J G Rarity, P R Tapster, R Loudon
When a one-photon state is mixed with a (separate) weak coherent state at a beamsplitter the probability for detecting one photon in each beamsplitter output approaches zero due to destructive interference. We demonstrate this non-classical interference effect using pulse-gated single photons and weak mode-locked laser pulses.
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It is shown that the visibility of multi-photon interference for classical sources grows rapidly with the order of interference. For three-photon and four-photon interference of two coherent sources, the visibility can be as high as 81.9% and 94.4%, respectively, - much higher than the 'classical limit' of two-photon interference (50%). High-visibility three-photon and four-photon interference has been observed in experiment, for both coherent and pseudo-thermal light.
Interference of photons emerging from independent sources is essential for modern quantum information processing schemes, above all quantum repeaters and linear-optics quantum computers. We report an observation of non-classical interference of two single photons originating from two independent, separated sources, which were actively synchronized with an r.m.s. timing jitter of 260 fs. The resulting (two-photon) interference visibility was 83(+/-)4 %.
Interference between fully-independent faint laser sources over two 8.5-km full polarization-controlled fiber links was performed, with stable visibility of 47.8%, an essential step towards practical implementation of quantum communication protocols.
The nature of two-photon interference is a subject that has aroused renewed interest in recent years and is still under debate. In this paper we report the first observation of two-photon interference with independent pseudo-thermal sources in which sub-wavelength interference is observed. The phenomenon may be described in terms of the classical statistical distribution of the two sources and their optical transfer functions.
The extended Dirac's principle describes the interference between different particles as an effect of the multiparticle system with itself. In this paper we present a novel example, based on the detection of particles emitted in multimode states by independent sources, which illustrates in a simple way the necessity of extending the original Dirac's criterion.
Difference-phase (or Hanbury Brown - Twiss type) intensity interference of classical light is considered in higher orders in the intensity. It is shown that, while the visibility of sum-phase (NOON-type) interference for classical sources drops with the order of interference, the visibility of difference-phase interference has opposite behavior. For three-photon and four-photon interference of two coherent sources, the visibility can be as high as 81.8% and 94.4%, respectively. High-visibility three-photon and four-photon interference of space-time and polarization types has been observed in e…
We analyze the double slit interference of a mesoscopic particle. We calculate the visibility of the interference pattern, introduce a characteristic temperature that defines the onset to decoherence and scrutinize the conditions that must be satisfied for an interference experiment to be possible.
Classical optical interference experiments correspond to a measurement of the first-order correlation function of the electromagnetic field. The converse of this statement: experiments that measure the first order correlation functions do not distinguish between the quantum and classical theories of light, does not always hold. A counterexample is given.
We show that a thermal light random in transverse direction can perform subwavelength double slit interference in a joint-intensity measurement. This is the classical version of quantum lithography, and it can be explained with the correlation of rays instead of the entanglement of photons.
We show the experimental observation of the classical sub-wavelength double-slit interference with a pseudo-thermal light source. The experimental results are in agreement with the recent theoretical prediction shown in quant-ph/0404078 (to be appeared in Phys. Rev. A).
We propose to use multi-photon interferences from statistically independent light sources in combination with linear optical detection techniques to enhance the resolution in imaging. Experimental results with up to five independent thermal light sources confirm this approach to improve the spatial resolution. Since no involved quantum state preparation or detection is required the experiment can be considered an extension of the Hanbury Brown and Twiss experiment for spatial intensity correlations of order N>2.
A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For classical light, the photonic system realizes an optical analogue of coherent population trapping in the continuum encountered in atomic physics, where destructive interference between different light leakage channels leads to the appearance of a trapped state embedded in the continuum. For nonclassical light, two-photon interference effects are predicted, …
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical ligh…
We experimentally demonstrate the non-monotonic dependence of genuine many-particle interference signals on the particles' mutual distinguishability. Our theoretical analysis shows that such non-monotonicity is a generic feature of the quantum to classical transition in multiparticle correlation functions of more than two particles.
We report investigation on quantum discord in classical second-order interference. In particular, we theoretically show that a bipartite state with D = 0.311 of discord can be generated via classical second-order interference. We also experimentally verify the theory by obtaining D = 0.197 +- 0.060 of non-zero discord state. Together with the fact that non-classicalities originated from physical constraints and information theoretic perspectives are not equivalent, this result provides an insight to understand the nature of quantum discord.
We show in this Comment that the interpretation of experimental data as well as the theory presented in Atatüre et al. [Phys. Rev. Lett. 84, 618 (2000)] are incorrect and discuss why such a scheme cannot be used to "recover" high-visibility quantum interference.
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 dem…
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 i…
Experimental Characterization and Model Validation of Interference in Classical-QKD Coexistence Transmission
本文通过实验验证了经典QKD共存传输中干扰的模型，实现了对噪声估计的精确评估。
Hong-Ou-Mandel (HOM) interference between independent photon sources (HOMI-IPS) is the fundamental block for quantum information processing, such as quantum gate, Shor's algorithm, Boson sampling, etc. All the previous HOMI-IPS experiments were carried out in time-domain, however, the spectral information during the interference was lost, due to technical difficulties. Here, we investigate the HOMI-IPS in spectral domain using the recently developed fast fiber spectrometer, and demonstrate the spectral distribution during the HOM interference between two heralded single-photon sources, and two…
We carry out a numerical simulation about the occurrence of interference fringes in experiments where an initial Gaussian wave packet evolves inside a billiard domain with two slits on the boundary. Our simulation extends a previous work by Casati and Prosen and it is aimed to test their surprising conclusion that the fringes disappear in the experiments with fully chaotic billiards. According to the results found, we are led to reassess this remarkable effect of classical dynamics on quantum interference. Actually, we highlight another factor which acts on interference: a symmetry condition (…
It is well known that in classical optics, the visibility of interference, in a two-beam light interference, is related to the optical coherence of the two beams. A wave-particle duality relation can be derived using this mutual coherence. The issue of wave-particle duality in classical optics is analyzed here, in the more general context of multipath interference. New definitions of interference visibility and path distinguishability have been introduced, which lead to a duality relation for multipath interference. The visibility is shown to be related to a new multi-point optical coherence f…
We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a non-classical path. The Gouy phase differs for classical or non-classical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter $κ$ used to estimate non-classical path contribution in a nontrivial way shedding some light in the implementation of experiments to detect non-classical path contributions.
Hanbury Brown and Twiss interference of electrons in free space from independent needle tip sources
本研究以两个激光触发针尖为独立电子源实现费米子型Hanbury Brown and Twiss干涉，通过量子路径理论和半经典方法分析，证实泡利不相容原理的反聚束与库仑排斥效应可明确区分。
We demonstrate a Hong-Ou-Mandel interference between two independent, intrinsically pure, heralded single photons from spontaneous parametric down conversion (SPDC) at telecom wavelength. A visibility of $85.5\pm8.3%$ was achieved without using any bandpass filter. Thanks to the group-velocity-matched SPDC and superconducting nanowire single photon detectors (SNSPDs), the 4-fold coincidence counts are one order higher than that in the previous experiments. The combination of bright single photon sources and SNSPDs is a crucial step for future practical quantum info-communication systems at tel…
We experimentally demonstrated the Hong-Ou-Mandel (HOM) interference between two photons after visible-to-telecommunication wavelength conversion. In the experiment, we prepared a heralded single photon by using spontaneous parametric down-conversion and the other photon from a weak laser source at 780 nm. We converted the wavelength of both photons to the telecommunication wavelength of 1522 nm by using difference-frequency generation in a periodically-poled lithium niobate, and then observed the HOM interference between the photons. The observed visibility is $0.76\pm 0.12$ which clearly sho…
Quantum superposition is the heart of quantum mechanics as mentioned by Dirac and Feynman. In an interferometric system, single photon self-interference has been intensively studied over the last several decades in both quantum and classical regimes. In Born rule tests, the Sorkin parameter indicates the maximum number of possible quantum superposition allowed to the input photons entering an interferometer, where multi-photon interference fringe is equivalent to that of a classical version by a laser. Here, an attenuated laser light in a quantum regime is investigated for self-interference in…
We elucidate generally the interference of independent Bose fields in view of the conditional probability for the particle number measurements, and clarify its relation to the source number statistics. Despite lack of intrinsic phases, the interference phase can be inferred from the particle number registered at one detector by using the classical mean fields. If the conditional number distributions for the other detectors, given the outcome of the first detector, exhibit sufficiently narrow peaks around the values specified by the estimated phases, the mean field description is valid in a sin…
The experimental study of the second-order interference with fermions is much less than the one with bosons since it is much more difficult to do experiments with fermions than with photons. Based on the conclusion that the behavior of two identical classical particles has exactly half fermionic and half bosonic characteristics (PRA \textbf{88}, 012130 (2013)), we have studied the second-order interference of fermions via the second-order interference of photons in Hanbury Brown-Twiss and Hong-Ou-Mandel interferometers, respectively. The experimental results are consistent with the theoretical…
In this paper we will be concerned with the explanation of the interference and diffraction patterns observed as an outcome of the Young double slit experiment. We will show that such explanation may be given {\it only} in terms of a corpuscular theory, which has been our approach since the first paper of this series. This explanation will be accomplished with an extension we make here of the domain of applicability of the Born-Sommerfeld rules that we derived in paper XI of this series.
Since the introduction of the decoy-state technique, phase-randomised weak coherent light pulses have been the key to increase the practicality of quantum-based communications. Their ultra-fast generation was accomplished via compact gain-switched (GS) lasers, leading to high key rates in quantum key distribution (QKD). Recently, the question arose of whether the same laser could be employed to achieve high-speed measurement-device-independent-QKD, a scheme that promises long-haul quantum communications immune to all detector attacks. For that, a challenging highvisibility interference between…
We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters and photodetectors. Our model enables us to simulate a quantum random walk with use of the wave nature of classical light fields. Furthermore, the proposed set-up allows the analysis of the effects of decoherence. The transition from a pure mean photon-number distribution to a classical one is studied varying the decoherence parameters.
Reflection of a microscopic particle from a mesoscopic/macroscopic `mirror' generates two-body correlated interference from the incident and reflected particle substates and their associated mirror substates. The microscopic momentum exchanged generates two mirror substates which interfere to produce fringes which do not vanish as the mirror mass increases. The small displacement between these mirror states can yield negligible environmental decoherence times. Mirror coherence lengths impose constraints on the extent of this interference, which are mitigated using interference of the two-body …
High visibility on-chip quantum interference among indistinguishable single-photons from multiples sources is a key prerequisite for integrated linear optical quantum computing. Resonant enhancement in micro-ring resonators naturally enables brighter, purer and more indistinguishable single-photon production without any tight spectral filtering. The indistinguishability of heralded single-photons from multiple micro-ring resonators has not been measured in any photonic platform. Here, we report on-chip indistinguishability measurements of heralded single-photons generated from independent micr…
We have observed high-contrast matter wave interference between 30 Bose-Einstein condensates with uncorrelated phases. Interference patterns were observed after independent condensates were released from a one-dimensional optical lattice and allowed to expand and overlap. This initially surprising phenomenon is explained with a simple theoretical model which generalizes the analysis of the interference of two independent condensates.
We discuss the interference in the two-particle distribution of the electrons emitted from two independent superconductors. It is clarified that, while the interference appearing in the antibunching correlation is due to the Hanbury Brown and Twiss effect, that in the positive correlation due to superconductivity is intrinsically different and is nothing but the first-order interference of Cooper pairs emitted from different sources. This is the equivalent of the interference of two independent Bose-Einstein condensates.
Improving quantum interference visibility between independent sources by enhancing the purity of correlated photon pairs
通过提高相关光子对的纯度，研究提高了独立光源间的量子干涉可见度，并实现了更高的三重巧合率，以增强多光子时间槽GHZ态的生成效率。
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We consider systematic unitary errors, random unitary errors, and decoherence processes. We show that unitary errors which destroy the interference destroy the efficiency of the algorithm, too. However, unitary errors may also create useless additional interference. In such a case the total amount of interference can increase, while the efficiency of the quantum…
Advances in quantum computing are a rapidly growing threat towards modern cryptography. Quantum key distribution (QKD) provides long-term security without assuming the computational power of an adversary. However, inconsistencies between theory and experiment have raised questions in terms of real-world security, while large and power-hungry commercial systems have slowed wide-scale adoption. Measurement-device-independent QKD (MDI-QKD) provides a method of sharing secret keys that removes all possible detector side-channel attacks which drastically improves security claims. In this letter, we…
Hong-Ou-Mandel interferometers are valuable tools in many Quantum Information and Quantum Optics applications that require photon indistinguishability. The theoretical limit for the Hong-Ou-Mandel visibility is 0.5 for indistinguishable weak coherent photon states, but several device imperfections may hinder achieving this value experimentally. In this work, we examine the dependence of the interference visibility on various factors, including (i) detector side imperfections due to after-pulses, (ii) mismatches in the intensities and states of polarization of the input signals, and (iii) the o…
Hong-Ou-Mandel interference of polarization qubits stored in independent room-temperature quantum memories
本文研究了室温量子存储器中偏振量子比特的Hong-Ou-Mandel干涉，实现了43%的HOM可见度，为大规模存储器辅助量子网络奠定基础。
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. This interference is a direct result of quantum exchange statistics, however, it is observed only in the joint probability to find the particles in two separated detectors. Here we report the first observation of such interference fringes between two independent and non-interacting electrons in an interferometer proposed by Yurke et al. and Samuelsson et al. Our experiment resembles the "Hanbury Brown and Twiss" (HBT) e…
We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added coherent sources, experimentally investigated recently by Zavatta et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our investigations is the visibility of the corresponding photon-photon correlation function. We present explicit results on the violations of the Cauchy-Schwarz inequality - which is a measure of nonclassicality - as well as of …
We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum random walk along with the usual interference in any such walk on any graph, closed or otherwise. We find that the quantum walker remains localized in comparison to the classical one, even in the absence of disorder, a phenomenon that is potentially attributable to the additional interference in the quantum case. This is to be contrasted with the situation on ope…
We investigate the quantum interference effects in two types of matter-wave mixing experiments: one with initial matter waves prepared in independent Fock states (type I) and the other with each individual particle prepared in a same coherent superposition of states (type II). In the type I experiment, a symmetric wavefunction of bosons leads to constructive quantum interference and shows final state stimulation, while an anti-symmetric wavefunction of fermions results in destructive quantum interference and inhibited matter wave mixing. In the type II experiment, a coherent superposition stat…
The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and non-locality -- local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and non-local features of the Aharonov-Bohm effect can be manifested in a classical model that incorporates random noise. The model also suggests new types of multi-particle topological non-local effects which have…
Quantum states can in a sense be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some feature of quantum states that classical probability distributions lack. One such feature is interference. We quantify interference and show that there can be no quantum speedup due to a small number of operations incapable of generating large amounts of interference (although large numbers of such operations can in fact lead to quantum speedup). Low-interfe…
The population decay due to a small opening in an otherwise closed cavity supporting chaotic classical dynamics displays a quantum correction on top of the classical exponential form, a pure manifestation of quantum coherence that acquires a universal form and can be explained by path interference. Being coherent, such enhancement is prone to decoherence effects due to the coupling of the system to an external environment. We study this interplay between incoherent and coherent quantum corrections to decay by evaluating, within a Caldeira-Legget scenario, off-diagonal contributions to the deco…
By analyzing the first-order interference of two independent thermal light beams with both classical and quantum theories, we conclude that it is impossible to observe the transient first-order interference pattern by superposing two independent thermal light beams even if the degeneracy parameter of thermal light is much greater than one. The result suggests that the classical model of thermal light field within the coherence time may not be the same as the one of laser light field within the coherence time.
Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. The exact quantum mechanical intensity distribution, as well as the corresponding trajectory distribution and the velocity field of a Gaussian wave packet are therewith computed. We utilize no quantum mechanics, but only familiar simulation techniques for diffusion, e.g., finite differences or coupled map lattices (CML).
The versatility of silicon photonic integrated circuits has led to a widespread usage of this platform for quantum information based applications, including Quantum Key Distribution (QKD). However, the integration of simple high repetition rate photon sources is yet to be achieved. The use of weak-coherent pulses (WCPs) could represent a viable solution. For example, Measurement Device Independent QKD (MDI-QKD) envisions the use of WCPs to distill a secret key immune to detector side channel attacks at large distances. Thus, the integration of III-V lasers on silicon waveguides is an interesti…
Single photon interference and quantum-classical phase transition with spontaneous superposition breaking
研究单光子与照相底片的量子动力学相互作用，揭示量子-经典相变及自发叠加破缺机制，探讨其在物理多个领域中的应用。
The second-order spatial and temporal interference patterns with two independent single-mode He-Ne lasers are observed in a Hong-Ou-Mandel interferometer. Two-photon interference in Feynman's path integral theory is employed to interpret the experimental results. The conditions to observe the second-order interference pattern with two independent single-mode continuous wave lasers are discussed. It is concluded that two-photon interference exists for not only identical photons, but also photons with different spectrums if the detection system can not distinguish them in principle. The second-o…
When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because the two possible paths where the photons leave in different output ports interfere destructively. This effect was first observed in parametric downconversion by Hong, Ou and Mandel, and then with single photons produced one after the other by the same quantum emitter. With the recent development of quantum information, a lot of attention has been devoted to this coalesce…
We propose a new interferometric setup which displays a completely destructive generalized N-photon Hong-Ou-Mandel interference. The key property of this scheme is that is does not require any optical elements like beam splitters or integrated waveguide structures. The interference is intrinsically produced by the evolution of N photons in free space when emitted by N identical statistically independent single photon sources and measured by N detectors in the far field. In this sense the setup is a most simple and natural implementation of the Hong-Ou-Mandel interference effect, i.e., of a com…
Two-photon interference with independent classical sources, in which superposition of two indistinguishable two-photon paths plays a key role, is of limited visibility of interference fringes with a maximum value of 50%. By using a random-phase grating to modulate the wavefront of a coherent light, we introduce superposition of multiple indistinguishable two-photon paths, which enhances the two-photon interference effect with a signature of visibility exceeding 50%. The result shows the importance of phase control in the control of high-order coherence of classical light.
Interference between two completely independent photons lies at the heart of many photonic quantum information applications such as quantum repeaters, teleportation, and quantum key distribution. Here, we report the observation of Hong-Ou-Mandel (HOM) interference with two independent continuous-wave coherent light sources that are neither synchronized nor share any common reference. To prepare highly indistinguishable photons from two independent laser sources, we employ high-precision frequency-stabilization techniques using the 5S1/2(F=3)-5P1/2(F'=3) transition line of 85Rb atoms. We succes…
It has often been remarked that single-photon interference experiments, however complicated, seem to behave very much in the same way as those performed in the classical regime, using the field generated by a laser. This observation has the status of being `well-known to those who know it', but perhaps mysterious to others. We discuss the reasons underlying the similarity and also some of the limitations of this simple idea.
The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a broader class of processes, which can be formulated as information-processing tasks, providing a clear cut between classical, quantum and higher-order theories. The tasks involve two parties and communication between them with the goal of winning certain parity games. We show that the order of interference is in one-to-one correspondence with the parity order …
Classical linear wave superposition produces the appearance of interference. This observation can be interpreted in two equivalent ways: one can assume that interference is an illusion because input components remain unperturbed, or that interference is real and input components undergo energy redistribution. Both interpretations entail the same observable consequences at the macroscopic level, but the first approach is considerably more popular. This preference was established before the emergence of quantum mechanics. Unfortunately, it requires a non-classical underlying mechanism and fails …
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