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Experiment on nonclassical fourth-order interference
Abstract
A new fourth-order interference experiment has been carried out and analyzed theoretically in classical and in quantum terms. Two photons produced in the process of parametric down-conversion provide the two inputs to a Mach-Zehnder type of interferometer, while two photodetectors coupled to a coincidence counter measure the output. The coincidence rate, after subtraction of accidentals, exhibits a cosine variation with the optical path difference, in agreement with quantum mechanics, but in disagreement with a classical analysis. By contrast, when two coherent light beams from a He:Ne laser are used as inputs to the interferometer, no fourth-order interference is observed.
... Furthermore, [17] showed the absence of interference when only detecting single detection events (Fig. 2c), as expected [16]. At the same time in parallel, a series of other experiments was investigating non-local two-photon interference [39] but employing balanced interferometers [40][41][42], in which case two-photon visibilities higher than 50% are reachable, while still having the absence of single-photon interference. Notably [40] demonstrated using their experimental arrangement the first Bell inequality violation using a degreeof-freedom other than polarization (Figs. ...
... Pairs of channels highlighted with the same color obey the phase and pump-energy matching condition for SPDC. To asses the full 16 channels (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42) of Alice's DWDM multiplexer, Bob's 8-channel DWDM is replaced with a narrowband filter with tunable resonance frequency (not shown in the figure). ...
... Notably, the polarization and the energy-time DOF are particularly robust quantum information carriers and have been distributed over free-space [9,38,39] and long-distance fiber [12,40] links, marking them as ideal candidates for future in-field applications. On the other hand, the originally proposed spatial encoding [26] is less noise resilient outside of a protected laboratory environment [41,42]. ...
Entanglement is a key resource in many quantum information tasks. From a fundamental perspective entanglement is at the forefront of major philosophical discussions advancing our understanding of nature. An experimental scheme was proposed in 1989 by Franson that exploited the unpredictability in the generation time of a photon pair in order to produce a then new form of quantum entanglement, known as energy-time entanglement. A later modification gave rise to the very popular time-bin entanglement, an important cornerstone in many real-world quantum communication applications. Both forms of entanglement have radically pushed forward our understanding of quantum mechanics throughout the 1990s and 2000s. A decade later modifications to the original proposals were proposed and demonstrated, which opens the path for the highly sought-after device-independence capability for entanglement certification, with a goal of ultra-secure quantum communication. In this review we cover the beginnings of energy-time and time-bin entanglement, many key experiments that expanded our understanding of what was achievable in quantum information experiments all the way down to modern demonstrations based on new technological advances. We will then point out to the future discussing the important place that energy-time and time-bin entanglement will have in upcoming quantum networks and novel protocols based on nonlocality.
... Multi-photon entangled states produced in the down-conversion process is often used in quantum information experiments and applications like quantum cryptography and the Bell inequalities. In particular, demonstrations of two-photon [17,18,19,20] and four-photon [21,22] interferences are holding promise for realizable applications with entanglement-enhanced performance. The principle of this enhance-ment lies in the fact that "the photonic de Broglie wavelength" [23] of an ensemble of photons with wavelength λ and number of photons n can be measured to be λ /n using a special interferometer. ...
... which has twofold increase in the fringe pattern. This is also clear from the Schrödinger evolution of the state given by Eq. (19). The reason of this two-fold increase lies in the fact that when the two photons, one from each input port, enter into the loop, they transform into the following two-photon path-entangled state, ...
... Here the state ρ(φ ) = U|ψ ψ|U † is the evolved density matrix corresponding to the state given in Eq. (24). This probability can be easily calculated by utilizing the Schrödinger picture evolution of the state vector |11 given in Eq. (19). The expression in Eq. (28) is a pure twophoton interference effect showing by halving the de Broglie wavelength of the source photons. ...
We show how the entangled photons produced in parametric down conversion can be used to improve the sensitivity of a Sagnac interferometer. Two-photon and four-photon coincidences increases the sensitivity by a factor of two and four respectively. Our results apply to sources with arbitrary pumping and squeezing parameters.
... The coherent superposition of states and the interference between probability amplitudes for indistinguishable processes in the total detection process have a crucial role in quantum mechanics and experimental quantum optics to observe interference phenomena. Thus, a number of experiments have been performed to elucidate two-photon quantum interference effects, such as the HOM effect 1,[8][9][10][11][12][13][14][15] and the N00N-state interference 2,3,11,[16][17][18][19][20][21] . Recently, we have reported that the two kinds of two-photon interference effects can be observed in the most generalized two-photon interferometric scheme, including a fully unfolded HOM scheme as well as a N00N-state interferometer 22 . ...
... Since the early 1990s, various apparatus for two-photon interference experiments have been utilized to investigate two-photon wavepacket interference phenomena, e.g., the Mach-Zehnder interferometer (MZI) 2,17,19,21,23,24 and the Michelson interferometer (MI) [25][26][27] . The majority of the experiments involving these devices were performed using two identical photons as the input state, where the two photons simultaneously entered the input port of an interferometer. ...
... The conceptual scheme for the generation of the TSSA and TSSB two-photon states is depicted in Fig. 1. As is well known, the conventional two-photon N00N state can be easily generated via the HOM interference effect, when two identical single photons enter a balanced beamsplitter (BS) simultaneously, as shown in Fig. 1a 2,17 . In this case, the two output photons are always probabilistically bunched at one of the two spatial modes as described by ...
We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.
... The Michelson interferometer [1,2], the Hong-Ou-Mandel (HOM) interferometer [3][4][5][6][7], and the Mach-Zehnder interferometer (MZI) [8][9][10][11][12][13][14] are examples of two-input/two-output setups which have been extensively used to study two-photon quantum interference effects, with applications in parameter estimation problems, such as phase estimation in quantum radar [15] or coordinates estimation in a quantum positioning system [16]. In these schemes a minimum (or a maximum) in the coincidence counts recorded at the output of the device is typically associated with the case where no relative delays affect the propagation of the photons along the two optical paths of the setup. ...
... In the HOM interferometer this correspondence yields the celebrated "Mandel dip" where, given a symmetric input biphoton (BP) source [17][18][19][20][21], a zero-coincidence signal can be uniquely linked to the absence of asymmetries in the signal propagation. Generalization of this effect to more than one parameter is naturally provided by MZIs [8][9][10][11][12][13][14] where, exploiting the presence of two 50:50 beam-splitters (BSs), one can in principle monitor two independent time delays with a single coincidence measurement. It turns out, however, that for these settings the zero-coincidence event does not exclusively correspond to the contemporary absence of the two delays unless [22] one includes the presence of an achromatic quarter wave plate [23][24][25]. ...
... Expanding Eq. (10), we observe that it contains two kinds of contributions: the first contains the terms where both photons belong to the same output port of the interferometer (either A k+1 or B k+1 ) and gives explicitly no contribution to (8); the second instead contains all the terms where one photon is in A k+1 and another one is in B k+1 , and it can actively contribute to R (θ 2 ,...,θ k ) BP (τ 1 , . . . , τ k ). ...
A generalized multiparameter Hong-Ou-Mandel interferometer is presented which extends the conventional “Mandel dip” configuration to the case where a symmetric biphoton source is used to monitor the contemporary absence of k independent time delays. Our construction results in a two-input/two-output setup, obtained by concatenating 50:50 beam splitters with a collection of adjustable achromatic wave plates. For k=1,2 and k=4 explicit examples can be exhibited that prove the possibility of uniquely linking the zero value of the coincidence counts registered at the output of the interferometer with the contemporary absence of all the time delays. Interestingly enough the same result cannot be extended to k=3. Besides, the sensitivity of the interferometer is analyzed when the time delays are affected by strong fluctuations, i.e., the fluctuations over timescales that are larger than the inverse of the frequency of the pump used to generate the biphoton state.
... The Michelson interferometer [1,2], the Hong-Ou-Mandel (HOM) interferometer [3][4][5][6][7], and the Mach-Zehnder interferometer (MZI) [8][9][10][11][12][13][14] are examples of twoinput/two-output set-ups which have been extensively used to study two-photon quantum interference effects, with applications in parameter estimation problems, such as phase estimation in the quantum radar [15], or coordinates estimation in quantum positioning system [16]. In these schemes a minimum (or a maximum) in the coincidence counts recorded at the output of the device is typically associated with the case where no relative delays affect the propagation of the photons along the two optical paths of the set-up. ...
... In the HOM interferometer this correspondence yields the celebrated "Mandel dip" where, given a symmetric input biphoton (BP) source [17][18][19][20][21], a zero-coincidence signal can be uniquely linked to the absence of asymmetries in the signal propagation. Generalization of this effect to more than one parameter are naturally provided by MZIs [8][9][10][11][12][13][14] where, exploiting the presence of two 50:50 BS, one can in principle monitor two independent time-delays with a single coincidence measurement. It turns out however that for these settings the zero-coincidence event does not exclusively correspond to the contemporary absence of the two delays unless [22] one includes the presence of an achromatic quarter wave-plate [23][24][25]. ...
... Expanding Eq.(10) we observe that it contains two kinds of contributions: the first contains the terms where both photons belong to a same output port of the interferometer (either A k+1 or B k+1 ) and gives explicitly no contribution to (8); the second instead contains all the terms where one photon in A k+1 and another one in B k+1 and which can actively contribute to R (θ2,··· ,θ k ) BP (τ 1 , ..., τ k ). Its analytic expression is given by ...
A generalized multi-parameter Hong-Ou-Mandel interferometer is presented which extends the conventional "Mandel dip" configuration to the case where a symmetric biphoton source is used to monitor the contemporary presence of k independent time-delays. Our construction results in a two-input/two-output setup, obtained by concatenating 50:50 beam splitters with a collection of adjustable achromatic wave-plates. For k=1,2 and k=4 explicit examples can be exhibited that prove the possibility of uniquely linking the zero value of the coincidence counts registered at the output of the interferometer, with the contemporary absence of all the time-delays. Interestingly enough the same result cannot be extended to k=3. Besides, the sensitivity of the interferometer is analyzed when the time-delays are affected by the fluctuations over time-scales that are larger than the inverse of the frequency of the pump used to generate the biphoton state.
... In any case, readers who are familiar with the original HOM scheme can give a quick look at this part and moving directly to the next section where we give an explicit construction to positively achieve our main goal. Since it is obtained by concatenating the original HOM interferometer with a second 50:50 beam splitter, the proposed scheme resembles the Mach-Zhender interferometer (MZI) setup studied e.g. in refs [18][19][20][21][22][23][24] : at variance with these works however our model includes also the presence of an achromatic wave-plate 25,26 which induces a frequency independent phase shift on the propagating signals, see Fig. 1b). In addition, these works presented in refs [18][19][20][21][22][23][24] . ...
... Since it is obtained by concatenating the original HOM interferometer with a second 50:50 beam splitter, the proposed scheme resembles the Mach-Zhender interferometer (MZI) setup studied e.g. in refs [18][19][20][21][22][23][24] : at variance with these works however our model includes also the presence of an achromatic wave-plate 25,26 which induces a frequency independent phase shift on the propagating signals, see Fig. 1b). In addition, these works presented in refs [18][19][20][21][22][23][24] . does not exhibit the required one-to-one correspondence between the zero-coincidence event and the contemporary nullification of two delays. ...
... Coincidence counts R BP (τ 1 , τ 2 ) of the BP state according to Eq.(33): the left panels from (a) to (d) refer to the case of θ = 0 (no achromatic phase shift), formally equivalent to the configurations analyzed in refs[18][19][20][21][22][23][24] ; the right panels from (e) to (h) instead refer to the case of θ = π/2 (a quarter-wave plate contributes the achromatic phase shift). Panels (a) and (e): contour plots of R BP (τ 1 , τ 2 ); Panels (b) and (f) plots of the function R BP (τ 1 , τ 1 ); Panels (c) and (g) plots of R BP (τ 1 , 0); Panels (d) and (h) finally report R BP (0, τ 2 ). ...
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.
... The experiments conducted by Ou et al. in 1990 were a clear contrast to classical theory [20]. Whereas interference does not occur classically, quantum theory argues that interference fringes with a visibility of 100% can be obtained. ...
... When the signal and the idler photons generated in the SPDC are incident on the Mach-Zehnder interferometer, as shown in Fig. 2, the probability P q (4,5) When the signal light s and the idler light i are input from the upper left, the beam splitter BSI creates an entangled state. Simultaneously measurement is conducted by moving the beam splitter BSO and changing the optical path length of the upward and downward turns [20]. of the simultaneous measurement of the photons at the two exits (detectors D4 and D5) varies according to the difference between the two optical path lengths of the interferometer (adjustment of BSO position), as shown in Eq. (13) [20]. 2 3 (4,5) 1 cos 2( ) (13) q P 2 and 3 are the phase changes due to their respective optical paths. ...
... When the signal and the idler photons generated in the SPDC are incident on the Mach-Zehnder interferometer, as shown in Fig. 2, the probability P q (4,5) When the signal light s and the idler light i are input from the upper left, the beam splitter BSI creates an entangled state. Simultaneously measurement is conducted by moving the beam splitter BSO and changing the optical path length of the upward and downward turns [20]. of the simultaneous measurement of the photons at the two exits (detectors D4 and D5) varies according to the difference between the two optical path lengths of the interferometer (adjustment of BSO position), as shown in Eq. (13) [20]. 2 3 (4,5) 1 cos 2( ) (13) q P 2 and 3 are the phase changes due to their respective optical paths. ...
Many experiments to verify nonlocal interaction and non-classical phenomena using entangled lights were conducted in the 1980s, and many physicists were interested in their unrecognizable correlation. These quantum mechanical effects were used in Aspect's experiments and Bell tests and had a great influence on the interpretation of quantum mechanics. However, their essence, including their "spooky" interaction, is unknown. In this study, we show that entangled light can be expressed by the product of electric fields and that the same result as quantum mechanics can be obtained using the product form.
... The key feature of NOON and similar photonic states 9 is that they produce interference fringes that oscillate faster than any classical interference pattern, a feature called phase super-resolution 10 . Super-resolution interference experiments have been reported using two- [11][12][13][14] , three-15 , four- 16,17 , six-9,10 and eight- 18,19 photon states. ...
... The output signal consisted of three possible types of detection outcome: C 11 , a coincidence detection between both output modes; C 20 , a detection occurring only in the transmitted output mode; and C 02 , a detection occurring only in the reflected output mode. The numbers of each type of detection in a time period τ were, respectively, φ c ( ) 11 , φ c ( ) 20 and φ c ( ) 02 . ...
... Detection events (~250,000 per phase value) were collected for a fixed amount of time for various φ ∈ −π∕ π∕ [ 2, 3 2 ) . We observed an interference visibility of (98.9 ± 0.02)%, calculated from fitting to the φ c ( ) 11 detection fringe. The transmissions of the reflected and transmitted outputs of the interferometer were measured to be η = . ...
Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and various materials properties. Without quantum enhancement, the minimum uncertainty in determining an unknown optical phase---is the shot noise limit (SNL): 1/sqrt(n), where n is the number of resources (e.g. photons) used. Entangled photons promise measurement sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is a path-entangled state of definite number of photons N. Despite theoretical proposals stretching back decades, no measurement using such photonic (definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all demonstrations have employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use an ultra-high efficiency source and high efficiency superconducting photon detectors to respectively make and measure a two-photon instance of the maximally-phase-sensitive NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit---that is, without artificially correcting for loss or any other source of imperfection. Our results enable quantum-enahanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.
... Since the early 1990s, various apparatus for two-photon interference experiments have been utilized to investigate two-photon wavepacket interference phenomena, e.g., the Mach-Zehnder interferometer (MZI) 2,12,14,16,17 and the Michelson interferometer (MI) [18][19][20] . The majority of the experiments involving these devices were performed using two identical photons as the input state, where the two photons simultaneously entered the input port of an interferometer. ...
... The conceptual scheme for the generation of the TSSA and TSSB two-photon states is depicted in Fig. 1. As is well known, the conventional two-photon N00N state can be easily generated via the HOM interference effect, when two identical single photons enter a balanced beamsplitter (BS) simultaneously, as shown in Fig. 1a 2,12 . In this case, the two output photons are always probabilistically bunched at one of the two spatial modes as described by ...
... Figure 3 shows the experimental results for the two-photon interference experiments with the two different kinds of input states shown in Fig. 1b. The conditions for the two input states before FBS2 were controlled by adjusting the first optical delay line (ODL1; 1 x ) before FBS1, and the two-photon coincidence fringes were measured for varying 2 x (with a 1-μm step size). When the input state was a superposition of the TSSA and TSSB states with the introduction of a large delay, 1 coh. ...
We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.
... The Hong-Ou-Mandel (HOM) interference effect [1] and the interference of the path-entangled two-photon state [2], the so-called N00N state [3], have played an important role in the fundamental study of quantum mechanics and in exploring quantum information technology [4,5]. From the late 1980s, various kinds of two-photon interference experiments have been performed to distinguish the quantum mechanical treatment of optical interference phenomena from conventional classical optics [6,7]. ...
... Meanwhile, two-photon interference in a Mach-Zehnder interferometer (MZI) has also been utilized as a practical tool to investigate two-photon wavepacket interference phenomena [2,12,16,17]. In particular, the most interesting feature can be shown when two correlated photons are incident on the MZI with a time delay that is considerably longer than their coherence time. ...
... The conceptual scheme for the generation of the HOMlike and N00N-like two-photon states is depicted in Fig. 1. As is well known, the conventional two-photon N00N state can easily be generated from the HOM interference effect when two identical single photons enter BS1 simultaneously, as shown in Fig. 1(a) [2,12]. In this case, the two output photons are always probabilistically bunched up at one of the two spatial modes, which is described by the following expression, ...
We propose and experimentally demonstrate two-photon interference effects in
a Mach-Zehnder interferometer in which two different kinds of two-photon states
are prepared by introducing a time delay between the two input photons. The
two-photon states are simultaneously prepared in a symmetrically superposed
state with two temporally separated photons in two different spatial modes or
in the same spatial mode within the interferometer. We observe two-photon
interference fringes involving both the Hong-Ou-Mandel interference effect and
the interference of path-entangled two-photon states simultaneously in a single
interferometric setup. The observed two-photon interference effect can provide
a simultaneous observation of the interferometric properties of the
single-photon and two-photon wavepackets
... To date, HOM-type TPI experiments have also been performed by employing electrons 19 , plasmons 20 , bosonic atoms 21,22 , phonons in trapped ions 23 , spin waves 24 , Rydberg excitations 25 , and microwave-frequency photons 26 , instead of optical photons. Other non-classical features of light interference have been experimentally observed in various types of interferometers such as the Mach-Zehnder, Michelson and Franson interferometers via the use of highly correlated photons [27][28][29][30][31][32][33] . In the meantime, many experiments have been carried out to investigate the classical analogues of the TPI [34][35][36][37] . ...
... ; this path-entangled state is highly phase-sensitive in the interferometer. Here, note that the two input photons do not have to possess identical properties in terms of the internal degrees of freedom, such as polarization and wavelength [27][28][29][30]39 . Moreover, they can differ in terms of external degrees of freedom, such as the input spatial modes and the arrival time of the two incident photons at BS1 30,39,40 (see Supplementary Note 1 for details) ...
The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we compare our results with the previous ones of correlated photons. The observed TPI fringe can be expressed in the form of three phase terms related to the individual single-photon and two-photon states, and the fringe pattern is strongly affected by the two single-photon-interference fringes and also by their visibilities. With the exception of essential differences such as valid and accidental coincidence events within a given resolving time and the two-photon spectral bandwidth, the interference phenomenon itself exhibits the same features for both correlated and uncorrelated photons in the single-photon counting regime.
... Such states are very useful in quantum precise phase measurement [35] and super-resolution quantum lithography [36]. The actual effect of N00N state in these applications increases with the photon number N. As we know, the two-photon N00N state could be easily experimentally generated through various methods [31], [37]- [40]. However, multi-photon N00N state (N > 2) is hard to produce because of technical difficulties [41]. ...
... Thus a N00N state is formed. Unlike conventional N00N states [37]- [41], this N00N state possesses optical angular momentum. In practical applications, band pass filters with certain center frequency could be place at the corresponding angles to improve the purity of the state. ...
We investigate wavefront engineering of photon pairs generated through spontaneous parametric down conversion in lithium niobate-based nonlinear photonic crystals (NPCs). Due to the complexity of domain structures, it is more convenient to describe photon interaction based on the nonlinear Huygens-Fresnel principle than conventional quasiphase matching regime. Analytical expressions are obtained to describe the transverse properties of down-converted photon states. The convenience of domain engineering in LiNbO3 crystals provides a potential platform for flexible wavefront manipulation of multiphoton states. The generation of N00N state with orbital angular momentum in a twisted NPC is studied utilizing this method. The obtained state is of great value in quantum cryptography, metrology, and lithography applications.
... The key feature of NOON and similar photonic states [9] is that they produce interference fringes that oscillate faster any classical interference pattern, a feature called phase super-resolution [10]. Super-resolution interference experiments have been reported using two- [11][12][13][14], three- [15], four- [16,17], six- [9,10] and eight- [18,19] photon states. ...
Interferometric phase measurement is widely used to precisely determine quantities such as length, speed, and material properties. Without quantum correlations, the best phase sensitivity achievable using n photons is the shot noise limit (SNL), . Quantum-enhanced metrology promises better sensitivity, but despite theoretical proposals stretching back decades, no measurement using photonic (i.e. definite photon number) quantum states has truly surpassed the SNL. Rather, all such demonstrations --- by discounting photon loss, detector inefficiency, or other imperfections --- have considered only a subset of the photons used. Here, we use an ultra-high efficiency photon source and detectors to perform unconditional entanglement-enhanced photonic interferometry. Sampling a birefringent phase shift, we demonstrate precision beyond the SNL without artificially correcting our results for loss and imperfections. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.
... We further find that the phases of coherent fields can also be used as tuning knobs to control the visibility of the pattern. It may be borne in mind that the process of spontaneous parametric down conversion has been a work horse for the last two decades in understanding a variety of issues in quantum physics and in applications in the field of imaging [24,25,26,27,28]. ...
We show how stimulated parametric processes can be employed in experiments on beyond the diffraction limit to overcome the problem of low visibility obtained by using spontaneous down conversion operating in the high gain regime. We further show enhancement of the count rate by several orders when stimulated parametric processes are used. Both the two photon counts and the visibility can be controlled by the phase of the stimulating coherent beam.
... For these purposes, a single interferometer is sufficient and indeed preferred, due to the ease of implementation and increased system stability. This work aligns with previous investigations of the non-classical nature of light, which have incorporated either a single Michelson interferometer [26] or a single Mach-Zehnder interferometer [19,27,28]. ...
Advances in quantum photonics have shown that chip-scale quantum devices are translating from the realm of basic research to applied technologies. Recent developments in integrated photonic circuits and single photon detectors indicate that the bottleneck for fidelity in quantum photonic processes will ultimately lie with the photon sources. We present and demonstrate a silicon nanophotonic chip capable of emitting telecommunication band photon pairs that exhibit the highest raw degree of time-energy entanglement from a micro/nanoscale source, to date. Biphotons are generated through cavity-enhanced spontaneous four-wave mixing (SFWM) in a high-Q silicon microdisk resonator, wherein the nature of the triply-resonant generation process leads to a dramatic Purcell enhancement, resulting in highly efficient pair creation rates as well as extreme suppression of the photon noise background. The combination of the excellent photon source and a new phase locking technique, allow for the observation of a nearly perfect coincidence visibility of (96.6 1.1), without any background subtraction, at a large pair generation rate of (4.40 0.07) 10 pairs/s.
... Since its discovery, it has undergone modifications and extensions, giving rise to various types of interferometers. One such extension is the N00N state interferometer (N00NI) [15][16][17], achieved by inserting a beam splitter with two balanced arms in front of the HOMI. The N00NI has found widespread use in quantum lithography [18,19], quantum high-precision measurement [20][21][22], quantum microscopy [23][24][25], error correction [26], and other fields. ...
We theoretically extend the original Hong–Ou–Mandel (HOM) interferometer to three parameters by concatenating 50:50 beam splitters with three independent and adjustable time delays. The coincidence probability of such an interferometer is obtained based on the linear transformation of the beam splitter matrix. We present a comprehensive analysis of the interference characteristics of the interferometer at different time delays with various types of frequency-correlated resources and input states. It is found that by properly setting the time delays, one can obtain typical interferograms that include multiple sub-interferograms associated with one- and two-parameter HOM interferometers, revealing richer and more complicated two-photon interference phenomena. In particular, additional enhancements of the interference signal at a specific delay can be achieved, and the symmetry of the interferograms on both sides can also be changed. This work provides comprehensive insights into the interference characteristics of the three-parameter HOM interferometer and enables the simultaneous optimal estimation of multiple time-delay parameters within a single interferometer, which holds potential for applications in multiparameter estimation and quantum metrology.
... Measuring a reduced de Broglie wavelength attracts constant interest in the quantum optics community [20][21][22], ranging from the most often demonstrated two-photon interference to the later reported 3-, 4-and 8-photon experiments and the recently observed 10-and 12-photon entanglement [23][24][25][26][27][28][29]. These demonstrations, on the one hand, are important benchmarks that show the considerable progress made in multiphoton manipulation, which is the physical basis for building photonic quantum information systems [30][31]. ...
Optical interferometers are pillars of modern precision metrology, but their resolution is limited by the wavelength of the light source, which cannot be infinitely reduced. Magically, this limitation can be circumvented by using an entangled multiphoton source because interference produced by an N-photon amplitude features a reduced de Broglie wavelength {\lambda}/N. However, the extremely low efficiency in multiphoton state generation and coincidence counts actually negates the potential of using multiphoton states in practical measurements. Here, we demonstrate a novel interferometric technique based on structured nonlinear optics, i.e., parametric upconversion of a structured beam, capable of superresolution measurement in real time. The main principle relies in that the orbital angular momentum (OAM) state and associated intramodal phase within the structured beam are both continuously multiplied in cascading upconversion to mimic the superresolved phase evolution of a multiphoton amplitude. Owing to the use of bright sensing beams and OAM mode projection, up to a 12-photon de Broglie wavelength with almost perfect visibility is observed in real time and, importantly, by using only a low-cost detector. Our results open the door to real-time superresolution interferometric metrology and provide a promising way toward multiphoton superiority in practical applications.
... A prominent example is the generation of the two-photon NOON state. [8,9] By feeding two single photons into the inputs of a balanced beam splitter, a NOON state with N = 2 can be easily and deterministically obtained at the outputs for the bunching effect of photons, which is also known as the Hong-Ou-Mandel effect. However, when N > 2, generating NOON states is not straightforward. ...
Maximal multi-photon entangled states, known as NOON states, play an essential role in quantum metrology. With the number of photons growing, NOON states are becoming increasingly powerful and advantageous for obtaining supersensitive and super-resolved measurements. In this paper, we propose a universal scheme for generating three- and four-photon path-entangled NOON states on a reconfigurable photonic chip via photons subtracted from pairs and detected by heralding counters. Our method is postselection free, enabling phase supersensitive measurements and sensing at the Heisenberg limit. Our NOON-state generator allows for integration of quantum light sources as well as practical and portable precision phase-related measurements.
... Some particular values of the coincidence probability are physically meaningful. A coincidence probability below 1/4 can not be achieved with classical a field as demonstrated in [Ou et al., 1990] or in other words, a visibility larger than 50%. Using the manipulation of photonic degrees of freedom, such as the transverse spatial modes and polarization [Walborn et al., 2003], one can also use this anti-bunching process, revealed by an anti-dip with a coincidence probability above 1/2, that can be associated with a fermionic-like behavior [Francesconi et al., 2020] and is also an entanglement witness [Autebert et al., 2015, Douce et al., 2013, Eckstein and Silberhorn, 2008, Fedrizzi et al., 2009]. ...
This thesis tackles the time-frequency continuous variables degree of freedom encoding of single photons and examine the formal mathematical analogy with the quadrature continuous variables of the electromagnetic field. We define a new type of qubit which is robust against time-frequency displacement errors. We define a new double-cylinder phase space which is particularly adapted for states which have a translational symmetry. We also study how to build a functional phase space distribution which allows to describe a quantum state with spectral and quadrature continuous variables degrees of freedom.
... In general, indistinguishability is considered a quantum resource. [412][413][414][415][416][417] Generation of N ¼ 2 N00N states via Hong-Ou-Mandel interference has been demonstrated with bulk optics configurations in path [418][419][420] and polarization 421 degrees of freedom. Polarization two-photon N00N states were also generated using the nonlocal correlation of entangled photons, 422 and were exploited for imaging of samples that surpasses SQL, even if without unconditional violation, because of losses and technical imperfections. ...
Quantum metrology is one of the most promising applications of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here, the authors review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to phase estimation. The authors describe the current state of the art in the field in terms of platforms and quantum resources. Furthermore, the authors present the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time. The authors conclude by discussing the current experimental and theoretical challenges and the open questions toward implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise.
... N00N states with N = 2 can be deterministically generated, through Hong-Ou-Mandel effect 274 , starting from two indistinguishable photons injected each along a different input of a Mach-Zehnder interferometer. This protocol has been demonstrated with bulk optics configurations in path [467][468][469] and polarization 470 degrees of freedom. Polarization twophoton N00N states were also generated using the nonlocal correlation of entangled photons 471 , and were exploited for imaging of samples that surpasses SQL, even if without unconditional violation, because of losses and technical imperfections 92 . ...
Quantum Metrology is one of the most promising application of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here we review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to phase estimation. We describe the current state of the art in the field in terms of platforms and quantum resources. Furthermore, we present the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time. We conclude by discussing the current experimental and theoretical challenges, and the open questions towards implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise.
... The other state corresponds to the case wherein the two photons are bunched together along the same path (1 or 2) beyond BS1, which can be described as e 2 1/ 2( 2 0 0 2 ) i BS1 1 2 2 1 2 → + ϕ ; this path-entangled state is highly phase-sensitive in the interferometer. Here, note that the two input photons do not have to possess identical properties in terms of the internal degrees of freedom, such as polarization and wavelength [27][28][29][30]39 . Moreover, they can differ in terms of external degrees of freedom, such as the input spatial modes and the arrival time of the two incident photons at BS1 30,39,40 (see Supplementary Note 1 for details) To observe the HOM-type TPI with classical light such as coherent light [41][42][43][44][45][46] and low-coherence fluorescent light 47,48 , a phase randomization has to be employed between the two interferometer arms in order to prevent the single-photon interference (SPI) effect as well as the interference of the path-entangled state 41,46 . ...
The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we compare our results with the previous ones of correlated photons. The observed TPI fringe can be expressed in the form of three phase terms related to the individual single-photon and two-photon states, and the fringe pattern is strongly affected by the two single-photon-interference fringes and also by their visibilities. With the exception of essential differences such as valid and accidental coincidence events within a given resolving time and the two-photon spectral bandwidth, the interference phenomenon itself exhibits the same features for both correlated and uncorrelated photons in the single-photon counting regime.
... Interestingly, the experimental measurements of the photonic de Broglie wavelength of biphotons was actually earlier than the theory. People measured the photonic de Broglie wavelength of biphotons in a series of experiments with SPDC (spontaneous parametric down conversion) light [2][3][4]. Later on, the de Broglie wavelength of biphotons was measured intently by using a similar Young's interferometer setup and a basic Mach-Zehnder interferometer [5,6]. ...
The photonic de Broglie wavelength of a non-degenerate entangled photon pair is measured by using a Young’s double slit interferometer, which proves that the non-degenerate entangled photon pairs have the potential to be used in quantum lithography. Experimental results show that the de Broglie wavelength of non-degenerate biphotons is well defined and its wavelength is neither the wavelength of the signal photon, nor the wavelength of the idler photon. According to the de Broglie equation, its wavelength corresponds to the momentum of the biphoton, which equals the sum of the momenta of signal and idler photons. The non-degenerate ghost interference/diffraction is also observed in these experiments.
... All these proposals rely on probabilistic generation techniques and complex experimental implementations. Indeed, experimental demonstration of genuine NOON states of light, entangled only in the spatial degrees of freedom, are still limited to 2 photons, obtained through the HOM interference [256,223,257]. Higher path-entangled photon number states has been obtained only through postselection. ...
Quantum phenomena can nowadays be engineered to realize fundamentally new applications. This is the field of quantum technology, which holds the promise of revolutionizing computation, communication and metrology. By encoding the information in quantum mechanical systems, it appears to be possible to solve classically intractable problems, achieve absolute security in distant communications and beat the classical limits for precision measurements. Single photons as quantum information carriers play a central role in this field, as they can be easily manipulated and can be used to implement many quantum protocols. A key aspect is the interfacing between photons and matter quantum systems, a fundamental operation both for the generation and the readout of the photons. This has been driving a lot of research toward the realization of efficient atom-cavity systems, which allows the deterministic and reversible transfer of the information between the flying photons and the optical transition of a stationary atom. The realization of such systems in the solid-state gives the possibility of fabricating integrated and scalable quantum devices. With this objective, in this thesis work, we study the light-matter interface provided by a single semiconductor quantum dot, acting as an artificial atom, deterministically coupled to a micropillar cavity. Such a device is shown to be an efficient emitter and receiver of single photons, and is used to implement basic quantum functionalities.First, under resonant optical excitation, the device is shown to act as a very bright source of single photons. The strong acceleration of the spontaneous emission in the cavity and the electrical control of the structure, allow generating highly indistinguishable photons with a record brightness. This new generation of single photon sources can be used to generate path entangled NOON states. Such entangled states are important resources for sensing application, but their full characterizatiob has been scarcely studied. We propose here a novel tomography method to fully characterize path entangled N00N state and experimentally demonstrate the method to derive the density matrix of a two-photon path entangled state. Finally, we study the effect of the quantum dot-cavity device as a non-linear filter. The optimal light matter interface achieved here leads to the observation of an optical nonlinear response at the level of a single incident photon. This effect is used to demonstrate the filtering of single photon Fock state from classical incident light pulses. This opens the way towards the realization of efficient photon-photon effective interactions in the solid state, a fundamental step to overcome the limitations arising from the probabilistic operations of linear optical gates that are currently employed in quantum computation and communication.
... where φ is a phase shift. The phase shift is determined by the photon propagation before the chip, and because the shift is double the value that would accumulate classically [30] it is highly sensitive to the environment. Experimentally, we explored this quantum-enhanced sensitivity by propagating a two-photon N00N state through one meter long optical fibers before the chip. ...
Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose a novel and scalable method to characterize quantum systems, where the complexity of the measurement process only scales linearly with the number of qubits. We experimentally demonstrate an integrated photonic chip capable of measuring two- and three-photon quantum states with reconstruction fidelity of 99.67%.
... where φ is a phase shift. The phase shift is determined by the photon propagation before the chip, and because the shift is double the value that would accumulate classically [30] it is highly sensitive to the environment. Experimentally, we explored this quantum-enhanced sensitivity by propagating a two-photon N00N state through one meter long optical fibers before the chip. ...
... For these purposes, a single interferometer is sufficient and indeed preferred, due to the ease of implementation and increased system stability. This work aligns with previous investigations of the non-classical nature of light, which have incorporated either a single Michelson interferometer [26] or a single Mach-Zehnder interferometer [19,27,28]. ...
Advances in quantum photonics have shown that chip-scale quantum devices are translating from the realm of basic research to applied technologies. Recent developments in integrated photonic circuits and single photon detectors indicate that the bottleneck for fidelity in quantum photonic processes will ultimately lie with the photon sources. We present and demonstrate a silicon nanophotonic chip capable of emitting telecommunication band photon pairs that exhibit the highest raw degree of time-energy entanglement from a micro/nanoscale source, to date. Biphotons are generated through cavity-enhanced spontaneous four-wave mixing (SFWM) in a high-Q silicon microdisk resonator, wherein the nature of the triply-resonant generation process leads to a dramatic Purcell enhancement, resulting in highly efficient pair creation rates as well as extreme suppression of the photon noise background. The combination of the excellent photon source and a new phase locking technique, allow for the observation of a nearly perfect coincidence visibility of (96.6 1.1), without any background subtraction, at a large pair generation rate of (4.40 0.07) 10 pairs/s.
... It results from the absorption and spontaneous conversion of a pump incident photon in a nonlinear crystal or fiber, producing in this manner two lower energy photons (the so-called signal and idler). The pairs of downconverted photons can be entangled in a multiparameter space of frequency, momentum, and polarization [1][2][3]4]. In Type II SPDC, the signal and idler photons are entangled in frequency, and wave and momentum have orthogonal polarizations. ...
We propose a novel scheme for the all-optical quantum simulation of topological phases by means of implementation of a discrete-time quantum walk architecture. The main novel ingredient is the inclusion of the nonlinear process of spontaneous parametric downconversion (SPDC) along the quantum network. By means of a simple theoretical model, the interplay between quantum walk lattice topology and spatial correlations of biphotons produced by SPDC is numerically explored. We describe different optical detection methods suitable for the implementation of our proposed experimental scheme.
... @BULLET Two-photon interference, where both faces of BS1 are simultaneously illuminated. These MZ experiments essentially aim at discriminating second and fourth-order interference as function of the employed light source [20][24]. Herein is only discussed single photon interference, and particularly the second step of the GRA experiment. ...
Optical lossless beam splitters are frequently encountered in fundamental physics experiments regarding the nature of light, including " which-way " determination of light particles, N. Bohr's complementarity principle, or the EPR paradox and all their measurement apparatus. Although they look as common optical components at first glance, their behaviour remains somewhat mysterious since they apparently exhibit stand-alone particle-like features, and then wave-like characteristics when inserted into a Mach-Zehnder interferometer. In this communication are examined and discussed some basic properties of these beamssplitters, both from a classical optics and quantum physics point of view. Herein some convergences and contradictions are highlighted, and the results of a few emblematic experiments demonstrating photon existence are discussed. An alternative empirical model in wave optics is also proposed in order to shed light on some remaining questions.
... The fundamental principle underlying modern quantum optical technologies utilizing correlated photon pairs is that a photon-pair interferes with the pair itself, when the indistinguishability of two-photon probability amplitudes is guaranteed in coincidence detection. Representative two-photon quantum interference phenomena include the Hong-Ou-Mandel (HOM) interference effect arising from various conditions [1][2][3] and interferences of the path-entangled photon-number state (N00N state) [4][5][6] , which lie at the heart of entanglement-based quantum communication and super-resolution metrology. ...
Superposition and indistinguishablility between probability amplitudes have
played an essential role in observing quantum interference effects of
correlated photons. The Hong-Ou-Mandel interference and interferences of the
path-entangled photon number state are of special interest in the field of
quantum information technologies. However, a fully generalized two-photon
quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and
path-entangled photon number states has not yet been proposed. Here we report
the experimental demonstrations of the generalized two-photon interferometry
with both the interferometric properties of the Hong-Ou-Mandel effect and the
fully unfolded version of the path-entangled photon number state using
photon-pair sources, which are independently generated by spontaneous
parametric down-conversion. Our experimental scheme explains two-photon
interference fringes revealing single- and two-photon coherence properties in a
single interferometer setup. Using the proposed interferometric measurement, it
is possible to directly estimate the joint spectral intensity of a photon pair
source.
High-dimensional quantum entanglement is an important resource for emerging quantum technologies such as quantum communication and quantum computation. The scalability of metres-long experimental setups limits high-dimensional entanglement in bulk optics. Advancements in quantum technology hinge on reproducible, and reconfigurable quantum devices—including photon sources, which are challenging to achieve in a scalable manner using bulk optics. Advances in nanotechnology and CMOS-compatible integration techniques have enabled the generation of entangled photons on millimeter-scale chips, significantly enhancing scalability, stability, replicability, and miniaturization for real-world quantum applications. In recent years we have seen several chip-scale demonstrations with different discrete degrees of freedom including path, frequency-bin, time-bin, and transverse modes, on many material platforms. A complete quantum photonic integrated circuit requires the generation, manipulation, and detection of quantum states, involving various active and passive quantum photonic components which further increase the degree of complexity. Here, we focus on the high-dimensional versions of qubits—qudits—and review the nonlinear optical processes that facilitate on-chip high-dimensional entangled photon sources, and the currently used material platforms. We discuss a range of current implementations of on-chip high-dimensional entangled photon sources and demonstrated applications. We comment on the current challenges due to the limitations of individual material platforms and present future opportunities in hybrid and heterogeneous integration strategies for the next generation of integrated quantum photonic chips.
Optical interferometers are pillars of modern precision metrology, but their resolution is limited by the wavelength of the light source, which cannot be infinitely reduced. Magically, this limitation can be circumvented by using an entangled multiphoton source because interference produced by an N-photon amplitude features a reduced de Broglie wavelength ∕N. However, the extremely low efficiency in multiphoton state generation and coincidence counts actually negates the potential of using multiphoton states in practical measurements. Here, a novel interferometric technique based on structured nonlinear optics is demonstrated, i.e., parametric upconversion of a structured beam, capable of superresolution measurement in real time. The main principle relies in that the orbital angular momentum (OAM) state and associated intramodal phase within the structured beam are both continuously multiplied in cascading upconversion to mimic the superresolved phase evolution of a multiphoton amplitude. Owing to the use of bright sensing beams and OAM mode projection, up to a 12-photon de Broglie wavelength with almost perfect visibility is observed in real time and, importantly, by using only a low-cost detector. The results open the door to real-time superresolution interferometric metrology and provide a promising way toward multiphoton superiority in practical applications.
The paper presents a classical and quantum description of the diffraction of two light beams incident on an ultrasonic wave at a positive and negative Bragg angle. The quantum description of the interaction with the ultrasonic wave was carried out for the two-photon NOON state. Study of diffraction of entangled pair of photon was performed in Mach–Zehnder interferometer wherein an output beam splitter is replaced by ultrasonic wave. It has been shown theoretically and experimentally that when a pair of photons generated from a parametric down-conversion was incident on two input ports of Mach–Zehnder interferometer with an acousto-optical beam splitter, then two-photon beats are observed at the output of the interferometer. The phenomenon of two-photon beats with the double frequency of the ultrasonic wave is the result of the Doppler effect on the ultrasonic wave. Time-correlated single-photon counting method was used to register the phenomenon of two-photon beats. The method of calibrating the interferometer with the use of an additional light source was presented in detail, which guarantees the observation of interaction of two-photon NOON state with ultrasonic wave.
Graphical abstract
Entanglement is an essential ingredient in current experimental implementations for quantum communication. Nevertheless, distributing the entangled states to distant users, in high quality, via widely installed fiber channels has been a daunting problem. Here, we report an experimental distribution of high-quality entangled qubits over long-distance fiber channels, especially by using time-bin mode due to its outstanding robustness in fiber-optic distributions. In particular, by employing actively operating feedback schemes, we clearly demonstrate that the time-bin entanglement can be reliably shared between two distant parties, each separated by up to 60 km in all fiber-based implementations; then, we prove the significance of our study in long-range, long-lasting quantum communication by showing a high value of two-photon interference visibilities and a violation of the Clauser–Horne–Shimony–Holt Bell inequality.
Since early 1990s, Mach–Zehnder interferometer has been used to investigate the interference of biphoton wave packets. Due to subpicosecond time coherence of biphoton generated by spontaneous parametric downconversion process, some physical processes are ignored in the interferometer, most likely the biphoton time‐domain interference. Here, the two‐photon interference phenomenon based on the Mach–Zehnder interferometer is theoretically studied, where the correlated photon pairs are produced by the four‐wave mixing in atomic system. In particular, the quantum interference effect to effectively control the coherent time of two‐photon by adjusting the input delay is used. In the damped Rabi oscillation regime, two‐photon bunching and antibunching effects are observed. In addition, in the group‐delay regime, the interference between biphoton precursor, slow‐light wave packets and also in between the precursor and the slow‐light wave packets is observed, which had never been reported before. These results may have potential applications in the fields of biphoton shaping and quantum information processing. The quantum interference of narrowband biphoton based on the Mach–Zehnder interferometer is comprehensively studied. Rich two‐photon interference phenomenon is observed whether in the damped Rabi oscillation regime or the group‐delay regime. In particular, the quantum interference effect to effectively control the coherent time of two photon by adjusting the input delay is used.
Quantum tomography: Overcoming quantum complexity by measuring multiple outputs A single chip can be used to fully characterize multi-photon quantum states, without incorporating any reconfigurable elements. This is a fundamental advance since finding a complete description of quantum system normally requires a number of different measurement configurations that grows exponentially with the system size. The group of Andrey Sukhorukov at the Australian National University developed a theoretical concept, and experimental device fabrication and two-photon measurements were realized by the group of Alexander Szameit at the Friedrich-Schiller-Universität Jena and University of Rostock in Germany. The light traversing the device undergoes an optical transformation and expands into a larger number of modes at the output. The authors then use a computationally efficient algorithm to deduce the initial quantum state from the correlations of output photons. The number of modes required only grows linearly with the photon number, demonstrating that the design provides a scalable approach to measuring larger quantum states despite their increasing complexity.
We report two-photon interference experiments performed with correlated photon pairs generated via spontaneous four-wave mixing in a Doppler-broadened atomic ensemble involving the 5S1/2-5P3/2-5D5/2 transition of ⁸⁷Rb atoms. When two photons with different wavelengths are incident on a polarization-based Michelson interferometer, two kinds of two-photon superposition states, the frequency-entangled state and dichromatic path-entangled state depending on whether the two photons are in different paths or in the same path, are probabilistically generated within the interferometer arms. Hong-Ou-Mandel-type interference fringes resulting from the frequency-entangled state are observed over the range of the single-photon coherence length, following introduction of a coarse path-length difference between the two interferometer arms and employing phase randomization. When the interferometer is highly phase-sensitive without phase randomization, a phase super-resolved fringe arising from the dichromatic path-entangled state is observed, both with and without the accompanying one-photon interference fringes.
The discovery 30 years ago of the interference of pairs of photons signaled the onset of an era for quantum optics
The purpose of this chapter is to collect experimental details and background material that are common to multiple chapters of this thesis. Section 2.2 discusses a model of spontaneous parametric down conversion and details various experimental down conversion setups used for multi-photon state generation: each description will refer to the chapters where they are employed. Section 2.3 reviews the underlying concepts of waveguide optics required for this thesis. Finally, Sect. 2.4 describes three different waveguide architectures that are employed in the experiments reported in this thesis. Simulation and fabrication of these architectures lies outside the scope of this thesis, and were performed by colleagues as stated in each corresponding section.
We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by n. These criteria negate certain mixtures of quantum states, thereby signifying a generalised n-scopic Schrodinger cat-type paradox. The first criterion is the correlation (here and are the boson operators for each mode). The correlation manifests as interference fringes in n-particle detection probabilities and is also measurable via quadrature phase amplitude and spin squeezing measurements. Measurement of enables a quantification of the overall n-th order quantum coherence, thus providing an avenue for high efficiency verification of a high-fidelity photonic NOON states. The second criterion is based on a quantification of the measurable spin-squeezing parameter . We apply the criteria to theoretical models of NOON states in lossy interferometers and double-well trapped BECs. By analysing existing BEC experiments, we demonstrate generalised atomic "kitten" states and atomic quantum coherence with atoms.
The existence of quantum entanglement is what makes quantum physics different from classical physics. First introduced by Schrödinger in his discussion of the famous cat paradox [1], the amazing effects of quantum entanglement are very counter-intuitive and sometimes mind-boggling. As a pioneer and an expert in both classical and quantum coherence theory, Mandel is the right person to use light for the exploration of quantum entanglement. Among many of Mandel’s contributions, the pioneering work and subsequent development on parametric down-conversion (PDC) opened up a whole field of research to experimentally observe the phenomena of quantum entanglement. Today, in the newly established field of quantum information science, quantum entanglement has become an essential ingredient in basically all the discussions. Schrödinger may have been the first person to mention the word of “Entanglement”, but it was Mandel who first demonstrated it experimentally and created further a variety of different entangled states, which include entangled states of polarization, of frequency, and of phase variables. Besides quantum entanglement, Mandel also exploited PDC in the study of fundamental physics as well as practical applications in optical communication.
To address correctly the question “What is two photons?” we first have to satisfactorily describe one photon. One possible answer, that preferred by the experimentalists, is “the photon was the quanta that caused the click in our photon counting detector”. In other words the smallest quantity of energy extractable from an electromagnetic field by a detector is a photon. These answers are certainly safe in the sense that they allow for interference effects to occur when more than one route to the detector exists. They do not however address non-classical light sources, the simplest of which is the one photon state. Recent experiments have produced approximations to such states using photon pair sources1–3. Such states also produce interference effects when input into interferometers1 supporting Dirac’s statement “A photon only interferes with itself”4. We must conclude therefore that a photon can be described as a “click” after detection but in order to describe fully the propogation of a quantum of light from a source we need to use a model where probability amplitudes (or field operators) are propagated down all possible paths to the detector where the square modulus of their vector sum provides a probability of detection.
Quantum-enhanced technologies require methods to precisely prepare and control quantum systems including performing state and process tomography verifying coherent quantum operation [2]—and the optical switching required for feed-forward for optical quantum computing[3].
We construct Einstein-Podolsky-Rosen (EPR) steering signatures for the nonlocality of the entangled "Schrodinger cat-type" superposition state described by , often called the NOON state. The signatures are a violation of an EPR steering inequality based on an uncertainty relation. The violation confirms a generalised EPR paradox, or "EPR steering", between the two modes and involves certification of an inter-mode correlation for both number and quadrature phase amplitude observables. We also explain how the signatures certify an Nth order quantum coherence, so the system (for larger N) can be signified to be in a "cat" superposition of mesoscopically distinct states. Realisation for larger would thus give evidence of mesoscopic EPR steering and entanglement. We include treatment of nonideal cases. Finally, we examine the limitations imposed for lossy scenarios, discussing how experimental realisations may be possible for N=2,3.
Optical parametric emission, whereby an intense “pump” beam incident on a nonlinear crystal is down-converted into radiation at the sub-harmonic frequency (ω/2), has proved to be an efficient means for amplifying light and producing photon statistics with non-classical distributions. In this course, we present the principles of optical parametric amplification, we review some recent experimental and theoretical investigations on the quantum fluctuations of parametric light and we discuss the potential applications that these studies suggest.
Multi-Photon Quantum Interference covers the phenomena of quantum interference through the multi-photon effects of photon correlation. The author's focus is on the temporal correlation among photons and how it influences the interference effect. Included is discussion of some of the well known multi-photon interference schemes, such as Hong-Ou-Mandel interferometer and Franson Interferometer for two-photon system, quantum state teleportation and swapping for four-photon system, and quantum state reconstruction for multi-photon system. A unique feature of the book is its quantitative characterization of photon indistinguishability and its connection to interference effects. © 2007 Springer Science+Business Media, LLC. All rights reserved.
It is shown that the two-photon phase coherence of parametrically generated photon pairs, which is at the origin of squeezed-light generation, can be directly probed using an intensity-correlation measurement. The resulting intensity correlation leads to a new violation of Bell's inequalities, which could be experimentally tested.
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.
A proposed experiment is analyzed theoretically. In the proposed experiment two coherent pump waves fall on two identical nonlinear crystals, down-converted signal and idler beams from the two crystals are mixed by two beam splitters, and the coincidence counting rate for photons leaving the beam splitters is measured. We show that this counting rate depends on the phase difference between the two coherent pump waves, and results from the interference of the vacuum with the down-converted photons. The experiment could be used to look for locality violations along the lines recently proposed by Grangier, Potasek, and Yurke [Phys. Rev. A 38, 3132 (1988)], but without the need for a coherent reference beam for homodyning.
We report on an interference effect arising from a two-photon entangled state produced in a potassium dihydrogen phosphate (KDP) crystal pumped by an ultraviolet argon-ion laser. Two conjugate beams of signal and idler photons were injected in a parallel configuration into a single Michelson interferometer, and detected separately by two photomultipliers, while the difference in its arm lengths was slowly scanned. The coincidence rate exhibited fringes with a visibility of nearly 50%, and a period given by half the ultraviolet (not the signal or idler) wavelength, while the singles rate exhibited no fringes.
We discuss the situation in which idler beams from two parametric down-converter crystals are allowed to interfere. We show that, when two mutually coherent signal beams derived from a common laser are injected into the down-converters, the two idler beams can become mutually coherent also. Moreover, the resulting interference pattern can, in principle, have 100% visibility when the number of injected photons per unit down-converter bandwidth is large. This is just the condition for stimulated down-conversion to dominate over spontaneous down-conversion.
A fourth-order interference technique has been used to measure the time intervals between two photons, and by implication the length of the photon wave packet, produced in the process of parametric down-conversion. The width of the time-interval distribution, which is largely determined by an interference filter, is found to be about 100 fs, with an accuracy that could, in principle, be less than 1 fs.
By measuring the joint probability for the detection of two photons at two points as a function of the separation between the points, the existence of nonclassical effects has been demonstrated in the interference of signal and idler photons in parametric down-conversion. In principle, the detection of one photon at one point rules out certain positions where the other photon can appear.
It is demonstrated in a photon coincidence experiment with two photodetectors, in which signal and idler photons produced by parametric down-conversion are allowed to interfere, that the visibility of the interference pattern is well above 50% and remains unchanged when one of the two light beams is attenuated ninefold compared with the other. These results violate classical probability for light waves.
A two-photon coincidence experiment of the kind recently proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] has been carried out with signal and idelr photons produced in the process of parametric down-conversion. The coincidence rate registered by the two detectors is found to exhibit a cosine variation with the optical path difference, with periodicity equal to the wavelength.