Dirac has written "Each photon then interferes only with itself. Interference between two different photons never occurs." Indeed, a practical definition is that "classical" optics consists of phenomena due to the interference of photons only with themselves. However, photons obey Bose statistics which implies a ``nonclassical'' tendency for them to ``bunch''. For a simple example of nonclassical optical behavior, we consider two pulses of photons of a single frequency that are simultaneously incident on two sides of a lossless, 50:50 beam splitter.
The Copenhagen interpretation has been long-lasted, whose core concepts are in the Heisenberg's uncertainty principle and nonlocal correlation of EPR. The second-order anticorrelation on a beam splitter represents these phenomena where it cannot be achieved classically. Here, the anticorrelation of nonclassicality on a beam splitter is interpreted in a purely coherence manner. Unlike a common belief in a particle nature of photons, the anticorrelation roots in pure wave nature of coherence optics, where quantum superposition between two input fields plays a key role. This interpretation may in…
Born rule is key to understanding quantum mechanics based on the probability amplitude for the measurement process of a physical quantity. Based on a typical particle nature of a photon, the quantum feature of photon bunching on a beam splitter between two output photons can be explained by Born rule even without clear definition of the relative phase between two input photons. Unlike conventional understanding on this matter, known as the Hong-Ou-Mandel effect, here, we present a new interpretation based on the wave nature of a photon, where the quantum feature of photon bunching is explained…
One of the most striking quantum phenomena is photon bunching resulting from coincidently impinging two-indistinguishable photons on a beam splitter (BS) from two different input ports. Such a nonclassical feature has also been observed even between two independent light sources through either coherence optics resulting in phase locking or post-selected measurements such as quantum beating-based gating. Recently, BS physics regarding quantum features has been discussed using pure coherence optics based on phase basis superposition of the BS. Here, we experimentally demonstrate coherent photon …
The bunching of two single photons on a beam-splitter is a fundamental quantum effect, first observed by Hong, Ou and Mandel. It is a unique interference effect that relies only on the photons' indistinguishability and not on their relative phase. We generalize this effect by demonstrating the bunching of two Bell states, created in two passes of a nonlinear crystal, each composed of two photons. When the two Bell states are indistinguishable, phase insensitive destructive interference prevents the outcome of four-fold coincidence between the four spatial-polarization modes. For certain combin…
Interference of single-photon wave packets at a beam splitter usually leads to an anticorrelation of the light intensity in the two output ports of the beam splitter. The effect may be regarded as ``bunching'' of the photons at the beam splitter and has widely been interpreted as a result of quantum mechanical interference between the probability amplitudes of indistinguishable bosonic particles. Here we show that when the wave packets are sufficiently distorted, then the opposite behaviour is observed, i.e., simultaneous clicks of the photodetectors in the two output ports are favoured, which…
To show the feasibility of a long distance partial Bell-State measurement, a Hong-Ou-Mandel experiment with coherent photons is reported. Pairs of degenerate photons at telecom wavelength are created by parametric down conversion in a periodically poled lithium niobate waveguide. The photon pairs are separated in a beam-splitter and transmitted via two fibers of 25km. The wave-packets are relatively delayed and recombined on a second beam-splitter, forming a large Mach-Zehnder interferometer. Coincidence counts between the photons at the two output modes are registered. The main challenge cons…
One of the most fundamental quantum features is the two-photon intensity correlation on a beam splitter, resulting in photon bunching into either output port. According to the conventional understanding of quantum mechanics, the origin of photon bunching on a beam splitter is in the indistinguishable characteristics between coincident photons, resulting in destructive quantum interference even without a clear definition of phase information of the paired photons. Here, a completely different approach is presented for the same quantum feature, where a strong mutual phase dependency is the essen…
The second order correlation function is traditionally used to characterize the photon statistics and to distinguish between classical and quantum states of light. In this article we study a simple setup offering the possibility to generate strong anti-bunched light. This is achieved by mixing on a beam splitter a coherent state with a state with a non-negative Wigner function, such as squeezed states or weak Schrödinger cat states. We elucidate the interference mechanism generating such strong antibunching and relate it to unconventionnal photon blockade. We also detail how this effect can be…
It is emphasized that the bunching parameter $β=P_B/P_D$ , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between the initial wavefunctions. This ratio is equal to $β=2/(1+I^2)$ , where $I$ is the overlap integral between the initial wavefunctions. That is, only when the initial wavefunctions are orthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1, when the two wavefunctions are identical. This simple equation explains the experimental evi…
We investigate the spin entanglement in the superconductor-quantum dot system proposed by Recher, Sukhorukov and Loss, coupling it to an electronic beam-splitter. The superconductor-quantum dot entangler and the beam-splitter are treated within a unified framework and the entanglement is detected via current correlations. The state emitted by the entangler is found to be a linear superposition of non-local spin-singlets at different energies, a spin-entangled two-particle wavepacket. Colliding the two electrons in the beam-splitter, the singlet spin-state gives rise to a bunching behavior, det…
Programmable Hong--Ou--Mandel interference in a giant-atom beam splitter
Center for Theoretical Physics & School of Physics and Optoelectronic Engineering, Hainan University（海南大学理论物理中心与物理光电工程学院）；Department of Microtechnology and Nanoscience, Chalmers University of Technology（查尔姆斯理工大学微技术与纳米科学系）
Australian Research Council Centre of Excellence for Engineered Quantum Systems（澳大利亚研究委员会工程量子系统卓越中心）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）；Silux Technologies Co., Ltd.（希鲁克斯科技有限公司）；QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（香港大学计算与数据科学学院量子信息计算倡议）
Correlations of detection events in photodetectors placed at the opposite sides of a beam splitter are studied in the frame of classical probability theory. It is assumed that there is always one photon present during one elementary measurement (one measurement act). Due to the conservation of energy, thereis a strict anticorrelation in detections in one elementary experiment, because the photon cannot excite both of the detectors at the same time. It is explicitely shown in several examples that the bunching or anti-bunching of the counts in serieses of elementary single-photon experiments ar…
Loss-induced anomalous generalized bunching in multiphoton interference
Graduate School of Engineering Science, The University of Osaka（大阪大学工程科学研究科）；Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）
Quantum entanglement generation is generally known to be impossible by any classical means. According to Poisson statistics, coherent photons are not considered quantum particles due to the bunching phenomenon. Recently, a coherence approach has been applied to interpret quantum features such as the Hong-Ou-Mandel (HOM) effect, Franson-type nonlocal correlation, and delayed-choice quantum eraser, where the quantum feature is due to basis-product superposition at the cost of 50 % photon loss. For this, it has been understood that a fixed sum-phase relation between paired photons is the bedrock …
The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thus argue that the presence of such nonlinearity would reduce the visibility in the standard HOM setup, offering some explanation for the diminution of the HOM visibility observed in many experiments. We u…
Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or anti-bunching. In presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al. recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multi-port beam splitters. Here we study the case in which $2^q$ particles (eith…
We observe the polarization squeezing in the mixture of a two mode squeezed vacuum and a simple coherent light through a linear polarization beam splitter. Squeezed vacuum not being squeezed in polarization, generates polarization squeezed light when superposed with coherent light. All the three Stokes parameters of the light produced on the output port of polarization beam splitter are found to be squeezed and squeezing factor also depends upon the parameters of coherent light.
Double-pair emission from type-II parametric down conversion results in a highly entangled 4-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and give a Bell theorem for a 4-photon test of local realistic hidden variable theories.
The aim of this work is to answer the question of how much quantum coherence a beam splitter is able to produce. To this end we consider as the variables under study both the amount of coherence of the input states as well as the beam splitter characteristics. We conclude that there is an optimal combination of these factors making the gain of coherence maximum. In addition, the two mode squeezed vacuum arises as the studied state most capable of gaining coherence when passing through a beam splitter. These results are qualitatively equivalent for the the l1-norm of coherence and for the relat…
We derive a lower limit to the amount of absorptive loss present in passive linear optical devices such as a beam splitter. We choose a particularly simple beam splitter geometry, a single planar slab surrounded by vacuum, which already reveals the important features of the theory. It is shown that, using general causality requirements and statistical arguments, the lower bound depends on the frequency of the incident light and the transverse resonance frequency of a suitably chosen single-resonance model only. For symmetric beam splitters and reasonable assumptions on the resonance frequency …
Light routing and manipulation are important aspects of integrated optics. They essentially rely on beam splitters which are at the heart of interferometric setups and active routing. The most common implementations of beam splitters suffer either from strong dispersive response (directional couplers) or tight fabrication tolerances (multimode interference couplers). In this paper we fabricate a robust and simple broadband integrated beam splitter based on lithium niobate with a splitting ratio achromatic over more than 130 nm. Our architecture is based on spatial adiabatic passage, a techniqu…
Time resolution at the quantum limit of two incoherent sources based on frequency resolved two-photon-interference
University of Portsmouth（朴茨茅斯大学）；School of Mathematics and Physics, University of Portsmouth（朴茨茅斯大学数学与物理学院）；Quantum Science and Technology Hub, University of Portsmouth（朴茨茅斯大学量子科学与技术中心）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）
We report on two optical realizations of the $1 \to 2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering that enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filt…
We study a general theory on the interference of a two-photon wavepacket in a beam splitter. The theory is carried out in the Schrödinger picture so that the quantum nature of the two-photon interference is explicitly presented. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the manners of two-photon interference which are distinguished according to increasing and decreasing the coincidence probability for the absence of interference. However, two-photon entanglement can be witnessed by the interference manner. We demonstrate …
Semi-transparent mirrors are standard elements in light optics for splitting light beams or creating two versions of the same image. Such mirrors do not exist in electron optics, although they could be beneficial in existing techniques such as electron interferometry and holography and enable novel electron imaging and spectroscopy techniques. We propose a design for an electron beam splitter using the concept of quantum interaction-free measurement (IFM). The design combines an electron resonator with a weak phase grating. Fast switching gates allow electrons to enter and exit the resonator. …
Unconditional security of quantum key distribution protocol can be guaranteed by the basic property of quantum mechanics. Unfortunately, the practical quantum key distribution system always have some imperfections, and the practical system may be attacked if the imperfection can be controlled by the eavesdropper Eve. Applying the fatal security loophole introduced by the imperfect beam splitter's wavelength dependent optical property, we propose wavelength-dependent attacking model, which can be applied to almost all practical quantum key distribution systems with the passive state modulation …
The indistinguishability of successively generated photons from a single quantum emitter is most commonly measured using two-photon interference at a beam splitter. Whilst for sources excited in the pulsed regime the measured bunching of photons reflects the full wavepacket indistinguishability of the emitted photons, for continuous wave (cw) excitation the inevitable dependence on detector timing resolution and driving strength obscures the underlying photon interference process. Here we derive a method to extract the photon indistinguishability from cw measurements by considering the relevan…
Preparation of entangled states of photons are useful for quantum computing and communication. In this paper, we present a simplistic protocol of entanglement generation using beam splitters with suitable reflectivity. The photons in an initial state with fully classical probability distribution pass through an optical network, made up of sequential beam splitters and are prepared in maximally entangled states. We also present the detailed theoretical analysis of entangled state generation, for an arbitrary number of photons, fed through the input ports of the beam splitters with equal probabi…
The Hong-Ou-Mandel effect lies at the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only a few works have considered polarization-frequency interaction within the interferometer. In this paper, we fill this gap. Our system of interest is a general biphoton polarization state that experiences effective dephasing noise by becoming entangled with the same photons' frequency state, as the photons propagate through birefringent media. The photons then meet at a beam splitter, where e…
Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entan…
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is squeezed. We demonstrate experimentally that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to but not enta…
We theoretically investigate quantum interference of two single photons at a lossy asymmetric beam splitter, the most general passive 2$\times$2 optical circuit. The losses in the circuit result in a non-unitary scattering matrix with a non-trivial set of constraints on the elements of the scattering matrix. Our analysis using the noise operator formalism shows that the loss allows tunability of quantum interference to an extent not possible with a lossless beam splitter. Our theoretical studies support the experimental demonstrations of programmable quantum interference in highly multimodal s…
We propose a scheme to split a cloud of cold non-interacting neutral atoms based on their dipole interaction with a single structured light beam which exhibits parabolic cylindrical symmetry. Using semiclassical numerical simulations, we establish a direct relationship between the general properties of the light beam and the relevant geometric and kinematic properties acquired by the atomic cloud as its passes through the beam.
We investigate two-photon quantum interference in an opaque scattering medium that intrinsically supports $10^6$ transmission channels. By adaptive spatial phase-modulation of the incident wavefronts, the photons are directed at targeted speckle spots or output channels. From $10^3$ experimentally available coupled channels, we select two channels and enhance their transmission, to realize the equivalent of a fully programmable $2\times2$ beam splitter. By sending pairs of single photons from a parametric down-conversion source through the opaque scattering medium, we observe two-photon quantu…
Over the last several decades, quantum entanglement has been intensively studied for potential applications in quantum information science. The Hong-Ou-Mandel (HOM) dip is the most important test tool for direct proof of entanglement between paired photons, whose coincidence detection results in anticorrelation due to photon bunching on a beam splitter. Although anticorrelation is due to destructive quantum interference between paired photons, a wavelength-sensitive interference fringe has never been observed in any HOM-type experiments. Here, a typical HOM dip is investigated for entangled ph…
The prototype of a quantum random number generator is a single photon which impinges onto a beam splitter and is then detected by single photon detectors at one of the two output paths. Prior to detection, the photon is in a quantum mechanical superposition state of the two possible outcomes with - ideally - equal amplitudes until its position is determined by measurement. When the two output modes are observed by a single photon detector, the generated clicks can be interpreted as ones and zeros - and a raw random bit stream is obtained. Here we implement such a random bit generator based on …
The uncanny ability of multiple particles to interfere with one another is one of the core principles of quantum mechanics, and serves as foundation for quantum information processing. In particular, the interplay of constructive and destructive interference with the characteristic exchange statistics of indistinguishable particles give rise to the Hong-Ou-Mandel (HOM) effect, where the bunching of bosons can lead to a perfect suppression of two-particle coincidences between the output ports of a balanced beam splitter. Conversely, in the case of two fermions, anti-bunching can systematically …
We report on a novel and efficient source of polarization squeezing using a single pass through an optical fiber. Simply passing this Kerr squeezed beam through a carefully aligned lambda/2 waveplate and splitting it on a polarization beam splitter, we find polarization squeezing of up to 5.1 +/- 0.3 dB. The experimental setup allows for the direct measurement of the squeezing angle.
Quantum Beam Splitter as a Deterministic Entanglement Source: Exact Photon-Number Statistics, Hong-Ou-Mandel Interference, and von Neumann Entropy Scaling from Balanced Inputs
We address the interaction of two Gaussian states interferring at a beam splitter and analyze the correlations exhibited by the resulting bipartite system. We demonstrate that nonlocal correlations (entanglement) arise if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities and on the transmissivity of the beam splitter. Our result clarifies the role of squeezing as a prerequisite for entanglement and provide a tool to optimize the generation of entanglement by passive devices.
The group theoretical aspect of the description of passive lossless optical four-ports (beam splitters) is revisited. It is shown through an example, that this approach can be useful in understanding interferometric schemes where a low number of photons interfere. The formalism is extended to passive lossless optical six-ports, their SU(3)-theory is outlined.
The two-photon Hong-Ou-Mandel (HOM) interference is a pure quantum effect which indicates the degree of indistinguishability of photons. The four-photon HOM interference exhibits richer dynamics in comparison to the two-photon interference and simultaneously is more sensitive to the input photon states. We demonstrate theoretically and experimentally an explicit dependency of the four-photon interference to the number of temporal modes, created in the process of parametric down-conversion. Moreover, we exploit the splitting ratio of the beam splitter to manipulate the interference between bunc…
Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic configurations can be constructed by linear combinations. In this presentation we discuss a formulation constructed in the general formalism of bosonic Fock space, in which the quantum excitation can be constructed directly on localized pulses of arbitrary shape. Although the two formulations are essentially equivalent, the direct formulation in terms of pulses has …
We present a study on two-particle indistinguishability and particle-species identification by introducing a Fisher-information (FI) approach---in which two particles pass through a two-wave mixing operation and the number of particles is counted in one of the output modes. In our study, we first show that FI can reproduce the Hong-Ou-Mandel (HOM) effect with two bosons or two fermions. In particular, it is found that even though bosons and fermions exhibit different physical behavior (i.e., "bunching" or "anti-bunching") due to their indistinguishability, the aspects of HOM-like dip are quant…
Beam-splitter-free, high-rate quantum key distribution inspired by intrinsic quantum mechanical spatial randomness of entangled photons
Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）；Indian Institute of Technology Dharwad（达瓦德印度理工学院）；Indian Institute of Science（印度科学学院）
We propose a new experiment employing two independent sources of spin correlated photon pairs. Two photons from different unpolarized sources each pass through a polarizer to a detector. Although their trajectories never mix or cross they exhibit 4th-order-interference-like correlations when the other two photons interfere on a beam splitter even when the latter two do not pass any polarizers at all. A wave packet calculation shows that the experiment permits a very discriminatory test of hidden variable theories.
We describe a multi-mode passive linear optical network which emulates the two-photon number statistics of a beam splitter, irrespective on where the two photons enter the network. This is done by firstly defining general properties that the generator of the network matrix must fulfil. We then show that the network's effective transmission coefficient can be freely set to replicate either the absence of coincidence counts (i.e. the Hong-Ou-Mandel dip), or a 100% coincidence rate, as well as all possible two-photon beam splitter statistics between these two extremal points. Finally, we demonstr…
Hong-Ou-Mandel (HOM) interference, the bunching of indistinguishable photons at a beam splitter, is a staple of quantum optics and lies at the heart of many quantum sensing approaches and recent optical quantum computers. Here, we report a full-field, scan-free, quantum imaging technique that exploits HOM interference to reconstruct the surface depth profile of transparent samples. We demonstrate the ability to retrieve images with micrometre-scale depth features with a photon flux as small as 7 photon pairs per frame. Using a single photon avalanche diode camera we measure both the bunched an…
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the…
Hong-Ou-Mandel interference of more than 10 indistinguishable atoms
Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)（德国航空航天中心）；Instituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (INO-CNR)（意大利国家光学研究所，国家研究委员会）；University of the Basque Country UPV/EHU（巴斯克大学）
Quantum Beam-Splitter Cooling and Thermometry in Large Trapped-Ion Crystals
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Center for Quantum Information, Communication and Computing, Indian Institute of Technology Madras（印度马德拉斯理工学院量子信息、通信与计算中心）
