A well known result for the interference of two single-mode fields is that the degree of coherence and the degree of indistinguishablity are same when we consider the detection of a single photon. In this article we present the relation between degree of coherence, path indistinguishability and the fringe visibility considering interference of multiple number of single-mode fields while being interested in the detection of a single photon only . We will also mention how Born's rule of interference for multiple sources is reflected in these results.
Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of identical particles is a source of coherence, even when they are independently prepared. In particular, under spatially local operations, states that are incoherent for distinguishable particles, can be coherent for indistinguishable particles under the same procedure. We present a phase discrimination protocol, in which we demonstrate the operational advantage…
Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles, in that for the latter a unique contribution exists linked to indistinguishability which cannot occur for nonidentical particles. We experimentally demonstrate by an optical setup this additional contribution to quantum coherence, showing that its amount directly depends on the degree of indistinguishability and exploiting it to run a quantum phase disc…
We investigate the relation between indistinguishability and quantum entanglement in Hong- Ou-Mandel-interference experiments theoretically and relate these quantum mechanical principles to the theorem of entanglement monogamy. Employing Glaubers theory of quantum coherence we compute the detection statistics in HOM-interference of frequency entangled photons, and find a new additional term in the coincidence detection probability, which is related to the spectral indistinguishability of the considered photons that arises from finite bandwidth effects, and therefore is relevant in the limit of…
Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric set-up to simultaneously measure the…
Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which modern technologies are founded. In general, the most prominent adversary of quantum coherence is noise arising from the interaction of the associated dynamical system with its environment. Under certain conditions, however, the existence of noise may drive quantum and classical systems to endure intriguing nontrivial effects. In this vein, here we demonstrate, both theoretically and experimentally, that when two indisting…
The subtle and fundamental issue of indistinguishability and interference between independent pathways to the same target state is examined in the context of coherent control of atomic and molecular processes, with emphasis placed on possible "which-way" information due to quantum entanglement established in the quantum dynamics. Because quantum interference between independent pathways to the same target state occurs only when the independent pathways are indistinguishable, it is first shown that creating useful coherence (as defined in the paper) between nondegenerate states of a molecule fo…
Indistinguishability of photonic qubits emitted from trapped $^{40}$Ca$^+$ ions via pulsed excitation
Fachrichtung Physik, Universität des Saarlandes（萨尔兰州立大学物理系）；Zentrum für Quantentechnologien (QuTe), Universität des Saarlandes（萨尔兰州立大学量子技术中心）；Luxembourg Institute of Science and Technology (LIST)（卢森堡科学与技术研究所）
With propagating through a dispersive medium, the temporal-spectral profile of laser pulses should be inevitably modified. Although such dispersion effect has been well studied in classical optics, its effect on a single-photon wave-packet, i.e., the matter wave of a single-photon, has not yet been entirely revealed. In this paper, we investigate the effect of dispersion on indistinguishability of single-photon wave-packets through the Hong-Ou-Mandel (HOM) interference. By dispersively manipulating two indistinguishable single-photon wave-packets before interfering with each other, we observe …
In quantum mechanics, useful experiments require multiple measurements performed on the identically prepared physical objects composing experimental ensembles. Experimental systems also suffer from environmental interference, and one should not assume that all objects in the experimental ensemble suffer interference identically from a single, uncontrolled environment. Here we present a framework for treating multiple quantum environments and fluctuations affecting only subsets of the experimental ensemble. We also discuss a kinematic effect of indistinguishability not applicable to closed syst…
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…
We show that temporal two-photon interference effects involving the signal and idler photons created by parametric down-conversion can be fully characterized in terms of the variations of two length parameters--called the biphoton path-length difference and the biphoton path-asymmetry- length difference--which we construct using the six different length parameters that a general two-photon interference experiment involves. We perform an experiment in which the effects of the variations of these two parameters can be independently controlled and studied. In our experimental setup, which does no…
Photon statistics is one of the key properties of the photon state for the study of quantum coherence and quantum information techniques. Here, we discuss the photon indistinguishability induced bunching effect which can significantly change photon statistics. Through the measurement of the second-order degree of coherence of a mixed photon state composed of a single-photon state and a weak coherent state, the statistical transition from a classical behavior to a nonclassical behavior is experimentally demonstrated by modifying the indistinguishability of the two-photon states. The study will …
In the present work, we derive a formalism that can be used to predict and interpret the time structure and achievable visibilities for two-photon interference (TPI) experiments using photons from two separate sources. The treatment particularly addresses photons stemming from solid state quantum emitters, which are often subject to pure dephasing (PD) and spectral diffusion (SD). Therefore, it includes the impact of phase- and emission frequency-jitter besides the influence of differing radiative lifetimes and a relative spectral detuning. While the treatment is mainly aimed at interference e…
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Here we show that so-called Sylvester interferometers are near-optimal for the task of discriminating the behaviors of distinguishable an…
Photons generated by spontaneous parametric down conversion (SPDC) are one of the most useful resources in quantum information science. Two of their most important characteristics are the purity and the indistinguishability, which determine just how useful they are as a resource. We show how these characteristics can both be accessed through Hong, Ou and Mandel (HOM) type interferences using a single pair source. We also provide simple and intuitive analytical formulas to extract their values from the depth of the resulting interference patterns. The validity of these expressions is demonstrat…
In the present work, the effect of resonant pumping schemes in improving the photon coherence is investigated on InAs/InGaAs/GaAs quantum dots emitting in the telecom C-band. The linewidths of transitions of multiple exemplary quantum dots are determined under above-band pumping and resonance fluorescence via Fourier-transform spectroscopy and resonance scans, respectively. The average linewidth is reduced from $9.74\,\mathrm{GHz}$ in above-band excitation to $3.50\,\mathrm{GHz}$ in resonance fluorescence underlining its superior coherence properties. Furthermore, the feasibility of coherent s…
It is shown that the degree of polarization of light, generated by superposition in a single-photon interference experiment, may depend on the indistinguishability of the photon-paths.
Bosonic interference is a fundamental physical phenomenon, and it is believed to lie at the heart of quantum computational advantage. It is thus necessary to develop practical tools to witness its presence, both for a reliable assessment of a quantum source and for fundamental investigations. Here we describe how linear interferometers can be used to unambiguously witness genuine n-boson indistinguishability. The amount of violation of the proposed witnesses bounds the degree of multi-boson indistinguishability, for which we also provide a novel intuitive model using set theory. We experimenta…
Photon indistinguishability plays a fundamental role in information processing, with applications such as linear-optical quantum computation and metrology. It is then necessary to develop appropriate tools to quantify the amount of this resource in a multiparticle scenario. Here we report a four-photon experiment in a linear-optical interferometer designed to simultaneously estimate the degree of indistinguishability between three pairs of photons. The interferometer design dispenses with the need of heralding for parametric down-conversion sources, resulting in an efficient and reliable optic…
We propose an application of quantum temporal imaging to restoring the indistinguishability of the signal and the idler photons produced in type-II spontaneous parametric down-conversion with a pulsed broadband pump. It is known that in this case, the signal and the idler photons have different spectral and temporal properties. This effect deteriorates their indistinguishability and the visibility of the Hong-Ou-Mandel interference, respectively. We demonstrate that inserting a time lens in one arm of the interferometer and choosing properly its magnification factor restores perfect indistingu…
We analyze signal coherence in the setup of Wang, Zou and Mandel, where two optical downconverters have indistinct idler modes. Quantum interference, caused by indistinguishability of paths, has a visibility proportional to the transmission amplitude between idlers. Classical interference, caused by induced emission, may be complete for any finite transmission.
Multi-photon interference is at the heart of the recently proposed linear optical quantum computing scheme and plays an essential role in many protocols in quantum information. Indistinguishability is what leads to the effect of quantum interference. Optical interferometers such as Michaelson interferometer provide a measure for second-order coherence at one-photon level and Hong-Ou-Mandel interferometer was widely employed to describe two-photon entanglement and indistinguishability. However, there is not an effective way for a system of more than two photons. Recently, a new interferometric …
We investigate schemes for generating indistinguishable single photons, a key feature of quantum networks, from a trapped ion coupled to an optical cavity. Through selection of the initial state in a cavity-assisted Raman transition, we suppress the detrimental effect of spontaneous emission present in previously demonstrated schemes in similar systems. We measure a visibility of 72(2)% without correction for background counts in a Hong-Ou-Mandel interference measurement for the new scheme, with 51(2)% for a commonly-used scheme with similar parameters. Schemes such as the one demonstrated her…
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…
Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a co…
The ability to entangle distant quantum nodes is essential for the construction of quantum networks and for quantum information processing. For solid-state quantum emitters used as qubits, it can be achieved by photon interference. When the emitter is subject to spectral diffusion, this process can become highly inefficient, impeding the achievement of scalable quantum technologies. We study two-photon interference in the context of a Hong-Ou-Mandel (HOM)-type experiment for two separate quantum emitters, with different detunings with respect to a specific target frequency. We evaluate the sec…
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.
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…
Stimulated emission of two photons is observed experimentally in the parametric amplification process and is compared to a three-photon interference scheme. We find that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons is a result of multi-photon interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.
We propose the concept of pair-wise coherence to study the relation between the l1 norm of coherence and the quantum interference in Young's multi-photon multi-path experiments, where the input photons may be entangled each other. We find that only the local coherence of each single photon can make quantum interference and the collective coherence between photons has no contribution to quantum interference. The visibility of interference fringe is commonly less than the l1norm of coherence of the corresponding input state, suggesting that the l1 norm of coherence is only the necessary but not …
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of interference patterns properly defined statistical moments permit a reliable characterization of quantum coherence.
We revisit Mandel's notion that the degree of coherence equals the degree of indistinguishability by performing Hong-Ou-Mandel- (HOM-)type interferometry with single photons elastically scattered by a cw resonantly driven excitonic transition of an InAs/GaAs epitaxial quantum dot. We present a comprehensive study of the temporal profile of the photon coalescence phenomenon which shows that photon indistinguishability can be tuned by the excitation laser source, in the same way as their coherence time. A new figure of merit, the coalescence time window, is introduced to quantify the delay below…
The relations between quantum coherence and quantum interference are discussed. A general method for generation of quantum coherence through interference-induced state selection is introduced and then applied to `simple' atomic systems under two-photon transitions, with applications in quantum optics and laser cooling.
Generation and manipulation of the quantum state of a single photon is at the heart of many quantum information protocols. There has been growing interest in using phase modulators as quantum optics devices that preserve coherence. In this Letter, we have used an electro-optic phase modulator to shape the state vector of single photons emitted by a quantum dot to generate new frequency components (modes) and explicitly demonstrate that the phase modulation process agrees with the theoretical prediction at a single photon level. Through two-photon interference measurements we show that for an o…
Asynchronous Multi-photon Interference for Quantum Networks
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Abbe Center of Photonics（阿贝光子学中心）；Institute of Applied Physics（应用物理研究所）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所）；Helmholtz Institute Jena（耶拿亥姆霍兹研究所）
We report on a universal method to measure the genuine indistinguishability of n-photons - a crucial parameter that determines the accuracy of optical quantum computing. Our approach relies on a low-depth cyclic multiport interferometer with N = 2n modes, leading to a quantum interference fringe whose visibility is a direct measurement of the genuine n-photon indistinguishability. We experimentally demonstrate this technique for a 8-mode integrated interferometer fabricated using femtosecond laser micromachining and four photons from a quantum dot single-photon source. We measure a four-photon…
A quantitative measure of quantum coherence was recently introduced, in the context of quantum information theory. This measure has also been propounded as a good quantifier of the wave nature of quantum objects. However, actually measuring coherence in an experiment is still considered a challenge. A procedure for measuring coherence in a multi-slit interference is proposed here. It can be used for experimentally testing duality relations for interference experiments involving more than two slits.
We report a two-photon interference effect, in which the entangled photon pairs are generated from two laser pulses well-separated in time. In a single pump pulse case, interference effects did not occur in our experimental scheme. However, by introducing a second pump pulse delayed in time, quantum interference was then observed. The visibility of the interference fringes shows dependence on the delay time between two laser pulses. The results are explained in terms of indistinguishability of biphoton amplitudes which originated from two temporally separated laser pulses.
The interference observed for a quanton, traversing more than one path, is believed to characterize its wave nature. Conventionally, the sharpness of interference has been quantified by its visibility or contrast, as defined in optics. Based on this visibility, wave-particle duality relations have been formulated for two-path interference. However, as one generalizes the situation to multi-path interference, it is found that conventional interference visibility is not a good quantifier. A recently introduced measure of quantum coherence has been shown to be a good quantifier of the wave nature…
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference and coherence of the wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Quantum coherence in the system is responsible f…
In a general, multi-mode scattering setup, we show how the permutation symmetry of a many-particle input state determines those scattering unitaries which exhibit strictly suppressed many-particle transition events. We formulate purely algebraic suppression laws that identify these events and show that the many-particle interference at their origin is robust under weak disorder and imperfect indistinguishability of the interfering particles. Finally, we demonstrate that all suppression laws so far described in the literature are embedded in the general framework that we here introduce.
We report observation of a counter-intuitive phenomenon in multi-path correlation interferometry with thermal light. The intensity correlation between the outputs of two unbalanced Mach-Zehnder interferometers (UMZI) with two classically correlated beams of thermal light at the input exhibits genuine second-order interference with the visibility of $1/3$. Surprisingly, the second-order interference does not degrade at all no matter how much the path length difference in each UMZI is increased beyond the coherence length of the thermal light. Moreover, the second-order interference is dependent…
We describe a detector that measures the mutual coherence of two optical fields directly using quantum interference, free from photon noise of the individual irradiances. Our approach utilizes Raman transition in an atomic system where the state evolution is driven by the mutual coherence of the fields interacting with the atoms. Feedback control is used to balance the interaction of the fields being characterized, providing a measure of the mutual coherence. We show that the sensitivity of the coherence measurement can be enhanced significantly above that of conventional interferometric metho…
