A measurement scheme of atomic qubits pinned at given positions is studied by analyzing the interference pattern obtained when they emit photons spontaneously. In the case of two qubits, a well-known relation is revisited, in which the interference visibility is equal to the concurrence of the state in the infinite spatial separation limit of the qubits. By taking into account the super-radiant and sub-radiant effects, it is shown that a state tomography is possible when the qubit spatial separation is comparable to the wavelength of the atomic transition. In the case of three qubits, the relations between various entanglement measures and the interference visibility are studied, where the visibility is defined from the two-qubit case. A qualitative correspondence among these entanglement relations is discussed. In particular, it is shown that the interference visibility is directly related to the maximal bipartite negativity.
We observe spatial fringes in the interference of two beams, which are controlled by a third beam through the phenomenon of induced coherence without induced emission. We show that the interference pattern depends on the alignment of this beam in an analogous way as fringes created in a traditional division-of-amplitude interferometer depend on the relative alignment of the two interfering beams. We demonstrate that the pattern is characterized by an equivalent wavelength, which corresponds to a combination of the wavelengths of the involved physical light beams.
Observation of the First-Order Interference Fringes Beyond Coherence Length Employing Commercial Continuous-wave Multi-mode Laser Diode: A Sight of Two-photon Interference
The interference pattern of the resonance fluorescence from a J=1/2 to J=1/2 transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. Thermal motion of the atoms is included. Agreement is obtained with experiments [Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not…
Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. However, the N-photon parity measurements required to achieve this optimal sensitivity are extremely difficult to realize with current photon detection technologies, requiring high-fidelity resolution of N+1 different photon distributions between the output ports. Recent experimental demonstrations of precision beyond the SNL have therefore used only one or two photon-number detection patterns instead of parity measurements. Here we investiga…
Two quantum states of two half-charge optical vortexes with relative azimuthal angle π are orthogonal, by which two half-charge spiral phase plates with intersection angle π can be used to demonstrate a parabolic coincident fringe in the Bell inequality experiment with high-dimensional two-photon orbital angular momentum entanglement and to thereby obtain a strong Bell parameter of 3.2. I theoretically demonstrate various orthogonal relations between two quantum states, each of which is a state with a rotational symmetry superposition made up of n fractional orbital angular momentum states, wh…
We show that it is possible to generate a novel single-photon fringe pattern by using two spatially separated identical bi-photon sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties with potential applications. A striking feature of the fringes is that although the pattern is obtained by detecting only one photon of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon. The fringe shift is characterized by a combination of wavelengths of both photons, which implies tha…
The elements of reality coined by Einstein, Podoslky, and Rosen promoted a series of fundamental discussions involving the notion of quantum correlations and physical realism. The superposition principle applied in the double-slit experiment with matter waves highlights the need for a critical review of the adoption of physical realism in the quantum realm. In this work, we employ a measure of physical irrealism and consider an initial contractive state in the double-slit setup for which position and momentum variables of a single particle are initially correlated. We investigate how the behav…
We observe interference in the light scattered from trapped $^{40}$Ca$^+$ ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three and four ions in a harmonic trap. Control of the trapping potential allows…
An interferometric scheme for the creation of momentum superposition states of mechanical oscillators, using a quantum mirror kicked by free photons is analyzed. The scheme features ultra-fast preparation with immediate detection and should allow for the observation of signatures of momentum superpositions in a massive macroscopic system at non-zero temperatures. It is robust against thermalized initial states, displacement and movement, mirror imperfections, and the measurements' back-actions.
We study the dynamics of ultracold atoms trapped in optical double-well potentials in presence of noise generated by an external environment. When prepared in a Fock number state, the system shows phase coherence in the averaged density profile obtained using standard absorption image techniques, that disappears in absence of noise. This effect indicates that also in many-body systems an external environment may enhance quantum coherence, instead of destroying it.
Quantum nonlinear interferometers (QNIs) can measure the infrared physical quantities of a sample by detecting visible photons. A QNI with Michelson geometry based on the spontaneous parametric down-conversion in a second-order nonlinear crystal is studied systematically. A simplified theoretical model of the QNI is presented. The interference visibility, coherence length, equal-inclination interference, and equal-thickness interference for the QNI are demonstrated theoretically and experimentally. As an application example of the QNI, the refractive index and the angle between two surfaces of…
We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease, but under certain conditions, to an increase of the fringe contrast. Here we explain this seemingly counter-intuitive effect based on a model fo…
We demonstrate optical interferometry beyond the limits imposed by the photon wavelength using 'triggered' entangled photon pairs from a semiconductor quantum dot. Interference fringes of the entangled biphoton state reveals a periodicity half of that obtained with the single photon, and much less than that of the pump laser. High fringe visibility indicates that biphoton interference is less sensitive to decoherence than interference of two sequential single photons. The results suggest that quantum interferometry may be possible using a semiconductor LED-like device.
Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here we present a theory of the phase sensitivity for the general case where the detection probability is given by an $N$ photon interference fringe. We find that the phase sensitivity has a complex dependence on both the intrinsic efficiency of detection $η$ and the interference fringe visibility $V$. Most importantly, the phase that gives maximum phase sensitivity is in general not the same as the phase at which the slope of the interference fringe is a maximum, as has previ…
The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we c…
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 …
Sequences of alternating-sign time-dependent electric field pulses lead to coherent interference effects in Schwinger vacuum pair production, producing a Ramsey interferometer, an all-optical time-domain realization of the multiple-slit interference effect, directly from the quantum vacuum. The interference, obeying fermionic quantum statistics, is manifest in the momentum dependence of the number of produced electrons and positrons along the linearly polarized electric field. The central value grows like $N^2$ for $N$ pulses [i.e., $N$ "slits"], and the functional form is well-described by a …
We show that matter-wave interference fringes formed by two overlapping atomic clouds can yield information about the non-local Bell correlations. To this end, we consider a simple atomic interferometer, where the clouds are released from the double-well potential and the relative phase is estimated from the density fit to this interference pattern. The Bell correlations can be deduced from the sensitivity of the phase obtained in this way. We examine the relation between these two quantities for a wide range of ground states of the double-well, scanning through the attractive and the repulsiv…
Decoherence is the main process behind the quantum to classical transition. It is a purely quantum mechanical effect by which the system looses its ability to exhibit coherent behavior. The recent experimental observation of diffraction and interference patterns for large molecules raises some interesting questions. In this context, we identify possible agents of decoherence to take into account when modeling these experiments and study theirs visible (or not) effects on the interference pattern. Thereby, we present an analysis of matter wave interferometry in the presence of a dynamic quantum…
We experimentally study the interference of dipole scattered light from two optically levitated nanoparticles in vacuum, which present an environment free of particle-substrate interactions. We illuminate the two trapped nanoparticles with a linearly polarized probe beam orthogonal to the propagation of the trapping laser beams. The scattered light from the nanoparticles are collected by a high numerical aperture (NA) objective lens and imaged. The interference fringes from the scattered vector light for the different dipole orientations in image and Fourier space are observed. Especially, the…
We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no…
We test the validity of Feynman's idea that a two-slit experiment performed with classical objects (bullets) does not produce observable interference fringes on the detection screen because the Compton's wavelength of the bullets is so tiny, that no real detector could resolve individual interference fringes, thus producing only an average signal which is the observed smooth curve. To test this idea, we study the two-slit experiment in two different situations using light to simulate both wave-like and particle-like bullets. In the first case, we consider coherent light with short wavelengths …
We demonstrate a hybrid approach to the generation of photon pairs of a short wavelength with high brightness, by combining parametric down-conversion (SPDC) and up-conversion techniques. Photon pairs were generated at the wavelength of 1550 nm via SPDC, and converted to 516.7 nm through up-conversion with the pump at 775 nm. The quantum sum-frequency interference of the up-converted photon pairs exhibited a fringe period of 258.3 nm, which was 6 times shorter than the original wavelength, demonstrating that the energy-time correlation of the photon pairs was preserved. The technique simultane…
N00N states -- maximally path-entangled states of N photons -- exhibit spatial interference patterns sharper than any classical interference pattern. This is known as super-resolution. However, even with perfectly efficient number-resolving detectors, the detection efficiency of all previously demonstrated methods to measure such interference decreases exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. Here, we create spatial super-resolution fringes with two-, three-, and four-photon N00N states…
Quantum mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation is recently generalized by Banaszek et. al., (Nature Communications 4, 2594, 2013) when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an …
We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Man…
We produce polarization entangled states with variable degree of entanglement for twin photons. Entanglement in polarization is coupled to entanglement in position that produces transverse coincidence interference fringes. We show both theoretically and experimentally that, due to this coupling, we can use the interference pattern to measure the polarization degree of entanglement.
The notion of wave-particle duality may be quantified by the inequality V^2+K^2 <=1, relating interference fringe visibility V and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially-mixed input states. A quantum eraser scheme has been realized that recovers interference fringes even when no which-way information is available to erase.
A photoelectron forced to pass through two atomic energy levels before receding from the residual ion shows interference fringes in its angular distribution as manifestation of a two-slit-type interference experiment in wave-vector space. This scenario was experimentally realized by irradiating a Rubidium atom by two low-intensity continuous-wave lasers [Pursehouse et al., Phys. Rev. Lett. 122, 053204 (2019)]. In a one-photon process the first laser excites the 5p level while the second uncorrelated photon elevates the excited population to the continuum. This same continuum state can also be …
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a …
The interaction between light and metal nanoparticles enables investigations of microscopic phenomena on nanometer length and ultrashort time scales, benefiting from strong confinement and enhancement of the optical field. However, the ultrafast dynamics of these nanoparticles are primarily investigated by multiphoton photoluminescence on picoseconds or photoemission on femtoseconds independently. Here, we presented two-photon photoluminescence (TPPL) measurements on individual Au nanobipyramids (AuNP) to reveal their ultrafast dynamics by two-pulse excitation on a global time scale ranging fr…
Nonlocal correlation is the key concept in quantum information processing, where quantum entanglement provides such a nonclassical property. Since the first proposal of noninterfering interferometer-based two-photon intensity correlation by Franson (Phys. Rev. Lett. 62, 2205 (1989)), the particle nature of photons has been intensively studied for nonlocal correlation using Mach-Zehnder interferometers (MZIs). Here, the role of MZIs is investigated with respect to the origin of nonlocal correlation in Franson-type experiments, where the wave nature of photons plays a critical role. Under the co…
In this work I demonstrate the interference of three photons, a generalisation of the famous Hong Ou Mandel (HOM) interference. I show that three-photon interference is governed by four parameters and measure three-photon interference independent of two-photon interference. I demonstrate that even when the states of the photons are highly distinguishable they can still exhibit strong quantum interference, challenging our intuition formed by the double slit and HOM interference. This is followed by a demonstration of four-photon interference, where surprisingly we can still observe a "fringe" w…
Often cited dictums in Quantum Mechanics include "observation disturbance causes loss of interference" and "ignorance is interference". In this paper we propose and describe a series of experiments with modified Mach-Zehnder interferometers showing that one has to be careful when applying such dictums. We are able to show that without interacting in any way with the light quantum (or quanta) expected to behave "wave-like", interference fringes can be lost by simply gaining (or having the potential to gain) the which-path knowledge. Erasing this information may revive the interference fringes. …
Interference of an array of independent Bose-Einstein condensates, whose experiment has been performed recently, is theoretically studied in detail. Even if the number of the atoms in each gas is kept finite and the phases of the gases are not well defined, interference fringes are observed on each snapshot. The statistics of the snapshot interference patterns, i.e., the average fringe amplitudes and their fluctuations (covariance), are computed analytically, and concise formulas for their asymptotic values for long time of flight are derived. Processes contributing to these quantities are cla…
Based on modern quantum measurement theory, we use Zurek's "triple model" to study, from the viewpoint of quantum information theory, the wave and particle nature of a photon in a symmetric Mach-Zehnder interferometer. In the process of quantum measurement, the state of both the system and the detector is not an entangled state but a correlated state. We find that the information gain about the photon is related to the correlations (including classical and quantum correlations) between the photon and the detector. We also derive the relationship between the information gain and the fringe visi…
In the first version of this paper (arXiv: 1003.2899v1, 15.03.2010) there is described first, traditional method of measuring the non-zero shift of interference fringe in the Michelson interferometer, operating on the effects of second order with respect to v/c, and are revealed hidden causes of the failure to measure the shift of interference fringe in the period from 1881 till 1960. It is shown that at the latitude of Obninsk within a 24-hour observation period the horizontal projection of aether wind velocity varies from 140 km/s to 480 km/s. The second version of this paper (arXiv: 1003.28…
We have demonstrated single-photon interference over 150 km using time-division interferometers for quantum cryptography, which were composed of two integrated-optic asymmetric Mach-Zehnder interferometers, and balanced gated-mode photon detectors. The observed fringe visibility was more than 80% after 150-km transmission.
In [J. C. Howell and J. A. Yeazell, Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. We model the decoherence due to light scattering during the propagation along an optical transmission line and propose a setup allowing an entanglement purification from a number of preparations which are partially decohered due to transmission. A purification is achieved even without any manual intervention. We consider a nondemolition configuration to measure the purity of the state as contrast…
With quantum interference of two-path spontaneous emissions, we propose a novel scheme to coherently control the atom--photon momentum entanglement through atomic internal coherence. A novel phenomenon called ``momentum phase entanglement'' is reported, and we found, under certain conditions, that more controllable entangled state can be produced with super--high degree of entanglement.
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.
We report the distribution of time bin entangled photon pairs over 300 km of optical fiber. We realized this by using a high speed and high signal to noise ratio entanglement generation and evaluation setup that consists of periodically poled lithium niobate waveguides and superconducting single photon detectors. The observed two-photon interference fringes exhibited a visibility of 84 %. We confirmed the violation of Bell's inequality by 2.9 standard deviations.
In diffraction experiments with particle beams, several effects lead to a fringe visibility reduction of the interference pattern. We theoretically describe the intensity one can measure in a double-slit setup and compare the results with the experimental data obtained with cold neutrons. Our conclusion is that for cold neutrons the fringe visibility reduction is due not to decoherence, but to initial incoherence.
We study a general theory on the interference of two-photon wavepacket in a beam splitter. We find that the symmetry of two-photon spectrum plays an important role in the manners of interference. We distinguish the coalescence and anti-coalescence interferences, and prove that the anti-coalescence interference is the signature of photon entanglement.
This letter reports telecom-band sequential time-bin entangled photon-pair generation at a repetition rate of 10 GHz in periodically-poled reverse-proton-exchange lithium niobate waveguides based on mode demultiplexing. With up-conversion single-photon detectors, we observed a two-photon-interference-fringe visibility of 85.32% without subtraction of accidental noise contributions, which can find broad application in quantum information and quantum entanglement research.
A complementarity relation is shown between the visibility of interference and bipartite entanglement in a two qubit interferometric system when the parameters of the quantum operation change for a given input state. The entanglement measure is a decreasing function of the visibility of interference. The implications for quantum computation are briefly discussed.
We consider a pair of three-level atoms interacting with the vacuum. The process of disentanglement due to spontaneous emission and the role of quantum interference between principal transitions in this process, are analysed. We show that the presence of interference can slow down disentanglement. In the limit of maximal interference, some part of initial entanglement can survive.
The ghost interference observed for entangled photons is theoretically analyzed using wave-packet dynamics. It is shown that ghost interference is a combined effect of virtual double-slit creation due to entanglement, and quantum erasure of which-path information for the interfering photon. For the case where the two photons are of different color, it is shown that fringe width of the interfering photon depends not only on its own wavelength, but also on the wavelength of the other photon which it is entangled with.
Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements al…
The well-known interference pattern of bright and dark fringes was first observed for light beams back in 1801 by Thomas Young. The maximum visibility fringes occur when the irradiance of the two beams is equal, and as the ratio of the beam intensities deviates from unity, fringe visibility decreases. An interesting outcome that might not be entirely intuitive, however, is that the wavefront of such unequal amplitude beams' superposition will exhibit a wavy behavior. In this work, we experimentally observe the backflow phenomenon within this wavy wavefront. Backflow appears in both optics (ret…
