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Observation of nonlocal interference in separated photon channels
Abstract
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.
... It exploited the random nature in the generation time of a photon pair from the cascaded decay in a three-level atomic system, which was then analyzed by unbalanced Mach-Zehnder interferometers. The scheme was demonstrated already shortly afterwards [17,18] and it quickly became the mainstay for longdistance Bell violation experiments during the 90s [19,20]. ...
... In 1964 a now well-known proposal to test the existence of local hidden variables was put forth by John Bell [4], in which an inequality based on the assumptions of measure-arXiv:2503.14675v1 [quant-ph] 18 Mar 2025 2 ment, parameter and outcome independence could be tested in an experiment with correlated particles. Throughout the 70s and 80s experimental violations of Bell inequalities were carried out [6,7] using polarization entanglement generated from atomic cascades. ...
... This remarkable non-local two-photon interference effect was demonstrated shortly after Franson's landmark proposal in two independent experiments (Figs. 2ad) [17,18]. ...
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.
... Elimination of local interference in the path-entangled photon pairs was first described in [1,2]. But the analysis was restricted only to the case with maximally strong entanglement. ...
... Mirrors M reflect the paths directly to the respective beam splitters (BS); A , B are the phase shifters; FA , GA , F B , G B are photon detectors. 2 The paths 1 and 2 in Fig.1 Turning to fermions, we describe in this section monitoring a single qubit state. The term qubit applies to spin ½ fermions, with two eigenstates each, like in the bi-photon case in [1][2][3]. ...
... 2 The paths 1 and 2 in Fig.1 Turning to fermions, we describe in this section monitoring a single qubit state. The term qubit applies to spin ½ fermions, with two eigenstates each, like in the bi-photon case in [1][2][3]. On the way we will point at similarities and differences between an electron qubit and two paths photon qubit. ...
Analysis of the recently proposed thought experiment with the path entangled photon pairs is extended here to spin entangled electron pairs. The detailed comparison of the two cases showed the range of distinctions and similarities in their monitoring. The general results contradict the Concurrency Rule stating that intimately linked characteristics of a simple system must change concurrently under changing conditions. Instead, the analysis showed that the systems coherence, while changing continuously with entanglement strength on the global scale, remains zero on the local level. This effect, common for bi photons and bi fermions, can be named total mutual intolerance between local and global coherence. We can thus predict mutual intolerance as a general effect for all pairs of entangled qubits regardless of their physical nature. Key words: Bi photon, bi fermion, entanglement, correlations, coherence transfer
... In this context, we consider Franson interference, which is a well-known second-order two-photon quantum interference phenomenon 3,4 . In particular, the two-photon coherence length of a time-energy entangled photon pair beyond the single-photon coherence length is a counterintuitive phenomenon [3][4][5][6][7][8][9][10][11][12][13] . ...
... In this context, we consider Franson interference, which is a well-known second-order two-photon quantum interference phenomenon 3,4 . In particular, the two-photon coherence length of a time-energy entangled photon pair beyond the single-photon coherence length is a counterintuitive phenomenon [3][4][5][6][7][8][9][10][11][12][13] . To avoid singlephoton interference in Franson interference, it is necessary that the path-length difference of the unbalanced interferometry setup is considerably longer than the coherence length of the one-photon state. ...
... Franson interference technique can determine the two-photon coherence length of an entangled photon pair 6 . The two-photon coherence length depends on the characteristics of the time-frequency entangled photon pair originating from various media [4][5][6][7][8][9][10][11][12][13] . ...
The phenomenon of Franson interference with time–energy entangled photon pairs beyond the single-photon coherence length observed upon nonlocal measurement at two space-like separated locations is of particular research interest. Herein, we determine the coherence length of temporally separated pairwise two-photon (TSPT) states of thermal photons emitted from a warm atomic ensemble in Franson-type interferometry, with the setup consisting of two spatially separated unbalanced Michelson interferometers beyond the coherence length of a thermal photon. Using a novel method of square-modulated thermal photons, we show that the sinusoidal Franson-type interference fringe of thermal photons is determined by the presence or absence of TSPT states (corresponding to the time delay between the long and short paths in Franson-type interferometry). We find that the indistinguishability of the TSPT state in the Franson-type interference is independent of the temporal separation of the thermal photons in the TSPT states.
... In this context, we consider Franson interference, which is a well-known second-order two-photon quantum interference phenomenon [3][4]. In particular, the two-photon coherence length of a time-energy entangled photon pair beyond the single-photon coherence length is a counterintuitive phenomenon [3][4][5][6][7][8][9][10][11][12][13]. ...
... In this context, we consider Franson interference, which is a well-known second-order two-photon quantum interference phenomenon [3][4]. In particular, the two-photon coherence length of a time-energy entangled photon pair beyond the single-photon coherence length is a counterintuitive phenomenon [3][4][5][6][7][8][9][10][11][12][13]. To avoid single-photon interference in Franson interference, it is necessary that the path-length difference of the unbalanced interferometry setup is considerably longer than the coherence length of the one-photon state. ...
... Franson interference technique can determine the two-photon coherence length of an entangled photon pair [6]. The two-photon coherence length depends on the characteristics of the time-frequency entangled photon pair originating from various media [4][5][6][7][8][9][10][11][12][13]. ...
The phenomenon of Franson interference with time–energy entangled photon pairs beyond the single-photon coherence length observed upon nonlocal measurement at two space-like separated locations is of particular research interest. Herein, we determine the coherence length of temporally separated pairwise two-photon (TSPT) states of thermal photons emitted from a warm atomic ensemble in Franson-type interferometry, with the setup consisting of two spatially separated unbalanced Michelson interferometers beyond the coherence length of a thermal photon. Using a novel method of square-modulated thermal photons, we show that the sinusoidal Franson-type interference fringe of thermal photons is determined by the presence or absence of TSPT states (corresponding to the time delay between the long and short paths in Franson-type interferometry). We find that the indistinguishability of the TSPT state in the Franson-type interference is independent of the temporal separation of the thermal photons in the TSPT states.
... Multidimensional quantum information processing has been shown to open a wide range of possibilities including increased quantum channel capacity [1], multidimensional entanglement [2], and loophole-free Bell Inequality tests [3]. In contrast to the internal polarization degree of freedom of a photon, external degrees of freedom related to space [4] and time [5][6][7] are described by infinite-dimensional Hilbert spaces. The spatial degree of freedom has recently been employed to encode multidimensional quantum information using photon orbital angular momentum [8][9][10]; this approach, however, is not suitable for the single-mode fiber-optical communication infrastructure. ...
... In this case superpositions of M low-frequency modes are sufficient for tomography and reconstruction of the wavefunction with high fidelity. High error rates could prevent the violation of Bell's inequalities by reducing the two-photon interference visibility below the classical field theory limit [4,6]. In our scheme the error rates depend on the specific realization, the photon bandwidth and on the modulator speed. ...
We propose a multidimensional quantum information encoding approach based on temporal modulation of single photons, where the Hilbert space can be spanned by an in-principle infinite set of orthonormal temporal profiles. We analyze two specific realizations of such modulation schemes, and show that error rate per symbol can be smaller than 1% for practical implementations. Temporal modulation may enable multidimensional quantum communication over the existing fiber optical infrastructure, as well as provide an avenue for probing high-dimensional entanglement approaching the continuous limit.
... But such effect is insensitive to phase change of the fields. On the other hand, a phase-dependent fourth-order interference effect occurs in Franson interferometer [7], which consists of two highly imbalanced interferometers beyond coherence length [8][9][10]. But it was shown that the effect exists only for two-photon quantum fields and disappears for stationary classical fields in time-unresolved coincidence measurement [11]. ...
... On the other hand, fourth-order correlations do contribute to the results by adding to the baseline in the form of intensity fluctuations in some cases [quantity λ in Eqs. (8) and (15)]. ...
Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve intensity correlations between multiple detectors and may have the advantage over the traditional second-order interference effect exhibited in only one detector. We discuss various scenarios with unbalanced delays in different paths in fourth-order interference exhibited in coincidence between two detectors. We find, in some cases, interference effect persists even when the delays are much larger than the coherence time of the sources. We also extend the discussion to nonstationary pulsed fields, which need to consider the pulse shape and require a different treatment. These results will be useful in remote sensing applications.
... But such effect is insensitive to phase change of the fields. On the other hand, phase-dependent fourth-order interference effect occurs in Franson interferometer 7 which consists of two highly imbalanced interferometers beyond coherence length [8][9][10] . But it was shown that the effect exists only for two-photon quantum fields and disappears for stationary classical fields 11 . ...
... On the other hand, fourth-order correlations do contribute to the results by adding to the baseline in the form of intensity fluctuations in some cases (quantity λ in Eqs. (8,15)). Their effect is to reduce the visibility of interference, as shown in Eq. (11). ...
Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve intensity correlations between multiple detectors and may have the advantage over the traditional second order interference effect exhibited in only one detector. We discuss various scenarios in fourth-order interference with unbalanced delays in different paths. We find in some cases, interference effect persists even when the delays are much larger than the coherence time of the sources. We also extend the discussion to non-stationary pulsed fields, which needs to consider the pulse shape and requires a different treatment. These results will be useful in remote sensing applications.
... Parametric amplifiers are extensively used in important technological sectors as radio astronomy [10], communications [11], radar systems [12], spectroscopy [13] and sensing [14]. In quantum technology, parametric amplifiers have become relevant for many applications ranging from the generation of squeezed states [5,6,15], entanglement and nonclassical states [16,17], and quantum-limited amplification [18] to quantum computing [19], quantum sensing and metrology [20,21]. ...
We study the dynamics of a driven atomic Josephson junction that we propose as a parametric amplifier. By periodically modulating the position of the barrier, we induce a small current across the junction, serving as our input signal. The pump field is implemented by modulating the barrier height at twice the Josephson plasma frequency. The resulting dynamics exhibit parametric amplification of the signal through nonlinear mixing between the signal and pump fields, which is reflected by specific patterns of density waves and phase excitations. We employ a classical-field dynamics method and benchmark our results against driven circuit dynamics. This work paves the way for tunable quantum amplifiers in atomtronic circuits, with potential applications in several fields including precision measurements and quantum information processing.
... The two photons generated from SPDC can be engineered to be entangled in various degrees of freedom. For instance, timebin or time-energy entangled photons can be obtained from SPDC with the Franson interference [10], which has been demonstrated on various crystal materials including beta barium borate (BBO) [11], lithium triborate (LBO) [12], potassium niobate (KNbO 3 ) [13], lithium iodate (LiIO 3 ) [14], periodically poled potassium titanyl phosphate (PPKTP) [15], and periodically poled lithium niobate (PPLN) [16]. However, the phase-matching condition, i.e., energy and momentum conservation, is the fundamental requirement in the design of quantum photon sources, which limits the set of wavelengths of photon sources. ...
Lithium niobate (LN) is a birefringent material, where the strong birefringence thermo-optic effect is promising for the generation of a quantum photon source with a widely tunable wavelength. Here, we demonstrate birefringent phase matching in a 20-mm-long waveguide fabricated on a 5- m-thick x-cut lithium niobate on insulator (LNOI). The waveguide is deviated from the optical axis of LN by an angle of 53.5 , enabling the phase matching between telecom and visible wavelengths. The phase-matching wavelength of this device can be thermally tuned with rate of 0.6 nm/K. We demonstrate the type-1 spontaneous parametric downconversion to generate photon pairs with a brightness of 4.7 MHz/mW and a coincidence-to-accidental ratio of up to 2.8 × 10⁵. Furthermore, the heralded single photon is obtained from the photon pair with an efficiency of 13.8% and a count rate of up to 37.8 kHz.
... The two photons generated from SPDC can be engineered to entangled in various degrees of freedom. For instance, time-bin or time-energy entangled photons can be obtained from SPDC with Franson interference [10], which has been demonstrated on various crystal materials including beta barium borate (BBO) [11], lithium triborate (LBO) [12], potassium niobate (KNbO 3 ) [13], lithium iodate (LiIO 3 ) [14] periodically poled potassium titanyl phosphate (PPKTP) [15] and periodically poled lithium niobate (PPLN) [16]. However, the phasematching condition, i.e., energy and momentum conservation, is the fundamental requirement in the design of quantum photon sources, which limits the set of wavelengths of photon sources. ...
Lithium niobate~(LN) is a birefringent material, where the strong birefringence thermo-optic effect is promising for the generation of quantum photon source with widely tunable wavelength. Here, we demonstrate birefringent phase-matching in a 20-mm-long waveguide fabricated on 5~m-thick x-cut lithium niobate on insulator. The waveguide is deviated from the optical axis of LN by an angle of 53.5, enabling the phase matching between telecom and visible wavelengths. The phase-matching wavelength of this device can be thermally tuned with rate of 0.617~nm/K. We demonstrate the type-1 spontaneous parametric down-conversion to generate photon pairs with brightness of 2.2~MHz/mW and coincidence-to-accidental ratio up to . Furthermore, the heralded single photon is obtained from the photon pair with efficiency of 13.8\% and count rate up to 37.8~kHz.
... The non-linear optical process of spontaneous parametric down-conversion (SPDC) [1,2,3] creates pairs of highly entangled single photon pairs [4,5]. Its use became ubiquitous in quantum optics (QO), where numerous experiments rely on this process [6,7,8,9,10,11,12,13]. ...
In this paper we propose and analyse a Gedankenexperiment involving three non-linear crystals and two objects inserted in the idler beams. We show that, besides the behaviour that can be extrapolated from previous experiments involving two crystals and one object, we are able to predict a new effect: under certain circumstances, one of the objects can be rendered undetectable to any single detection rate on the signal photons with discarded idler photons. This effect could find applications in future developments of quantum imaging techniques.
... The experiment proposed by Franson [7] concerning a Bell inequality for nonpolarization variables, relies on the entanglement of a continuous variable, energy. There are number of experimental realizations [8,9] of the Franson interferometer. Kwiat et al. [9] have achieved sinusoidal fringes of the two-photon interference with visibility greater than 70.7%. ...
We propose a two-photon beating experiment based upon biphotons generated from a resonant pumping two-level system operating in a backward geometry. On the one hand, the linear optical-response leads biphotons produced from two sidebands in the Mollow triplet to propagate with tunable refractive indices, while the central-component propagates with unity refractive index. The relative phase difference due to different refractive indices is analogous to the pathway-length difference between long-long and short-short in the original Franson interferometer. By subtracting the linear Rayleigh scattering of the pump, the visibility in the center part of the two-photon beating interference can be ideally manipulated among [0, 100%] by varying the pump power, the material length, and the atomic density, which indicates a Bell-type inequality violation. On the other hand, the proposed experiment may be an interesting way of probing the quantum nature of the detection process. The interference will disappear when the separation of the Mollow peaks approaches the fundamental timescales for photon absorption in the detector.
... Consequently, quantum interference may be observed as a function of the phase relation between these two contributions. This type of entanglement analysis necessitates, however, a postselection procedure in order to exclude contributions in which the paired photons take opposite paths (shortlong and long-short) [14], otherwise interference fringe visibilities are limited to 50% [37]. ...
We report a fully guided-wave source of polarisation entangled photons based on a periodically poled lithium niobate waveguide mounted in a Sagnac interferometer. We demonstrate the source's quality by converting polarisation entanglement to postselection-free energy-time entanglement for which we obtain a near-optimal S-parameter of , i.e. a violation of the Bell inequality by more than 35 standard deviations. The exclusive use of guided-wave components makes our source compact and stable which is a prerequisite for increasingly complex quantum applications. Additionally, our source offers a great versatility in terms of photon pair emission spectrum and generated quantum state, making it suitable for a broad range of quantum applications such as cryptography and metrology. In this sense, we show how to use our source for chromatic dispersion measurements in optical fibres which opens new avenues in the field of quantum metrology.
... Depending on the kind of entanglement, they exhibit different quantum-optical phenomena. For instance, timefrequency-entangled photon pairs have been used for observing automatic dispersion cancellation [4,5] in Hong-Ou-Mandel (HOM) interference [6], Franson interference [7,8], and phase superresolution [9]. In other instances, position-wavevector-entangled photon pairs have been used for observing ghost imaging [10], two-photon Young interference [11][12][13][14][15], two-photon focused beam spots [16], and automatic aberration cancellation [17]. ...
The quantum interference of entangled photons forms a key phenomenon underlying various quantum-optical technologies. It is known that the quantum interference patterns of entangled photon pairs can be reconstructed classically by the time-reversal method; however, the time-reversal method has been applied only to time-frequency-entangled two-photon systems in previous experiments. Here, for the first time, we apply the time-reversal method to the position-wavevector-entangled two-photon systems: the two-photon Young interferometer and the two-photon beam focusing system. We experimentally demonstrate that the time-reversed systems classically reconstruct the same interference patterns as the position-wavevector-entangled two-photon systems.
... In this section, we demonstrate that the photon pairs generated from FDMR are indeed entangled. We verify this entanglement by measuring the visibility of two-photon interference using a folded Franson interferometer [59][60][61][62]. To implement the folded Franson interferometer, we utilize a fiber-based unbalanced Michelson interferometer with a path delay of τ d = 1.44 ns, as shown in Fig. 4(a) and explained in the Supplemental Material [53]. ...
Entanglement is a valuable resource in quantum information technologies. The practical implementation of entangled photon sources faces obstacles from imperfections and defects inherent in physical systems, resulting in a loss or degradation of entanglement. The topological photonic insulators, however, have emerged as promising candidates, demonstrating an exceptional capability to resist defect-induced scattering, thus enabling the development of robust entangled sources. Despite their inherent advantages, building programmable topologically protected entangled sources remains challenging due to complex device designs and weak material nonlinearity. Here, we present a development in entangled photon-pair generation achieved through a nonmagnetic and tunable anomalous Floquet insulator, utilizing an optical spontaneous four-wave-mixing process. We verify the nonclassicality and time-energy entanglement of the photons generated by our topological system. Our experiment demonstrates a substantial enhancement in nonclassical photon-pair generation compared to devices reliant only on topological edge states. Our results could lead to the development of resilient quantum sources with potential applications in quantum technology.
Published by the American Physical Society 2024
... Notably, interference between pairs of photons that travel together through the interferometer persists with a fringe period at half the pair wavelength [ Fig. 5(d)]. This feature suggests quantum interference due to the energy-time entanglement of the pairs, and would not be observed if the light was generated from a coherent or a thermal source with a similar spectrum [58]. A fringe visibility of 43 ± 3% is observed in this region far from the coherence length, which is close to the theoretical maximum of 50% for this experiment due to the temporal resolution of the detectors. ...
Efficient on-chip entangled photon pair generation at telecom wavelengths is an integral aspect of emerging quantum optical technologies, particularly for quantum communication and computing. However, moving to shorter wavelengths enables the use of more accessible silicon detector technology, and opens up applications in imaging and spectroscopy. Here, we present high brightness ((1.6 ± 0.3) × 10⁹ pairs/s/mW/nm) visible–near-IR photon pair generation in a periodically poled lithium niobate nanophotonic waveguide. The degenerate spectrum of the photon pairs is centered at 811 nm with a bandwidth of 117 nm when pumped with a spectrally multimode laser diode. The measured on-chip source efficiency of (2.3 ± 0.5) × 10¹¹ pairs/s/mW is on par with source efficiencies at telecom wavelengths and is also orders of magnitude higher than the efficiencies of other visible sources implemented in bulk crystal or diffused waveguide-based technologies. Further improvements in the brightness and efficiencies are possible by pumping the device with a single-frequency laser, which would also shrink the pair bandwidth. These results represent the shortest wavelength of photon pairs generated in a nanophotonic waveguide reported to date by nearly an octave.
... [1][2][3][4][5][6][7] The entangled states of photons can be described as a variety of degrees of freedom, such as polarization, frequency-time, position-momentum, path, and spatial mode. [8][9][10][11][12][13][14][15][16][17][18][19][20] Particularly, polarization-entangled photons are useful as practical quantum resources for photonic quantum information, such as entanglement swapping, the multiphoton entangled state, and the photonic quantum computer. [21][22][23][24][25][26][27][28][29][30][31][32][33] Polarization-entangled photon pairs have been extensively generated via the spontaneous The polarization-entangled photon pair from a warm atomic ensemble is a promising quantum source owing to its effectiveness, simplicity, robustness, and reliability for the manipulation of photonic quantum information based on atom-photon interactions. ...
Atomic ensembles are important quantum resources for the generation, manipulation, and quantum memory of entangled photons. In photonic quantum information based on atom–photon interactions, high‐quality entangled‐photon‐pair sources are essential for realizing quantum information networks consisting of channels to connect the nodes through atomic ensembles. Here, a proof‐of‐concept for controlling polarization‐entangled photon‐pair sources from atomic ensembles by an external magnetic field under a magnetic noise environment is demonstrated. In the unshielded magnetic field, the polarization entangled state of the photon pair could be optimized to the target state by adjusting the magnetic field in an atomic vapor cell. The polarization‐interference fringe, Bell's inequality value, quantum state tomography, and Hong–Ou–Mandel interference of the polarization entangled photon pairs from the cascade‐type 5S1/2–5P3/2–5D5/2 transition of ⁸⁷Rb according to the direction of the external magnetic field. Accordingly, a magnetic field is found to be a promising means for controlling entangled two‐qubit states based on atom–photon.
... In the particular version employing collinear temporal modes that we used for the experimental implementation, the scheme is reminiscent of a Franson's interferometer for the analysis of time-frequency entanglement. [23][24][25] As in that case, the results of coincidence measurements depend on both the phases in the remote locations A and B. Here, thanks to the stimulated photon addition process onto populated signal modes, the entanglement of the heralded state in A presents an enhanced sensitivity on the remote phase that allows us to perform phase measurements on the sample in B with a sensitivity scaling with the intensity of the seed coherent states in A. ...
A remote phase sensing scheme is proposed, inspired by the high sensitivity of the entanglement produced by coherent multimode photon addition on the phase set in the remote heralding apparatus. By exploring the case of delocalized photon addition over two modes containing identical coherent states, the optimal observable to perform remote phase estimation from heralded quadrature measurements is derived. The technique is experimentally tested with calibration measurements and then used for estimating a remote phase with a sensitivity that is found to scale with the intensity of the local coherent states, which never interacted with the sample.
... Conversely, if the time delay is larger than the photon coherence time, only the Franson-type interference remains and its measurement, in this experimental condition, is widely employed in the literature to prove energy-time entanglement of photon pairs [59,267,268]. ...
Nonclassical states of light are key resources for quantum information technologies thanks to their easy transmission, robustness to decoherence and variety of degrees of freedom to encode information. In this context, this PhD thesis is dedicated to the development of novel semiconductor photon pair sources. Exploiting the high flexibility offered by spontaneous parametric down conversion (SPDC) in AlGaAs waveguides, we demonstrate the generation and the engineering of high-dimensional nonclassical states of light encoded in frequency. First, we employ a source based on a counter-propagating phase-matching scheme and demonstrate that tailoring the spatial profile (intensity and phase) of the pump beam enables the control of the photon pair spectral correlations and wavefunction symmetry directly at the generation stage, without any post-selection. In particular, tuning the pump beam waist allows to produce correlated, anti-correlated and separable frequency states, while modifying the spatial phase profile allows to switch between symmetric and antisymmetric spectral wavefunctions and to modify the exchange statistics of the photons, as evidenced measured via Hong-Ou-Mandel interferometry. We also investigate more complex quantum states: we demonstrate that this source, thanks to its geometry and to an anti-reflection coating, can also emit photon pairs entangled in a hybrid polarization/frequency degree of freedom. We then start the development of a novel device formed by a lattice of parallel co-propagating nonlinear waveguides, design to emit spatially entangled photon pairs via cascaded quantum walks. We report the optimization of its clean room fabrication processes and first optical characterizations of this novel device.
... In conclusion, we have demonstrated the possibility of performing remote phase sensing by coherently adding a single photon over two separated field modes. In the particular version employing collinear temporal modes that we used for the experimental implementation, the scheme is reminiscent of a Franson's interferometer for the analysis of time-frequency entanglement [16][17][18]. As in that case, the results of coincidence measurements depend on both the phases in the remote locations A and B. Here, thanks to the stimulated photon addition process onto populated signal modes, the entanglement of the heralded state in A presents an enhanced sensitivity on the remote phase φ that allows us to perform phase measurements on the sample in B with a sensitivity scaling with the intensity of the seed coherent states in A. Actually, the phase-changing sample does not even need to be in Bob's lab and could be located anywhere along the path of one of the idler modes (or even distributed in the white zone between the A and B blocks of Fig. 1 and Fig. 2). ...
We propose a remote phase sensing scheme inspired by the high sensitivity of the entanglement produced by coherent multimode photon addition on the phase set in the remote heralding apparatus. By exploring the case of delocalized photon addition over two modes containing identical coherent states, we derive the optimal observable to perform remote phase estimation from heralded quadrature measurements. The technique is experimentally tested with calibration measurements and then used for estimating a remote phase with a sensitivity that is found to scale with the intensity of the (local) coherent states, which never interacted with the sample.
... In that setup, the role of the particles' position and momentum can be assumed by the field quadrature amplitudes, and the partially entangled state may be implemented by a two-mode squeezed vacuum state. The pair of double slits is isomorphic to a pair of Mach-Zehnder interferometers (as in the famous Franson experiment [40][41][42]), where the distance between the slits is equivalent to the delay between the two-interferometer arms, and the interference pattern measured on the screen can be replaced by a homodyne measurement. ...
Complementarity between one-particle visibility and two-particle visibility in discrete systems can be extended to bipartite quantum-entangled Gaussian states implemented with continuous-variable quantum optics. The meaning of the two-particle visibility originally defined by Jaeger, Horne, Shimony, and Vaidman with the use of an indirect method that first corrects the two-particle probability distribution by adding and subtracting other distributions with varying degree of entanglement, however, deserves further analysis. Furthermore, the origin of complementarity between one-particle visibility and two-particle visibility is somewhat elusive and it is not entirely clear what is the best way to associate particular two-particle quantum observables with the two-particle visibility. Here, we develop a direct method for quantifying the two-particle visibility based on measurement of a pair of two-particle observables that are compatible with the measured pair of single-particle observables. For each of the two-particle observables from the pair is computed corresponding visibility, after which the absolute difference of the latter pair of visibilities is considered as a redefinition of the two-particle visibility. Our approach reveals an underlying mathematical symmetry as it treats the two pairs of one-particle or two-particle observables on equal footing by formally identifying all four observable distributions as rotated marginal distributions of the original two-particle probability distribution. The complementarity relation between one-particle visibility and two-particle visibility obtained with the direct method is exact in the limit of infinite Gaussian precision where the entangled Gaussian state approaches an ideal Einstein-Podolsky-Rosen state. The presented results demonstrate the theoretical utility of rotated marginal distributions for elucidating the nature of two-particle visibility and provide tools for the development of quantum applications employing continuous variables.
... Energy-time entangled photonic states have been realized through SPDC, [205][206][207][208][209] following the proposal by Franson. 210 Entanglement in such systems is characterized by the analysis of Bell states 211 from correlated interference effects. ...
Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.
... Franson suggested an ingenious setup to visualize the energy-time entanglement of two photons emitted from a three-level system (3LS) in ladder configuration via an interference in the second-order coherence function [21]. The Franson interferometer has been realized in a variety of experiments [28][29][30][31][32][33][34][35][36][37]. The visibility of the interference fringes depends crucially on the decay rates of the 3LS and a high visibility can be obtained in a parameter regime where the upper state of the 3LS decays slowly in comparison to the middle state. ...
The visibility of the two-photon interference in the Franson interferometer serves as a measure of the energy-time entanglement of the photons. We propose to control the visibility of the interference in the second-order coherence function by implementing a coherent time-delayed feedback mechanism. Simulating the non-Markovian dynamics within the matrix product state framework, we find that the visibility for two photons emitted from a three-level system (3LS) in ladder configuration can be enhanced significantly for a wide range of parameters by slowing down the decay of the upper level of the 3LS.
... In that setup, the role of the particles' position and momentum can be assumed by the field quadrature amplitudes, and the partially entangled state may be implemented by a two-mode squeezed vacuum state. The pair of double slits is isomorphic to a pair of Mach-Zehnder interferometers (as in the famous Franson experiment [40][41][42]), where the distance between the slits is equivalent to the delay between the two-interferometer arms, and the interference pattern measured on the screen can be replaced by a homodyne measurement. ...
Complementarity between one- and two-particle visibility in discrete systems can be extended to bipartite quantum-entangled Gaussian states. The meaning of the two-particle visibility originally defined by Jaeger, Horne, Shimony, and Vaidman with the use of an indirect method that first corrects the two-particle probability distribution by adding and subtracting other distributions with varying degree of entanglement, however, deserves further analysis. Furthermore, the origin of complementarity between one-particle visibility and two-particle visibility is somewhat elusive and it is not entirely clear what is the best way to associate particular two-particle quantum observables with the two-particle visibility. Here, we develop a direct method for quantifying the two-particle visibility based on measurement of a pair of two-particle observables that are compatible with the measured pair of single-particle observables. For each of the two-particle observables the corresponding visibility is computed, after which the absolute difference of the latter pair of visibilities is considered as a redefinition of the two-particle visibility. Our approach reveals a mathematical symmetry as it treats the two pairs of one-particle or two-particle observables on equal footing by formally identifying all four observable distributions as rotated marginal distributions of the original two-particle probability distribution. The complementarity relation between one-particle visibility and two-particle visibility obtained with the direct method is exact in the limit of infinite Gaussian precision where the entangled Gaussian state approaches an ideal EPR state. The presented results demonstrate the theoretical utility of rotated marginal distributions for elucidating the nature of two-particle visibility and provide tools for the development of quantum applications employing continuous variables.
... The projection of n photons results in 2 n possible amplitudes. In order to demonstrate the quantum nonlocality of the produced states, the n-photon amplitudes are interfered 43,44 . This nonlocal interference is achieved by rotating the measurement basis of the first n − 1 photons to the diagonal basis via a Hadamard rotation. ...
... Later, the research was extended to investigate the characteristic of nonclassical light, especially entangled photon pairs generated by spontaneous parametric down-conversion (SPDC). The surprising correlation features, which can only be interpreted by quantum mechanics without classical equivalence [3][4][5][6][7][8] , have led to many promising applications in various photonic quantum technologies [9][10][11][12][13][14] . ...
... The projection of n photons results in 2 n possible amplitudes. In order to demonstrate the quantum nonlocality of the produced states, the n-photon amplitudes are interfered 43,44 . This nonlocal interference is achieved by rotating the measurement basis of the first n − 1 photons to the diagonal basis via a Hadamard rotation. ...
Light states composed of multiple entangled photons—such as cluster states—are essential for developing and scaling-up quantum computing networks. Photonic cluster states can be obtained from single-photon sources and entangling gates, but so far this has only been done with probabilistic sources constrained to intrinsically low efficiencies, and an increasing hardware overhead. Here, we report the resource-efficient generation of polarization-encoded, individually-addressable photons in linear cluster states occupying a single spatial mode. We employ a single entangling-gate in a fiber loop configuration to sequentially entangle an ever-growing stream of photons originating from the currently most efficient single-photon source technology—a semiconductor quantum dot. With this apparatus, we demonstrate the generation of linear cluster states up to four photons in a single-mode fiber. The reported architecture can be programmed for linear-cluster states of any number of photons, that are required for photonic one-way quantum computing schemes. Generating photonic cluster states using a single non-heralded source and a single entangling gate would optimise scalability and reduce resource overhead. Here, the authors generate up to 4-photon cluster states using a quantum dot coupled to a fibre loop, with a fourfold generation rate of 10 Hz.
... Since violation of Bell's inequality had been reported from both phase [10] and polarization bases [11], Franson proposed a different type of nonlocal correlation using energy and time conjugate relations satisfying Heisenberg uncertainty principle [12]. For Franson-type experiments, a photon pair entering two independent Mach-Zehnder interferometers (MZIs) is manipulated to be indistinguishable for two-photon coincidence detection, violating Bell's inequality in a very delicate manner presenting as an interference fringe [11][12][13][14][15][16][17][18][19][20]. In the Franson-type nonlocal correlation, however, both photons passing through individual MZIs never interfere with each other until measured independently by separate photon detectors. ...
Nonlocal correlation is the key concept in quantum information processing, where quantum entanglement provides such a nonclassical property. Since the first proposal of noninterfering interferometer-based two-photon intensity correlation by Franson (Phys. Rev. Lett. 62, 2205 (1989)), the particle nature of photons has been intensively studied for nonlocal correlation using Mach-Zehnder interferometers (MZIs). Here, the role of MZIs is investigated with respect to the origin of nonlocal correlation in Franson-type experiments, where the wave nature of photons plays a critical role. Under the coincidence-provided quantum superposition between independent MZIs, we prove that nonlocal correlation can be created from non-entangled photons through the MZIs.
... Whether that rhythm is tightly connected to a standard frequency as defined in the International System (SI) turns out to be irrelevant. Another striking feature of this experiment is the employment of photon pairs entangled in such a way that phase correlations matter [11][12][13]. A source S generates a sequence of weak light pulses, theoretically described as single photons, into an optical fiber. ...
Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clocks, which precludes synchronizing every clock to every other clock. General relativity imposes additional barriers to synchronization, barriers that invite seeking an alternative depending on any global concept of time. To this end, we focus on how clocks are actually used in some experimental situations. We show how working with clocks without worrying about time makes it possible to generalize some designs for quantum key distribution and also clarifies the need for alternatives to the special-relativistic definition of synchronization.
... Whether that rhythm is tightly connected to a standard frequency as defined in the International System (SI) turns out to be irrelevant. Another striking feature of this experiment is the employment of photon pairs entangled in such a way that phase correlations matter [11][12][13]. A source S generates a sequence of weak light pulses, theoretically described as single photons, into an optical fiber. ...
Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clocks, which precludes synchronizing every clock to every other clock. General relativity imposes additional barriers to synchronization, barriers that invite seeking an alternative depending on any global concept of time. To this end, we focus on how clocks are actually used in some experimental situations. We show how working with clocks without worrying about time makes it possible to generalize some designs for quantum key distribution and also clarifies the need for alternatives to the special-relativistic definition of synchronization.
... In 1990, two independent groups (Rarity and Tapster, and Ou, Zou, Wang and Mandel [26][27][28]) reported nearly simultaneously on similar interferometer experiments using momentum-entangled pairs of photons A and B to study the state |Y> = |A1>|B1> + |A2>|B2> . ...
An argument first proposed by John von Neumann shows that measurement of a superposed quantum system creates an entangled "measurement state" (MS) in which macroscopically distinct detector states appear to be superposed, a paradoxical prediction implying the measurement has no definite outcome. We argue that this prediction is based on a misunderstanding of what the MS represents. We show, by studying the phase dependence of entangled photon states generated in parametric down conversion, that the MS represents not a superposition of detector states, but rather a superposition of coherent (i.e. phase-dependent) correlations between detector states and system states. In fact an argument by Einstein shows that a nonlocal entangled state is required, at least briefly, following a quantum system's interaction with a detector. Such a state does not represent a paradoxical macroscopic superposition. This resolves the paradox of indefinite outcomes of measurements.
... Franson interference (FI) is a fourth-order two-particle interference effect proposed by Franson [18] that was first demonstrated in 1990 [19,20]. Unlike the Hong-Ou-Mandel interference effect [21], where the two particles need to be brought to the same space-time location for interference, the FI is observed with the two particles at vastly separate locations. ...
... Turning to the entangled state (2): two independent groups, Rarity and Tapster and also Ou, Zou, Wang, and Mandel, reported in 1990 on essentially identical interferometer experiments using momentum-entangled photon pairs to study the state |AB>. [29][30][31] Because it varies the phase over 0 to π, this "RTO experiment" sheds new light on |AB>. We will describe the experiment, then present its quantum-theoretical analysis and predicted results, then compare these predictions with the experimental outcomes. ...
The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the phase is fixed at zero for perfect correlations, nonlocality experiments cover the full range of superposition phases and can thus show precisely what entangled states superpose. For two-state systems, these experiments reveal that the measurement state is not a superposition of two macroscopically different detector states but instead a superposition of two coherent correlations between distinct detector states and corresponding system states. In the measurement situation (i.e. at zero phase), and assuming the Schrodinger's cat scenario, the entangled state can be read as follows: An undecayed nucleus is perfectly correlated with an alive cat, AND a decayed nucleus is perfectly correlated with a dead cat, where "AND" indicates the superposition. This is not paradoxical.
... 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] . ...
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.
... Although the uncertainty in time and frequency domain for individual particle should meet the requirement of uncertainty principle, the sum of the frequency of signal and idler multiplies the difference between arrive times of the two photon should have a very small value, and violates an inequality for two photons existed classical correlations [53]. A two-photon Franson-type interference is used to characterize the correlations between the two photons; the phases between the two unbalanced Michelson interferometers (UMI) are correlated [54,55]. To generate a time-energy entangled photon pair, a laser with long coherent time is needed (see Figure 3(a)); the time difference between two paths in UMI should be much larger than the coherence time of the single photon but much shorter than the coherent time of the pump laser [53]. ...
Nonclassical photon sources are key components in quantum information science and technology. Here, the basic principles and progresses for single photon generation and their further manipulation based on second- or third-order nonlinear processes in various degrees of freedom are briefly reviewed and discussed. Based on spontaneous parametric down-conversion and spontaneous four-wave mixing, various nonlinear materials such as quasi-phase-matching crystals, dispersion-shifted fibers, and silicon-on-insulator waveguides are used for single photon generation. The kinds of entanglement generated include polarization, time-energy, time-bin, and orbital angular momentum. The key ingredient for photon pair generation in nonlinear processes is described and discussed. Besides, we also introduce quantum frequency conversion for converting a single photon from one wavelength to another wavelength, while keeping its quantum properties unchanged. Finally, we give a comprehensive conclusion and discussion about future perspectives for single photon generation and manipulation in nonlinear processes. This chapter will provide an overview about the status, current challenge, and future perspectives about single photon generation and processing in nonlinear processes.
... 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 nonclassical 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] . ...
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.
In Chap. 1, classical optical interferometry was discussed. In this chapter, we look at interference effects more closely. In particular, we wish to consider cases where the interference is inherently quantum, in the sense that it cannot be mimicked by classical optical fields obeying Maxwell’s equations. Essentially what we will find is that classical interference arises from single-photon interference: each photon interferes only with itself. For example, in the Young two-slit experiment, each photon has an amplitude to go through one slit and an amplitude to pass through the other. The interference arises because those two amplitudes interfere with each other for each photon individually. To have intrinsically quantum interference, it will be necessary to have two-photon interference (or more generally, multi-photon interference): a two-photon amplitude for a pair of photons will interfere with another amplitude for the same two-photon pair to take a different path.
Spin interferometry of the 4th order for independent polarized as well as unpolarized photons arriving simultaneously at a beam splitter and exhibiting spin correlation while leaving it, is formulated and discussed in the quantum approach. Beam splitter is recognized as a source of genuine singlet photon states. Also, typical nonclassical beating between photons taking part in the interference of the 4th order is given a polarization dependent explanation.
Chirped-pulse interferometry (CPI) captures the metrological advantages of quantum Hong-Ou-Mandel (HOM) interferometry in a completely classical system. Modified HOM interferometers are the basis for a number of seminal quantum-interference effects. Here, the corresponding modifications to CPI allow for the first observation of classical analogues to the HOM peak and quantum beating. They also allow a new classical technique for generating phase super-resolution exhibiting a coherence length dramatically longer than that of the laser light, analogous to increased two-photon coherence lengths in entangled states.
Franson's Bell experiment with energy-time entanglement [Phys. Rev. Lett. 62, 2205 (1989)] does not rule out all local hidden variable models. This defect can be exploited to compromise the security of Bell inequality-based quantum cryptography. We introduce a novel Bell experiment using genuine energy-time entanglement, based on a novel interferometer, which rules out all local hidden variable models. The scheme is feasible with actual technology.
We report the recovery of interference in an interferometer with path imbalance well beyond coherence length of the input field. This is achieved by direct amplitude measurement via homodyne detection.
Photon-pair sources are critical building blocks for photonic quantum systems. Leveraging Kerr nonlinearity and cavity-enhanced spontaneous four-wave mixing, chip-scale photon-pair sources can be created using microresonators built on photonic integrated circuit. For practical applications, a high microresonator quality factor Q is mandatory to magnify photon-pair sources’ brightness and reduce their linewidth. The former is proportional to Q4, while the latter is inversely proportional to Q. Here, we demonstrate an integrated, microresonator-based, narrowband photon-pair source. The integrated microresonator, made of silicon nitride and fabricated using a standard CMOS foundry process, features ultralow loss down to 0.03 dB/cm and intrinsic Q factor exceeding 107. The photon-pair source has brightness of 1.17×109 Hz/mW2/GHz and linewidth of 25.9 MHz, both of which are record values for silicon-photonics-based quantum light source. It further enables a heralded single-photon source with heralded second-order correlation gh(2)(0)=0.0037(5), as well as an energy-time entanglement source with a raw visibility of 0.973(9). Our work evidences the global potential of ultralow-loss integrated photonics to create novel quantum light sources and circuits, catalyzing efficient, compact, and robust interfaces to quantum communication and networks.
Franson interference can be used to test the nonlocal features of energy-time entanglement and has become a standard in quantum physics. However, most of the previous Franson interference experiments were demonstrated in the time domain, and the spectral properties of Franson interference have not been fully explored. Here, we theoretically and experimentally demonstrate spectrally resolved Franson interference using biphotons with different correlations, including positive correlation, negative correlation, and non-correlation. It is found that the joint spectral intensities of the biphotons can be modulated along both the signal and idler directions, which has potential applications in generating high-dimensional frequency entanglement and time-frequency grid states. This work may provide a new perspective for understanding the spectral-temporal properties of the Franson interferometer.
The entangled “measurement state” (MS), predicted by von Neumann to arise during quantum measurement, seems to display paradoxical properties such as multiple macroscopic outcomes. But analysis of interferometry experiments using entangled photon pairs shows that entangled states differ surprisingly from simple superposition states. Based on standard quantum theory, this paper shows that the MS (i) does not represent multiple detector readings but instead represents nonparadoxical multiple statistical correlations between system states and detector readings, (ii) implies that exactly one outcome actually occurs, and (iii) implies that when one outcome occurs, the other possible outcomes simultaneously collapse nonlocally. Point (iii) resolves an issue first raised in 1927 by Einstein who demonstrated that quantum theory requires instantaneous state collapse. This conundrum’s resolution requires nonlocal correlations, which from today’s perspective suggests the MS should be an entangled state. Thus, contrary to previous presumed proofs of the measurement problem’s insolubility, we find the MS to be the collapsed state and just what we expect upon measurement.
The visibility of the two-photon interference in the Franson interferometer serves as a measure of the energy-time entanglement of the photons. We propose to control the visibility of the interference in the second-order coherence function by implementing a coherent time-delayed feedback mechanism. Simulating the non-Markovian dynamics within the matrix product state framework, we find that the visibility for two photons emitted from a three-level system (3LS) in ladder configuration can be enhanced significantly for a wide range of parameters by decelerating the decay of the upper level of the 3LS.
We report the demonstration of a second-order interference experiment by use of thermal light emitted from a warm atomic ensemble in two spatially separated unbalanced Michelson interferometers (UMIs). This novel multipath correlation interference with thermal light has been theoretically proposed by Tamma [New J. Phys.18, 032002 (2016)NJOPFM1367-263010.1088/1367-2630/18/3/032002]. In our experiment, the bright thermal light used for second-order interference is superradiantly emitted via collective two-photon coherence in Doppler-broadened cascade-type Rb87 atoms. Owing to the long coherence time of the thermal light from the atomic ensemble, we observe its second-order interference in the two independent UMIs by means of time-resolved coincidence detection. The temporal waveforms of the interfering thermal light in the two spatially separated UMIs exhibit similarities with the temporal two-photon waveform of time–energy entangled photon pairs in Franson interferometry. Our results can contribute toward a better understanding of the relation between first- and second-order interferences that are at the heart of photonics-based quantum information science.
In this Letter, we propose a new approach to process high-dimensional quantum information encoded in a photon frequency domain. In contrast to previous approaches based on nonlinear optical processes, no active control of photon energy is required. Arbitrary unitary transformation and projection measurement can be realized with passive photonic circuits and time-resolving detection. A systematic circuit design for a quantum frequency comb with arbitrary size has been given. The criteria to verify quantum frequency correlation has been derived. By considering the practical condition of the detector’s finite response time, we show that high-fidelity operation can be readily realized with current device performance. This work will pave the way towards scalable and high-fidelity quantum information processing based on high-dimensional frequency encoding.
We have observed beating between the blue (488 nm) and the green (514.5 nm) lines of an argon ion laser by use of a fourth order interference technique. The method involves the use of a Mach-Zehnder interferometer with photoelectric coincidence detection. The observed (approximately) 30 fs period of the beat note is far shorter than the time resolution of the detectors.
Simultaneity in optical photon pairs parametric production, verifying quantum mechanical description of fluorescence
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.
An experiment has been carried out in which two pairs of light beams produced by down conversion in two nonlinear crystals driven by a common pump were mixed by two beam splitters, and the coincidence rate for simultaneous detections of mixed signal and idler photons was measured. It is found that the down-converted light carries information about the phase of the pump field through the entanglement of the down-converted photons with the vacuum.
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.
When signal and idler photons produced in the process of parametric down-conversion are mixed together and directed to two photodetectors that respond to nonoverlapping optical frequencies centered at omega1 and omega2, it is found that the joint probability of two-photon detection exhibits a modulation of the form cos(omega1-omega2)tau, where c(tau) is the path difference. The experimental results are well described by a simple quantum-mechanical analysis.
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.
An exposition is given of the fundamental ideas of the recently opened field of two-particle interferometry, which employs spatially separated, quantum mechanically entangled two-particle states. These ideas are illustrated by a realizable arrangement, in which four beams are selected from the output of a laser-pumped down-converting crystal, with two beams interferometrically combined at one locus and two at another. When phase shifters are placed in these beams, the coincident count rates at the two loci will oscillate as the phases are varied, but the single count rates will not.
The quantum-mechanical uncertainty in the position of a particle or the time of its emission is shown to produce observable effects that are inconsistent with any local hidden-variable theory. A new experimental test of local hidden-variable theories based on optical interference is proposed.