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 combinations of the two Bell states, we demonstrate the opposite effect of anti-bunching. We relate this result to the number of distinguishable modes in parametric down-conversion.
The complementary principle of quantum mechanics relates qualitatively the visibility of quantum interference with path indistinguishability. Here we propose a scheme of constructive quantum interference involving superposition between an $N$-photon state and a single-photon state to characterize quantitatively the degree of temporal distinguishability of the $N$-photon state. This scheme is based on a generalized photon bunching effect. Such a scheme can be extended to other more general cases.
We report an interference experiment in which the two-photon entangled state interference cannot be pictured in terms of the overlap and bunching of two individual photons on a beamsplitter. We also demonstrate that two-photon interference, or photon bunching effect on a beamsplitter, does not occur if the two-photon Feynman amplitudes are distinguishable, even though individual photons do overlap on a beamsplitter. Therefore, two-photon interference cannot be viewed as interference of two individual photons, rather it should be viewed as two-photon or biphoton interfering with itself. The res…
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）
We propose a novel scheme to achieve two-photon super bunching of thermal light through multiple two-photon-path interference, in which two mutually first-order incoherent optical channels are introduced by inserting a modified Michelson interferometer into a traditional two-photon HBT interferometer, and the bunching peak-to-background ratio can reach 3 theoretically. Experimentally, the super bunching peak-to-background ratio was measured to be 2.4, much larger than the ratio 1.7 measured with the same thermal source in a traditional HBT interferometer. The peak-to-background ratio of two-ph…
Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behaviour. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether n independent imperfect single photons can ultimately bunch into the Fock state $|n \rangle$. We thereby introduce an experimental Fock-state bunching capability for…
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.
Quantum coupling between mechanical oscillators and atomic gases generating entanglement has been recently experimentally demonstrated using their subsequent interaction with light. The next step is to build a hybrid atom-mechanical quantum gate showing bosonic interference effects of single quanta in the atoms and oscillators. We propose an experimental test of Hong-Ou-Mandel interference between single phononic excitation and single collective excitation of atoms using the optical connection between them. A single optical pulse is sufficient to build a hybrid quantum-nondemolition gate to ob…
We demonstrate the effect of interference, similar to the Hong-Ou-Mandel effect, for two single-photon pulses by writing them sequentially inside a quantum memory cell in a tripod configuration.
The nonclassical effect of photon anti-bunching is observed in the mixed field of a narrow band two-photon source and a coherent field under certain condition. A variety of different features in photon statistics are found to be the consequence of a two-photon interference effect with dependence on the relative phase of the fields. Besides the anti-bunching effect, we find another one of the features to be also nonclassical. These features emphasize the importance of quantum entanglement.
Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is one of the key signatures of quantum light and is tied to sub-Poissonian photon number statistics. Recently, it has been reported that photon anti-bunching or conditional sub-Poissonian photon number statistics can be obtained via second-order interference of mutually incoherent weak lasers and heralding based on photon counting. Here, we report theoretical analysis on the limits of manipulating conditional photon statistics via interference of weak lasers. It is shown that conditional photon number statistics can become…
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…
Progress in the reliable preparation, coherent propagation and efficient detection of many-body states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of many-boson and many-fermion interference required for the description of current experiments and for the understanding of novel approaches to quantum computing. The field is motivated via the two-particle case, for which the uncorrelated, classical dynamics of distinguishable particles is compared to the quantum behaviour of identical bosons and fermions. B…
In quantum mechanics, photons are bosons -- there is no restriction on the number of them that occupy the same quantum state, so many of them can bunch together, and this is well known as photon bunching effect. However, photon bunching and multiphoton interference of bunched photons have never been directly observed from a broadband thermal chaotic light source. Nevertheless, it has been known that the interference intensity of a number N of bunched photons oscillates with a wavelength of N times shorter than the wavelength of the constituent single photons, which should be observable in Four…
In this theoretical study we demonstrate that entangled states are able to significantly extend the functionality of Hong-Ou-Mandel (HOM) interferometers. By generating a coherent superposition of parametric-down-conversion photons and spatial entanglement in the input channel, the coincidence probability measured at the output changes from a typical HOM-type dip (photon bunching) into much richer patterns including an anti-bunching peak and rapid oscillation fringes with twice the optical frequency. The considered system should be realizable on a single chip using current waveguide technology…
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 obtain photon statistics by using a quantum jump approach tailored to a system in which one or two qubits are coupled to a one-dimensional waveguide. Photons confined in the waveguide have strong interference effects, which are shown to play a vital role in quantum jumps and photon statistics. For a single qubit, for instance, bunching of transmitted photons is heralded by a jump that increases the qubit population. We show that the distribution and correlations of waiting times offer a clearer and more precise characterization of photon bunching and antibunching. Further, the waiting times…
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）
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…
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…
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…
Two-photon anti-bunching at a beamsplitter is only possible if the photons are entangled in a specific state, anti-symmetric in the spatial modes. Thus, observation of anti-bunching is an indication of entanglement in a degree of freedom which might not be easily accessible in an experiment. We experimentally demonstrate this concept in the case of the interference of two frequency entangled photons with continuous frequency detunings. The principle of anti-symmetrisation of the spatial part of a wavefunction and subsequent detection of hidden entanglement via anti-bunching at a beamsplitter m…
Interference and diffraction of two-identical-particles are considered in the context of open quantum systems. This theoretical study is carried out within two approaches, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett (CL) one where a master equation for the reduced density matrix is used under the presence of dissipation and temperature of the environment. Two simple but very illustrative examples are considered, diffraction by a single and two Gaussian slits by analyzing the mean square separation between particles, single-particle probability …
Photon correlations are investigated for a single laser-excited ion trapped in front of a mirror. Varying the relative distance between the ion and the mirror, photon correlation statistics can be tuned smoothly from an antibunching minimum to a bunching-like maximum. Our analysis concerns the non-Markovian regime of the ion-mirror interaction and reveals the field establishment in a half-cavity interferometer.
A solid state device to discriminate all the four Bell states is proposed. The device is composed of controlled absorption crystals, rotators, and retarders. The controlled absorption, where the state of one photon affects the absorption of the other photon, is realized by two photon absorption in a cubic crystal. The controlled absorption crystal detects a particular Bell state and is transparent for the other Bell states. The rotators and retarders transform a Bell state to another. This device may solve the problems in the early quantum teleportation experiments in photon polarization state…
Although quantum physics is well understood in inertial reference frames (flat spacetime), a current challenge is the search for experimental evidence of non-trivial or unexpected behaviour of quantum systems in non-inertial frames. Here, we present a novel test of quantum mechanics in a non-inertial reference frame: we consider Hong-Ou-Mandel (HOM) interference on a rotating platform and study the effect of uniform rotation on the distinguishability of the photons. Both theory and experiments show that the rotational motion induces a relative delay in the photon arrival times at the exit beam…
In this paper, we propose a protocol for complete Bell-state analysis for two superconducting-quantum-interference-device qubits. The Bell-state analysis could be completed by using a sequence of microwave pulses designed by the transition- less tracking algorithm, which is an useful method in the technique of shortcut to adiabaticity. After the whole process, the information for distinguishing four Bell states will be encoded on two auxiliary qubits, while the Bell states keep unchanged. One can read out the information by detecting the auxiliary qubits. Thus the Bell-state analysis is nondes…
Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The exiting researches on two-photon interference were mainly limited in one degree of freedom (DoF), hence it is still a challenge to realize the quantum interference in multiple DoFs. Here we demonstrate the HOM interference between two hyper-entangled photons in two DoFs of polarization and orbital angular momentum (OAM) for all the sixteen hyper-entangled Bell states. We observe hyper-entangled two-photon interference with bunching effect for ten symmetric states (nine Boson-Boson st…
We report novel interference effects in wave packet scattering of identical particles incident on the same side of a resonant barrier, different from those observed in Hong-Ou-Mandel experiments. These include significant changes in the mean number of transmissions and full counting statistics, as well as "bunching" and "anti-bunching" effects in the all-particles transmission channel. With several resonances involved, pseudo-resonant driving of the two-level system in the barrier, may result in sharp enhancement of scattering probabilities for certain values of temporal delay between the part…
Bell states are a fundamental resource in photonic quantum information processing. These states have been generated successfully in many photonic degrees of freedom. Their manipulation, however, in the momentum space remains challenging. Here, we present a scheme for engineering the symmetry of two-photon states entangled in the transverse momentum degree of freedom through the use of a spatially variable phase object. We demonstrate how a Hong-Ou-Mandel interferometer must be constructed to verify the symmetry in momentum entanglement via photon "bunching"/"anti-bunching" observation. We also…
A number of recent interference experiments involving multiple photons are reviewed. These experiments include generalized photon bunching effects, generalized Hong-Ou-Mandel interference effects and multi-photon interferometry for demonstrations of multi-photon de Broglie wavelength. The multi-photon states used in these experiments are from two pairs of photons in parametric down-conversion. We find that the size of the interference effect in these experiments, characterized by the visibility of interference pattern, is governed by the degree of distinguishability among different pairs of ph…
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…
We propose an all-optical scheme to control the photon statistics using hybrid quantum plasmonic system. With the aid of dressed states assisted quantum interference effects, it is shown that the photon correlations of a signal field can be continuously modulated from bunching to antibunching under the control of a pump field. Apart from the exact multimode model, a single-mode model and an analytical treatment are also provided to help us identify the roles of multimode coupling and quantum interference between probability amplitudes. The proposed scheme, in contrast to the cavity quantum ele…
Many quantum information protocols require a Bell-state measurement of entangled systems. Most optical Bell-state measurements utilize two-photon interference at a beam splitter. By creating polarization-entangled photons with spontaneous parametric down-conversion using a first-order Hermite-Gaussian pump beam, we invert the usual interference behavior and perform an incomplete Bell-state measurement in the coincidence basis. We discuss the possibility of a complete Bell-state measurement in the coincidence basis using hyperentangled states [Phys. Rev. A, \textbf{58}, R2623 (1998)].
We numerically show that time delayed coherent feedback controls the statistical output characteristics of driven quantum emitters. Quantum feedback allows to enhance or suppress a wide range of classical and nonclassical features of the emitted quantum light. As exemplary quantum system, we use a pumped cavity containing two emitters. By applying phase-selective feedback, we demonstrate that photon antibunching and bunching can be increased in orders of magnitude due to intrinsically and externally controllabe quantum interferences. Our modelling is based on a fully non-Markovian quantum simu…
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）
Quality of individual photons and their ability to interfere is traditionally tested by measuring the Hong-Ou-Mandel photon bunching effect. However, this phase insensitive measurement only tests the particle aspect of the quantum interference. Motivated by these limitations, we formulate a witness capable of recognizing both the quality and the coherence of two photons from a single set of measurements. We exploit the conditional nonclassical squeezing which is sensitive to both the quality of the single photons and their indistinguishability and we show that it can be used to irectly reveal …
The implementation of quantum repeaters needed for long-distance quantum communication requires the generation of quantum entanglement distributed among the elementary links. These entanglements must be swapped among the quantum repeaters through Bell-state measurements. This study aims to improve the entanglement generation rate by frequency multiplexing the Bell-state measurements. As a preliminary step of the frequency-multiplexed Bell-state measurements, three frequency modes are mapped to a temporal mode by an atomic frequency comb prepared in $\mathrm{Pr^{3+}}$ ion-doped $\mathrm{Y_2SiO_…
We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: Dipolar forces and atomic saturability, which ranges from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for two-polariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mis…
Based on the Bell theorem, it has been believed that a theoretical computation of the Bell correlation requires explicit use of an entangled state. Such a physical superposition of light waves occurs in the downconverter sources used in Bell experiments. However, this physical superposition is eliminated by wave propagation to spatially separated detectors. Bell correlations must therefore result from local waves, and the source boundary conditions of their previously entangled state. In the present model, Bell correlations are computed from disentangled separated waves, boundary conditions of…
Bell state measurement (BSM) plays crucial roles in photonic quantum information processing. The standard linear optical BSM is based on Hong-Ou-Mandel interference where two photons meet and interfere at a beamsplitter (BS). However, a generalized two-photon interference is not based on photon-photon interaction, but interference between two-photon probability amplitudes. Therefore, it might be possible to implement BSM without interfering photons at a BS. Here, we investigate a linear optical BSM scheme which does not require two photon overlapping at a BS. By unleashing the two photon coexi…
We propose using an array of potential wells as an interferometer, in which the beam splitters are provided by tunneling during an appropriate time through the barrier between wells. This arrangement allows demonstration of generalized Hong-Ou-Mandel effects with multiple particles traversing one or several beam splitters. Other interferometer effects can occur, including a violation of the Bell-Clauser-Horne-Shimony-Holt form of the Bell inequality. With interactions, one sees various effects including so-called fermionization, collective tunneling, and self-trapping.
We theoretically generate nonclassical states from coherent state heralded by Knill-Laflamme-Milburn (KLM)-type SU(3) interference. Injecting a coherent state in signal mode and two single-photon sources in other two auxiliary modes of SU(3) interferometry, a broad class of useful nonclassical states are obtained in the output signal port after making two single-photon-counting measurements in the two output auxiliary modes. The nonclassical properties, in terms of anti-bunching effect and squeezing effect as well as the negativity of the Wigner function, are studied in detail by adjusting the…
A silicon quantum photonic circuit was proposed and demonstrated as an integrated quantum light source for telecom band polarization entangled Bell state generation and dynamical manipulation. Biphoton states were firstly generated in four silicon waveguides by spontaneous four wave mixing. They were transformed to polarization entangled Bell states through on-chip quantum interference and quantum superposition, and then coupled to optical fibers. The property of polarization entanglement in generated photon pairs was demonstrated by two-photon interferences under two non-orthogonal polarizati…
Recently, Chen \em et al\rm.\ [New J. Phys. {\bf 13} (2011) 083018] presented experimental results, accompanied by quantum-mechanical analysis, showing that the quantum interference behavior of Bell states could be simulated in a modified Mach-Zehnder interferometer whose inputs are pseudothermal light beams obtained by passing laser light through a rotating ground-glass diffuser. Their experiments and their theory presumed low-flux operation in which the simulated quantum interference is observed via photon-coincidence counting. We first show that the Chen \em et al\rm.\ photon-coincidence co…
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…
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…
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.
