures of the optical field and the atomic spin wave. ...
Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interaction between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between atom and light and a coherent mixing of light wave with excited atomic spin wave in a Raman process. We construct a new kind of hybrid interferometer based on the atom-light coherent superposition state. Interference fringes are observed in both optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.
... The theory of this passive four-port device has been developed in Refs. [5,4,38,41,72,76,77,78,93,102,124,138,143,145,150,155,183,199]. Here we follow mostly Refs. ...
Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes. The article develops the quantum theory of simple optical instruments and applies the theory to a few characteristic situations, to the splitting and interference of photons and to the manifestation of Einstein-Podolsky-Rosen correlations in parametric downconversion. How to model irreversible devices such as absorbers and amplifiers is also shown. Finally, the article develops the theory of Hawking radiation for a simple optical black hole. The paper is intended as a primer, as a nearly self-consistent tutorial. The reader should be familiar with basic quantum mechanics and statistics, and perhaps with optics and some elementary field theory. The quantum theory of light in dielectrics serves as the starting point and, in the concluding section, as a guide to understand quantum black holes.
... The weak coherent state |α and weak LO field in a coherent state |β are treated as a product state of two independent coherent states |α, β in the input of the beam splitter [12]. ...
Intrinsic quantum correlations of weak coherent states are observed between two parties through a novel detection scheme, which can be used as a supplement to the existence decoy-state BB84 and differential phase-shift quantum key distribution (DPS-QKD) protocols. In a proof-of-principle experiment, we generate bi-partite correlations of weak coherent states using weak local oscillator fields in two spatially separated balanced homodyne detections. We employ nonlinearity of post-measurement method to obtain the bi-partite correlations from two single-field interferences at individual homodyne measurement. This scheme is then used to demonstrate bits correlations between two parties over a distance of 10 km through a transmission fiber. We believe that the scheme can add another physical layer of security to these protocols for quantum key distribution.
... By now a two input approach to the beam-splitter is almost universally accepted even when one of the inputs is the vacuum 6 (e.g. [38]), but some workers still use a single input ( [34], p. 222 7 ; [39], p. 494 8 ). The two input approach leads to an elegant mathematical description of the action of a beam-splitter in terms of a unitary 2 × 2 transformation matrix which has the form of a rotation matrix [40]. ...
Grangier, Roger and Aspect (GRA) performed a beam-splitter experiment to demonstrate the particle behaviour of light and a Mach-Zehnder interferometer experiment to demonstrate the wave behaviour of light. The distinguishing feature of these experiments is the use of a gating system to produce near ideal single photon states. With the demonstration of both wave and particle behaviour (in two mutually exclusive experiments) they claim to have demonstrated the dual particle-wave behaviour of light and hence to have confirmed Bohr's principle of complementarity. The demonstration of the wave behaviour of light is not in dispute. But we want to demonstrate, contrary to the claims of GRA, that their beam-splitter experiment does not conclusively confirm the particle behaviour of light, and hence does not confirm particle-wave duality, nor, more generally, does it confirm complementarity. Our demonstration consists of providing a detailed model based on the Causal Interpretation of Quantum Fields (CIEM), which does not involve the particle concept, of GRA's which-path experiment. We will also give a brief outline of a CIEM model for the second, interference, GRA experiment.
... Four-port devices such as beam splitters are indispensable to optical investigation, and a number of fundamental experiments in quantum optics necessarily require the use of them. The quantum theory of dispersionless and nonabsorbing beam splitters has been well established [1][2][3][4][5][6][7]. A beam splitter can be realized by a multislab dielectric plate, which is a dispersive and absorbing device in general. ...
The recently derived input-output relations for the radiation field at a dispersive and absorbing four-port device [T. Gruner and D.-G. Welsch, Phys. Rev. A 54, 1661 (1996)] are used to derive the unitary transformation that relates the output quantum state to the input quantum state, including radiation and matter and without placing frequency restrictions. It is shown that for each frequency the transformation can be regarded as a well-behaved SU(4) group transformation that can be decomposed into a product of U(2) and SU(2) group transformations. Each of them may be thought of as being realized by a particular lossless four-port device. If for narrow-bandwidth radiation far from the medium resonances the absorption matrix of the four-port device can be disregarded, the well-known SU(2) group transformation for a lossless device is recognized. Explicit formulas for the transformation of Fock-states and coherent states are given.
... Such devices essentially couple the input light modes into the output modes as it was early realized in the investigation of quantum noise arising in interferometers [2] and produced by linear amplifiers [3][4][5][6][7]. Due to its ubiquity in quantum optical setups, the lossless beam splitter has been thoroughly investigated [8][9][10][11] and shown to support relevant quantum optical effect [12] as manipulation of the photon statistics [13,14] two-photon interference [15][16][17] and generation of entangled output states out of nonclassical input states [18,19]. The theoretical description of the lossless beam splitter has also been extended to more general passive and lossless optical systems [20] with particular emphasis on planar devices [21][22][23][24]. ...
We develop a general approach to describe the scattering of quantum light by a lossy macroscopic object placed in vacuum with no restrictions on both its dispersive optical response and its spatially inhomogeneous composition. Our analysis is based on the modified Langevin noise formalism, a recently introduced version of macroscopic quantum electrodynamics where scattering (s) modes are explicitly separated from electric (e) and magnetic (m) medium excitations; accordingly the formalism involves three kinds of non-interacting boson polaritons such that, in the lossless limit, s-polaritons reduce to standard photons whereas e- and m-polaritons disappear. We analytically derive the input-output unitary relation joining the boson operators of the ingoing and outgoing polaritons, a nontrivial result hinging upon original relations which comprehensively describe the transmission-emission-absorption interplay pertaining the classical radiation scattering, relations we here deduce by resorting to the dyadic Green's function properties. Besides we exploit the input-output relation to connect the output state of the field to the input one, this unveiling the role played by various classical electromagnetic dyadics in quantum optical scattering. We specialize the discussion to the most common situation where the object is initially not electromagnetically excited, with the ingoing electromagnetic state only containing s-polaritons, and we analyze the impact of the classical transmission and absorption dyadics on the transitions from ingoing to outgoing s-polariton and on the creation of outgoing e- and m-polaritons, respectively. Since the scattered radiation is collected in the far-field and the object is usually left unmeasured, we analytically derive the reduced density operator of the outgoing s-polaritons.
... Practically, the resulting statistical distributions are identical to the intensity distributions obtained by using classical (coherent) light. If multiple photons or atoms are used as experimental platforms to encode systems S and C, the quantum operations of the two systems require high-order coherence in photons, such as the Hong-Ou-Mandel effect [43,44], controlled-NOT operation [45]. In this case, the experimental results deviate from the classical behavior. ...
The manipulation and transformation of quantum resources are key parts of quantum mechanics. Among them, asymmetry is one of the most useful operational resources, which is widely used in quantum clocks, quantum metrology, and other tasks. Recent studies have shown that the asymmetry of quantum states can be significantly amplified with the assistance of correlating catalysts that are finite-dimensional auxiliaries. In the experiment, we perform translationally invariant operations, ensuring that the asymmetric resources of the entire system remain nonincreasing, on a composite system composed of a catalytic system and a quantum system. The experimental results demonstrate an asymmetry amplification of 0.0172±0.0022 in the system following the catalytic process. Our Letter showcases the potential of quantum catalytic processes and is expected to inspire further research in the field of quantum resource theories.
... Practically, the resulting statistical distributions are identical to the intensity distributions obtained by using classical (coherent) light. If multiple photons or atoms are used as experimental platforms to encode systems S and C, the quantum operations of the two systems require highorder coherence in photons, such as Hong-Ou-Mandel effect [43,44], controlled-NOT operation [45]. In this case, the experimental results deviate from the classical behavior. ...
The manipulation and transformation of quantum resources are key parts of quantum mechanics. Among them, asymmetry is one of the most useful operational resources, which is widely used in quantum clocks, quantum metrology, and other tasks. Recent studies have shown that the asymmetry of quantum states can be significantly amplified with the assistance of correlating catalysts which are finite-dimensional auxiliaries. In the experiment, we perform translationally invariant operations, ensuring that the asymmetric resources of the entire system remain non-increasing, on a composite system composed of a catalytic system and a quantum system. The experimental results demonstrate an asymmetry amplification of 0.0172\pm0.0022 in the system following the catalytic process. Our work showcases the potential of quantum catalytic processes and is expected to inspire further research in the field of quantum resource theories.
... By accounting for (22), it results that matrix L determining the input-output relations between the microwave and optical fields corresponds to the matrix of a lossless beam splitter with a transmission coefficient T and a reflection coefficient R [56], [57], i.e.: 11 The interaction Hamiltonian is obtained in the condition of the rotatingwave approximation [27]. 12 We consider a weakly coupled system, i.e., g << γx [43]. ...
Superconducting and photonic technologies are envisioned to play a key role in the Quantum Internet. However the hybridization of these technologies requires functional quantum transducers for converting superconducting qubits into "flying" qubits able to propagate through the network (and vice-versa). In this paper, quantum transduction is theoretically investigated for a key functionality of the Quantum Internet, namely, multipartite entanglement distribution. Different communication models for quantum transduction are provided, in order to make the entanglement distribution possible. The proposed models departs from the large heterogeneity of hardware solutions available in literature, abstracting from the particulars of the specific solutions with a communication engineering perspective. Then, a performance analysis of the proposed models is conducted through key communication metrics, such as quantum capacity and entanglement generation probability. The analysis reveals that -- although the considered communication metrics depend on transduction hardware parameters for all the proposed models -- the particulars of the considered transduction paradigm play a relevant role in the overall entanglement distribution performance.
... Linear optical unitaries [32][33][34] alone have been shown to reach peak splitting efficiencies of only 50% [35,36]. This is unlike the Hong-Ou-Mandel system [37,38], where an input encoded in a superposition of two optical paths can be separated perfectly using linear optical elements. A two-level emitter exceeds the 50% splitting efficiency limit of linear optics but cannot achieve perfect routing due to the timebandwidth trade-off. ...
Directing indistinguishable photons from one input port into separate output ports is a fundamental operation in quantum information processing. The simplest scheme for achieving routing beyond random chance uses the photon blockade effect of a two-level emitter. But this approach is limited by a time-energy uncertainty relation. We show that a linear optical unitary transformation applied after the atom enables splitting efficiencies that exceed this time-energy limit. We show that the linear optical unitary improves the splitting efficiency from 67% to 82% for unentangled photon inputs, and from 77% to 90% for entangled photon inputs. We then optimize the temporal mode profile of the entangled photon wave function to attain the optimal splitting efficiency of 92%, a significant improvement over previous limits derived using a two-level atom alone. These results provide a path towards optimizing single photon nonlinearities and engineering programmable and robust photon-photon interactions for practical, high-fidelity quantum operations.
... un. [21]. ...
We investigated influence of multiwalled carbon nanotubes (CNTs) on spectral characteristics of composites “thermo-expanded graphite – carbon nanotubes (TEG–CNTs)”. The introduction of CNTs in an amount of 0-3% by weight of TEG composites results in a significant increase in the strength characteristics and thermal stability of the composites. This result indicates that CNTs is ideal filler for composites based on TEG compositions and structures. Measurements the giant two-polar oscillations with very small half-width 0.5 cm–1 testify the strong interaction of surface polaritons with photons. When frequencies of local oscillations of surface bonds of carbon nanotubes and modes along “nanotube-TEG” boundaries matches, then the light absorption increases 102–105 times. Thus, IR absorption with two-polar oscillations was measured at 0% of nanotubes in TEG at frequency of 2750 cm–1. It is own optical mode in the thermally expanded graphite. 5 peaks with two-polar oscillations were measured in the IR absorption spectra at 1% of carbon nanotubes. And 8 peaks with two-polar oscillations were measured at 3 % of carbon nanotubes at optical mode frequencies along the boundaries of thermally expanded graphite - carbon nanotubes. When frequencies of local oscillations of carbon nanotubes and composite’s modes matches, then the light absorption extremely increases (in 102–105 times), and two-polar IR absorption oscillations with negative components are formed. In general, two-photon interference is a result of quantum entanglement of dipole-active oscillations and splitting of photons according to the Hong-Ou-Mendel (HOM) quantum effect. Two-photon entanglement is built on the basis of the most entanglement states, also known as Bell's states. The HOM–quantum effect on composites “expanded graphite-carbon nanotubes” is promising for the development of highly coherent optical quantum computers.
... where i implies there is a π 2 -phase difference between reflection and transmission [35], n and s represent the upper and lower paths, respectively. ...
Measurement-device-independent quantum key distribution (MDI-QKD) provides an effective approach to remove all detector side channel attacks. MDI-QKD only contains one bit of information for a photon in two-dimensional space, thus performing poorly in information capacity. In contrast, the amount of information increases logarithmically in high-dimensional quantum key distribution, and multi-degree-of-freedom coupling is a feasible option. In this paper, we propose a high-dimensional measurement-device-independent quantum key distribution protocol based on polarization and orbital angular momentum coupling. We illustrate the feasibility with protocol details, deduce and simulate the secure key rate and quantum bit error rate (QBER). The simulations show that the key generation rate and the upper bound of QBER are higher compared to the standard two-dimensional case.
... In fact, an optical beam splitter is a modest essential component in classical optics [34], quantum optics [35], and quantum information processing [36]. In this regard, the symmetrical beam splitter is assumed to be used in most existing investigations to reduce the complexity of problems [37][38][39], however, asymmetrical optical beam splitter is more applicable since it is difficult to have symmetrical beam splitter for practical purpose. ...
In this paper, we investigate the creation of quantum correlations such as entanglement, the Gaussian quantum discord and quantum steering in a quantum system under consideration via the linear beam splitter with squeezed thermal and a single-mode Gaussian states at the inputs. This quantum system generates bright entangled output two-mode light. Specifically, the quantum entanglement can be enhanced through increasing the purity of the Gaussian state and the squeezing parameter at the input states. The quantum correlations reveal similar characteristics for each case. That means when we increase the non-classicality, purity and squeezing parameter, the quantum correlations show enhanced profile. On the other hand, upon increasing the mean thermal photon number at the input, the quantum correlations indicate inverse relation.
... Published two months later in the same journal, we nd a paper by Ou, Hong, and Mandel outlining how to express the output of a BS using the diagonal coherent state representation [3]; in particular, they give the explicit example of what happens when two photons, one horizontally and one vertically polarized, are incident from different input ports. Indeed, they note that, for a balanced BS, the simultaneous detections at the two output ports behaves like the singlet state for two orthogonally polarized photons, i.e. a Bell state measurement, as we know it today. ...
Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.
... Published two months later in the same journal, we find a paper by Ou, Hong, and Mandel outlining how to express the output of a beam splitter using the diagonal coherent state representation [3]; in particular, they give the explicit example of what happens when two photons, one horizontally and one vertically polarized, are incident from different input ports. Indeed, they note that, for a balanced beam splitter, the simultaneous detections at the two output ports behaves like the singlet state for two orthogonally polarized photons, i.e., a Bell state measurement, as we know it today. ...
Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.
... www.nature.com/scientificreports/ which for τ 1 ...
A modification of the standard Hong-Ou-Mandel interferometer is proposed which allows one to replicate the celebrated coincidence dip in the case of two-independent delay parameters. In the ideal case where such delays are sufficiently stable with respect to the mean wavelength of the pump source, properly symmetrized input bi-photon states allow one to pinpoint their values through the identification of a zero in the coincidence counts, a feature that cannot be simulated by semiclassical inputs having the same spectral properties. Besides, in the presence of fluctuating parameters the zero in the coincidences is washed away: still the bi-photon state permits to recover the values of parameters with a visibility which is higher than the one allowed by semiclassical sources. The detrimental role of loss and dispersion is also analyzed and an application in the context of quantum positioning is presented.
... Indeed, the quantum and statistical properties of photons interfering in a BS have brought to light very profound implications such as the Hong-Ou-Mandel interference effect [17], which in turn has opened the door to very intriguing applications in quantum metrology and computing [18]. As it turns out, the quantum properties of bulk BSs have been throughly explored by many authors [19][20][21][22], however, none of those investigations has pointed out the occurrence of multiphoton discrete fractional Fourier dynamics in such elementary systems. We start our analysis by considering a waveguide BS being excited by N indistinguishable photons prepared in the state |m, N − m = |m |N − m , see Fig. (3 a). ...
We demonstrate that when a waveguide beam splitter (BS) is excited by N indistinguishable photons, the arising multiphoton states evolve in a way as if they were coupled to each other with coupling strengths that are identical to the ones exhibited by a discrete fractional Fourier system. Based on the properties of the fractional Fourier transform, we then derive a multiphoton suppression law for 50/50 BSs, thereby generalizing the Hong–Ou–Mandel effect. Furthermore, we examine the possibility of performing simultaneous multiphoton quantum random walks by using a single waveguide BS in combination with photon-number-resolving detectors. We anticipate that the multiphoton lattice-like structures unveiled in this work will be useful to identify new effects and applications of high-dimensional multiphoton states.
... Indeed, the quantum and statistical properties of photons interfering in a BS have brought to light very profound implications such as the Hong-Ou-Mandel interference effect [17], which in turn has opened the door to very intriguing applications in quantum metrology and computing [18]. As it turns out, the quantum properties of bulk BSs have been throughly explored by many authors [19][20][21][22], however, none of those investigations has pointed out the occurrence of multiphoton discrete fractional Fourier dynamics in such elementary systems. We start our analysis by considering a waveguide BS being excited by N indistinguishable photons prepared in the state |m, N − m = |m |N − m , see Fig. (3 a). ...
We demonstrate that when a waveguide beam splitter (BS) is excited by N indistinguishable photons, the arising multiphoton states evolve in a way as if they were coupled to each other with coupling strengths that are identical to the ones exhibited by a discrete fractional Fourier system. Based on the properties of the discrete fractional Fourier transform, we then derive a multiphoton suppression law for 50/50 BSs, thereby generalizing the Hong-Ou-Mandel effect. Furthermore, we examine the possibility of performing simultaneous multiphoton quantum random walks by using a single waveguide BS in combination with photon number resolving detectors. We anticipate that the multiphoton lattice-like structures unveiled in this work will be useful to identify new effects and applications of high-dimensional multiphoton states.
... Historically, the successful use of quantum Hamiltonians with a Coulomb term was never taken as an indication of the quantum nature of the EM field. The definitive experimental proof for photons involves phenomena like photon anti-bunching [6] and the Hong-Ou-Mandel effect [7]. The identification of gravitons is not easier [8]. ...
This is a comment on articles Phys. Rev. Lett. 119, 240401 (2017) [arXiv:1707.06050] and Phys. Rev. Lett. 119, 240402 (2017) [arXiv:1707.06036]. We argue that gravity-induced entanglement by Newtonian forces is agnostic to the quantum or classical nature of the gravitational true degrees of freedom.
We derive a lower limit to the amount of absorptive loss present in passive linear optical devices such as a beam splitter. We choose a particularly simple beam splitter geometry, a single planar slab surrounded by vacuum, which already reveals the important features of the theory. It is shown that, using general causality requirements and statistical arguments, the lower bound depends on the frequency of the incident light and the transverse resonance frequency of a suitably chosen single-resonance model only. For symmetric beam splitters and reasonable assumptions on the resonance frequency , the lower absorption bound is .
We propose a quantum beam splitter (QBS) with tunable reflection and transmission coefficients. More importantly, our device based on a Hermitian parity-time (PT) symmetric system enables the generation and manipulation of asymmetric quantum coherence of the output photons. For the interference of two weak coherent-state inputs, our QBS can produce antibunched photons from one output port and bunched photons from the other, showcasing high parity asymmetry and strong coherence control capabilities. Beyond the Hong-Ou-Mandel effect, perfect photon blockade with vanishing g(2)(0) is achievable in two-photon interference. These striking effects of the QBS fundamentally arise from the parity-symmetry-breaking interaction and the quantum interference between the photon scattering channels. Our results could inspire novel applications and the development of innovative photonic devices for the manipulation of weak quantum light.
In a fiber-based quantum network, the utilization of the telecom band is crucial for long-distance quantum information (QI) transmission between quantum nodes. However, the near-infrared wavelength is identified as optimal for storing and processing QI through alkaline atoms. Recognizing the challenge of efficiently bridging the frequency gap between atomic quantum devices and telecom fibers while maintaining the QI carried by photons, quantum frequency conversion (QFC) serves as a pivotal quantum interface. In this study, we explore an efficient telecom-band QFC mechanism based on diamond-type four-wave mixing (FWM) with rubidium energy levels. The mechanism enables the conversion of photons between the near-infrared wavelength of 795 nm and the telecom band of 1367 or 1529 nm. Using the Heisenberg-Langevin approach, we optimize conversion efficiency (CE) across varying optical depths while considering quantum noises and present corresponding experimental parameters. Unlike previous works neglecting the applied field absorption loss, our results are more relevant to practical scenarios. Moreover, by employing the reduced-density-operator theory to construct a theoretical framework, we demonstrate that this diamond-type FWM scheme can maintain the quantum characteristics of input photons with high fidelity, such as quadrature variances and photon statistics. Importantly, these properties remain unaffected by vacuum field noise, enabling the system to achieve high-purity QFC. Another significant contribution lies in examining how this scheme impacts QI encoded in photon-number, path, and polarization degrees of freedom. These encoded qubits exhibit remarkable entanglement retention under sufficiently high CE. In the case of perfect CE, the scheme can achieve unity fidelity. This comprehensive exploration establishes a theoretical foundation for the application of the diamond-type QFC scheme based on atomic ensembles in quantum networks, laying essential groundwork for advancing the scheme in distributed quantum computing and long-distance quantum communication.
We demonstrate theoretically and experimentally how the diffraction and interferometric resolution limit for single-mode coherent cw laser light can be overcome by multi-photon interference. By use of a Mach-Zehnder interferometer, operated in the single input and single or double output port geometries, we observe a fringe width reduction of the conventional interference pattern, predicted by the wave or single photon quantum theory, by a factor of up to through coincident detection of N=2,3,4 photons. Our scheme does not require squeezed or entangled light to overcome the standard quantum limit and greatly facilitates precision interferometry experiments.
We report an AlGaAsOI quantum photonic circuit with multiple pair sources and tunable interferometers. We demonstrate Hong-Ou-Mandel interference between two microring resonators and a tunable Bell state generator producing Ψ ⁺ and Φ ⁻ bi-photon entangled states.
We investigated influence of multiwalled carbon nanotubes (CNT) on spectral characteristics of composites “rubber-carbon nanotubes”on the base of butadiene-nitrile rubber at 0–10 % of CNTs. IR reflectance maxima of composites were measured in the spectral area of the rubber CH deformation and valence vibrations. IR absorption spectra of composites “rubber-carbon nanotubes” after vulcanization includes some giant two-polar oscillations. IR absorption spectrum of composites “rubber-carbon nanotubes” at 1 % of CNTs without vulcanization includes the alone two-polar oscillation. Two-photon interference is a result of quantum entanglement of dipole-active vibrations and photon splitting according to Hong-Ou-Mandel (HOM) quantum effect. Two-photon maximal entanglement saturation is called as Bell states. HOM quantum effect is perspective for high-coherent optical quantum computers on composites “rubber-carbon nanotubes”.
Theoretical calculations are presented for the statistical properties of synchrotron radiation within the framework of quantum optics using the density operator formalism. The effect of non-negligible angular divergence of the electron beam is taken into account for the first time. Further, this chapter considers possible simplifications and closed forms of the equation for the variance of the number of detected photons in the case of arbitrary degree of coherence and in the case of temporally incoherent radiation. Theoretical predictions are made for the previous experiment at Brookhaven National Lab, where fluctuations of wiggler radiation were measured in the Vacuum-Ultraviolet electron storage ring. Estimations are made for the experiment in the Integrable Optics Test Accelerator storage ring at Fermilab.
The beam splitter is an important optical element in quantum optics experiments. The classical and quantum treatment of the beam splitter is presented. We derive the photodetection probabilities for a single photon on a beam splitter, including single photon detection and double photon detection (coincidence counting). The correlation function is introduced for classical and quantum light. We show that the beam splitter creates an entangled state from a single photon input. The Hanbury Brown–Twiss experiment is introduced for characterizing light sources.
The Hong-Ou-Mandel (HOM) interferometer using entangled photon source possesses important applications in quantum precision measurement and relevant areas. In this paper, a simultaneous measurement scheme of multiple independent delay parameters based on a cascaded HOM interferometer is proposed. The cascaded HOM interferometer is composed of \begin{document} n \end{document} concatenated 50∶50 beam splitters and independent delay parameters \begin{document}\end{document}, \begin{document}\end{document}, ···, \begin{document}\end{document}. The numbers \begin{document}\end{document} refer to the standard HOM interferometer, the second-cascaded HOM interferometer, and the third-cascaded HOM interferometer, respectively. Through the theoretical study of the cascaded HOM interference effect based on frequency entangled photon pairs, it can be concluded that there is a corresponding relationship between the dip position and the independent delay parameter in the second-order quantum interferogram. In the standard HOM interferometer, there is a dip in the second-order quantum interferogram, which can realize the measurement of delay parameter \begin{document}\end{document}. In the second-cascaded HOM interferometer, there are two symmetrical dips in the second-order quantum interferogram, which can realize the simultaneous measurement of two independent delay parameters \begin{document}\end{document} and \begin{document}\end{document}. By analogy, in the third-cascaded HOM interferometer, there are six symmetrical dips in the second-order quantum interferogram, which can realize the simultaneous measurement of three independent delay parameters \begin{document}\end{document}, \begin{document}\end{document} and \begin{document}\end{document}. Therefore, multiple independent delay parameters can be measured simultaneously based on a cascaded HOM interferometer. In the experiment, the second-cascaded HOM interferometer based on frequency entangled photon source is built. The second-order quantum interferogram of the second-cascaded HOM interferometer is obtained by the coincidence measurement device. Two independent delay parameters \begin{document}\end{document} and \begin{document}\end{document} are measured simultaneously by recording the positions of two symmetrical dips, which are in good agreement with the theoretical results. At an averaging time of 3000 s, the measurement accuracy of two delay parameters \begin{document}\end{document} and \begin{document}\end{document} can reach 109 and 98 fs, respectively. These results lay a foundation for extending the applications of HOM interferometer in multi-parameter quantum systems.
We consider a recursive device that is based on a Mach-Zehnder interferometer and linear optical elements which allow self-feedback through multiple internal reflection of radiation between two parallel arrays of opposite faced mirrors. By a carefully chosen experimental arrangement and for certain input states it is possible to observe at the open ends of the device time generated coherent superpositions \textit{in perpetuum}.
Cavity-enhanced single photon sources exhibit mode-locked biphoton states with comblike correlation functions. Our ultrabright source additionally emits single photon pairs as well as two-photon NOON states, dividing the output into an even and an odd comb, respectively. With even-comb photons we demonstrate revivals of the typical nonclassical Hong-Ou-Mandel interference up to the 84th dip, corresponding to a path length difference exceeding 100 m. With odd-comb photons we observe single photon interference fringes modulated over twice the displacement range of the Hong-Ou-Mandel interference.
The concept of coherence which has conventionally been used in optics is found to be inadequate to the needs of recently opened areas of experiment. To provide a fuller discussion of coherence, a succession of correlation functions for the complex field strengths is defined. The order function expresses the correlation of values of the fields at 2n different points of space and time. Certain values of these functions are measurable by means of n-fold delayed coincidence detection of photons. A fully coherent field is defined as one whose correlation functions satisfy an infinite succession of stated conditions. Various orders of incomplete coherence are distinguished, according to the number of coherence conditions actually satisfied. It is noted that the fields historically described as coherent in optics have only first-order coherence. On the other hand, the existence, in principle, of fields coherent to all orders is shown both in quantum theory and classical theory. The methods used in these discussions apply to fields of arbitrary time dependence. It is shown, as a result, that coherence does not require monochromaticity. Coherent fields can be generated with arbitrary spectra.
Methods are developed for discussing the photon statistics of arbitrary fields in fully quantum-mechanical terms.
In order to keep the classical limit of quantum electrodynamics plainly in view, extensive use is made of the
coherent states of the field. These states, which reduce the field correlation functions to factorized forms,
are shown to offer a convenient basis for the description of fields of all types. Although they are not orthogonal
to one another, the coherent states form a complete set. It is shown that any quantum state of the field may be
expanded in terms of them in a unique way. Expansions are also developed for arbitrary operators in terms of
products of the coherent state vectors. These expansions are discussed as a general method of representing the
density operator for the field. A particular form is exhibited for the density operator which makes it possible to
carry out many quantum-mechanical calculations by methods resembling those of classical theory. This representation
permits clear insights into the essential distinction between the quantum and classical descriptions of the field.
It leads, in addition, to a simple formulation of a superposition law for photon fields. Detailed discussions are
given of the incoherent fields which are generated by superposing the outputs of many stationary sources.
These fields are all shown to have intimately related properties, some of which have been known for the particular
case of blackbody radiation.
DOI:https://doi.org/10.1103/PhysRevLett.16.534
DOI:https://doi.org/10.1103/PhysRevLett.10.277
The problem of relating the semiclassical and quantum treatments of statistical states of an optical field is re-examined. The case where the rule of association between functions and operators is that of antinormal ordering is studied in detail. It is shown that the distribution function for each mode corresponding to this case is a continuous bounded function, and is also a boundary value of an entire analytic function of two variables. The nature of the distribution for the normal ordering rule of association and its relation to this entire function are discussed. It is shown that this distribution can be regarded as the limit of a sequence of tempered distributions in the following sense: One can find a sequence of density operators ρ̂(ν) which converges in the norm to the density operator ρ̂ of any given field (consisting of a single mode), such that each member of the sequence can be expressed in the form ρ̂(ν)=∫φ(ν)(z)|z〉〈z|d2z, where φ(ν) is a tempered distribution.
In Part I of this three-part study it was shown that the use of two-photon coherent state (TCS) radiation may yield siginificant performance gains in free-space optical communicatinn if the receiver makes a quantum measurement of a single field quadrature. In Part II it was shown that homodyne detection achieves the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes the linear modulation TCS performance gain found in Part I. Furthermore, it was shown in Part il that ff homodyne detection does exactly correspond to the field quadrature measurement, then a large binary communication performance gain is afforded by homodyne detection of antipodal TCS signals. The full equivalence of honmdyne detection and single-quadrature field measurement, as well as that of heterodyne detection and two-quadrature field measurement, is established. Furthermore, a heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. This coafiguration termed TCS heterodyne detection is shown to realize all the quantum measurements described by arbitrary TCS. The foregoing results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.
Principles of optics
- I See
- M For
- E Born
- Wolf
I ] See for example M. Born and E. Wolf, Principles of optics (6th Ed., Pergamon Press, Oxford, 1980) section