Two-photon interference of multimode two-photon pairs produced by an optical parametric oscillator has been observed for the first time with an unbalanced interferometer. The time correlation between the multimode two photons has a multi-peaked structure. This property of the multimode two-photon state induces two-photon interference depending on delay time. The nonclassicality of this interference is also discussed.
We measure the joint Q-function of a multi-spatial-mode field using a charge-coupled device array detector in an unbalanced heterodyne configuration. The intensity pattern formed by interference between a weak signal field and a strong local oscillator is resolved using Fourier analysis and used to reconstruct quadrature amplitude statistics for 22 spatial modes simultaneously. The local oscillator and signal propagate at an angle of 12 mrad thus shifting the classical noise to modes that do not overlap with the signal. In this configuration, balanced detection is not necessary.
Optical rigidity in aLIGO gravitational-wave detector, operated on dark port regime, is unstable. We show that the same interferometer with excluded symmetric mechanical mode but with unbalanced arms allows to get stable optical spring for antisymmetric mechanical mode. Arm detuning necessary to get stability is shown to be a small one - it corresponds to small power in signal port. We show that stable optical spring may be also obtained in Michelson-Sagnac interferometer with both power and signal recycling mirrors and unbalanced arms.
We experimentally observe the two-photon interference of multimode photon pairs produced by an optical parametric oscillator far below threshold via a michelson interferometer, which shows a multipeaked structure. We find that the correlation function when the interferometer is unbalanced is clearly dependent on the path difference and phase between two interfering beams, but the shape of correlation function in balanced case is independent on the small path difference and phase beside the height. All experimental results are well agreed with the theoretical prediction.
Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. In contrast to earlier work, the limits are found to be independent of the number of interfering modes. However, the reported bounds are consistent with the Heisenberg limit. A short discussion on the concept of well-defined relative phase is also included.
We propose a novel interferometer by using optical transverse modes in multimode waveguide that can beat the standard quantum limit. In the scheme, the classical simulation of $N$-partical quantum entangled states is generated by using $N$ independent classical fields and linear optical elements. Similar to the quantum-enhanced measurements, the classical simulation can also achieve $\sqrt{N}$ enhancement over the precision of the measurement $N$ times for independent fields. Due to only using classical fields and linear optical elements, the scheme can be realized much more easily.
It is known that quantum interference can disappear with the mere possibility of distinguishability without actually performing the act. We create such distinguishability in an unbalanced SU(1,1) interferometer and indeed observe no interference in the direct photodetection of the outputs. On the other hand, such distinguishability can be erased with a projective measurement. Here, we report a method of homodyne detection that can also recover interference effect. We find that it is the indistinguishability in amplitude measurement that leads to the recovery of interference, and the quantum na…
Global multimode squeezing in a train of ultrashort pulses from unbalanced SU(1,1) interferometers
The State Key Laboratory of Precision Measurement Technology and Instruments, College of Precision Instrument and Opto-Electronics Engineering, Tianjin University（天津大学精密仪器与光电子工程学院）
Measurement-induced nonclassical effects in a two-mode interferometer are investigated theoretically using numerical simulations and analytical results. We demonstrate that for certain parameters measurements within the interferometer lead to the occurrence of two-mode squeezing. The results strongly depend on the detection probability, the phase inside the interferometer, and the choice of the input states. The appropriate parameters for maximized squeezing are obtained. We analyze the influence of losses and confirm that the predicted effects are within reach of current experimental techniqu…
Multimode integrated interferometers have great potential for both spectral engineering and metrological applications. However, material dispersion of integrated platforms constitutes an obstacle which limits the performance and precision of such interferometers. At the same time, two-colour non-linear interferometers present an important tool for metrological applications, when measurements in a certain frequency range are difficult. In this manuscript, we theoretically develop and investigate an integrated multimode two-colour SU(1,1) interferometer that operates in a supersensitive mode. By…
In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Phys. Rev. A 105, 012604 (2022)], the second beam splitter transmission coefficient is detection-scheme dependent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide de…
Nonlinear SU(1,1) interferometers are fruitful and promising tools for spectral engineering and precise measurements with phase sensitivity below the classical bound. Such interferometers have been successfully realized in bulk and fiber-based configurations. However, rapidly developing integrated technologies provide higher efficiencies, smaller footprints, and pave the way to quantum-enhanced on-chip interferometry. In this work, we theoretically realised an integrated architecture of the multimode SU(1,1) interferometer which can be applied to various integrated platforms. The presented int…
We develop general tools to characterise and efficiently compute relevant observables of multimode $N$-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a $d$-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different $d$ modes.
Field-Widened Multimode Interferometer with Long Time-Bin Delay Using a Multi-Pass Herriott Cell
National Research Council of Canada（加拿大国家研究委员会）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics & Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；Department of Physics, Simon Fraser University（西蒙菲莎大学物理系）
By exploiting the correlation properties of ultracold atoms in a multi-mode interferometer, we show how quantum enhanced measurement precision can be achieved with strong robustness to particle loss. While the potential for enhanced measurement precision is limited for even moderate loss in two-mode schemes, multi-mode schemes can be more robust. A ring interferometer for sensing rotational motion with non-interacting fermionic atoms can realize an uncertainty scaling of $1/(N\sqrtη)$ for $N$ particles with a fraction $η$ remaining after loss, which undercuts the shot noise limit of two mode i…
We demonstrate two approaches for unbalanced interferometers as time-bin qubit analyzers for quantum communication, robust against mode distortions and polarization effects as expected from free-space quantum communication systems including wavefront deformations, path fluctuations, pointing errors, and optical elements. Despite strong spatial and temporal distortions of the optical mode of a time-bin qubit, entangled with a separate polarization qubit, we verify entanglement using the Negative Partial Transpose, with the measured visibility of up to 0.85$\pm$0.01. The robustness of the analyz…
In this paper we provide the answer to the following question: given an arbitrary pure input state and a general, unbalanced, Mach-Zehnder interferometer, what transmission coefficient of the first beam splitter maximizes the quantum Fisher information (QFI)? We consider this question for both single- and two-parameter QFI, or, in other words, with or without having access to an external phase reference. We give analytical results for all involved scenarios. It turns out that, for a large class of input states, the balanced (50/50) scenario yields the optimal two-parameter QFI, however this is…
All Reflective Field-widened Unbalanced Interferometer for Quantum Sensing and Communication Applications
University of Waterloo（滑铁卢大学）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）；National Research Council of Canada（加拿大国家研究委员会）；Department of Chemical Engineering, University of Waterloo（滑铁卢大学化学工程系）；Department of Physics, Simon Fraser University（西蒙菲莎大学物理系）
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…
The phase uncertainty of an unseeded nonlinear interferometer, where the output of one nonlinear crystal is transmitted to the input of a second crystal that analyzes it, is commonly said to be below the shot-noise level but highly dependent on detection and internal loss. Unbalancing the gains of the first (source) and second (analyzer) crystals leads to a configuration that is tolerant against detection loss. However, in terms of sensitivity, there is no advantage in choosing a stronger analyzer over a stronger source, and hence the comparison to a shot-noise level is not straightforward. In…
Scattershot photon sources are known to have useful properties for optical quantum computing and boson sampling purposes, in particular for scaling to large numbers of photons. This paper investigates the application of these scattershot sources towards the metrological task of estimating an unknown phase shift. In this regard, we introduce three different scalable multimode interferometers, and quantify their quantum Fisher information performance using scattershot sources with arbitrary system sizes. We show that two of the interferometers need the probing photons to be in certain input conf…
The Cramér-Rao bound and the quantum Fisher information have been tools used extensively for interferometric phase sensitivity. Most scenarios considering a Mach-Zehnder interferometer with two input sources focused on the phase-matched case, when the Fisher information is maximal. Under this constraint, the best sensitivity is achieved for a balanced (50/50) input beam splitter. In this paper, we take a different approach: we allow the beam splitter transmission coefficient as well as the input phase mismatch to be variable parameters. We then search for a pair of these parameters that maximi…
Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers
Heinz Nixdorf Institute, Paderborn University（海因茨·诺伊多夫研究所，帕德博恩大学）；Department of Electrical Engineering and Information Technology, Paderborn University（电气与信息工程系，帕德博恩大学）；Department of Physics, Paderborn University（物理系，帕德博恩大学）
We perform a comprehensive set of experiments that characterize bosonic bunching of up to 3 photons in interferometers of up to 16 modes. Our experiments verify two rules that govern bosonic bunching. The first rule, obtained recently in [1,2], predicts the average behavior of the bunching probability and is known as the bosonic birthday paradox. The second rule is new, and establishes a n!-factor quantum enhancement for the probability that all n bosons bunch in a single output mode, with respect to the case of distinguishable bosons. Besides its fundamental importance in phenomena such as Bo…
We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as non-unit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's ineq…
We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization…
We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine-tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to charact…
Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling machines. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original Hong-Ou-Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentall…
We propose a quantum cryptographic system based on a planar lightwave circuit (PLC) and report on optical interference experiments using PLC-based unbalanced Mach-Zehnder interferometers (MZIs). The interferometers exhibited high-visibility (>0.98) interference even when the polarisation in the optical fibre connecting the two MZIs was randomly modulated. The results demonstrate that a PLC-based setup is suitable for achieving a polarisation-insensitive phase-coding cryptographic system.
We observed two-photon phase super-resolution in an unbalanced Michelson interferometer with classical Gaussian laser pulses. Our work is a time-reversed version of a two-photon interference experiment using an unbalanced Michelson interferometer. A measured interferogram exhibits two-photon phase super-resolution with a high visibility of 97.9% \pm 0.4%. Its coherence length is about 22 times longer than that of the input laser pulses. It is a classical analogue to the large difference between the one- and two-photon coherence lengths of entangled photon pairs.
A novel thermal light interferometer was recently introduced in V. Tamma and J. Seiler, New J. Phys. 18, 032002 (2016). Here, two classically correlated beams, obtained by beam splitting a thermal light beam, propagate through two unbalanced Mach-Zehnder interferometers. Remarkably, second-order interference between the long and the short paths in the two interferometers was predicted independently of how far, in principle, the length difference between the long and short paths is beyond the coherence length of the source. This phenomenon seems to contradict our common understanding of second …
We have constructed an efficient source of photon pairs using a waveguide-type nonlinear device and performed a two-photon interference experiment with an unbalanced Michelson interferometer. Parametric down-converted photons from the nonlinear device are detected by two detectors located at the output ports of the interferometer. Because the interferometer is constructed with two optical paths of different length, photons from the shorter path arrive at the detector earlier than those from the longer path. We find that the difference of arrival time and the time window of the coincidence coun…
The interferometer is one of the most important devices for revealing the nature of light and for precision optical metrology. Though lots of experiments were performed for probing photons behaviors in various configurations, a complete study of photons behavior in a birefringent interferometer has not ever been performed. Based on an environmental turbulence immune Mach-Zehnder interferometer, tunable photonic beatings by rotating a birefringent crystal versus the temperature of the crystal for both single-photon and two-photon are observed. Furthermore, the two-photon interference fringes be…
A linear optical probabilistic scheme for the optimal cloning of a pair of orthogonally-polarized photons is devised, based on single- and two-photon interferences. It consists in a partial symmetrization device, realized with a modified unbalanced Mach-Zehnder interferometer, followed by two independent Hong-Ou-Mandel interferometers. This scheme has the advantage that it enables quantum cloning without the need for stimulated amplification in a nonlinear medium. It can also be modified so to make an optical two-qubit partial SWAP gate, thereby providing a potentially useful tool to linear op…
We give a full description of the problem of Multi-Boson Correlation Sampling (MBCS) at the output of a random interferometer for single input photons in arbitrary multimode pure states. The MBCS prob- lem is the task of sampling at the interferometer output from the probability distribution associated with polarization- and time-resolved detections. We discuss the richness of the physics and the complexity of the MBCS problem for nonidentical input photons. We also compare the MBCS problem with the standard bo- son sampling problem, where the input photons are assumed to be identical and the …
We report on a Bell experiment with space-like separation assuming that the measurement time is related to gravity-induced state reduction. Two energy-time entangled photons are sent through optical fibers and directed into unbalanced interferometers at two receiving stations separated by 18 km. At each station, the detection of a photon triggers the displacement of a macroscopic mass. The timing ensures space-like separation from the moment a photon enters its interferometer until the mass has moved. 2-photon interference fringes with a visibility of up to 90.5% are obtained, leading to a vio…
We bring together a cavity-enhanced light-matter interface with a multimode interferometer (MMI) integrated onto a photonic chip and demonstrate the potential of such hybrid systems to tailor distributed entanglement in a quantum network. The MMI is operated with pairs of narrowband photons produced a priori deterministically from a single 87Rb atom strongly coupled to a high-finesse optical cavity. Non-classical coincidences between photon detection events show no loss of coherence when interfering pairs of these photons through the MMI in comparison to the two-photon visibility directly meas…
The concept of mode locking in laser is applied to a two-photon state with frequency entanglement. Cavity enhanced parametric down-conversion is found to produce exactly such a state. The mode-locked two-photon state exhibits a comb-like correlation function. An unbalanced Hong-Ou-Mandel type interferometer is used to measure the correlation function. A revival of the typical interference dip is observed. We will discuss schemes for engineering of quantum states in time domain.
We experimentally demonstrate a hybrid configuration for Quantum Key Distribution, that combines the simplicity of Distributed Phase Reference protocols with the self-referencing features and polarization insensitivity of the so-called Plug & Play system. Additionally, all the components are arranged in a server-client scheme to allow for practical key distribution. Blank, coherent pulse pair trains are generated at the reception end of the link by means of a pulse sequence and an unbalanced interferometer, and sent to the other end. The emitter writes the qubits by erasing one of the pulses f…
We investigate a method to produce photon pairs by four-wave mixing in photonic crystal fibers (PCFs). By controlling the wavelength of the pump light, which determines the phase matching condition for four-wave mixing, we can obtain a broader spectrum of photon pairs than undesired Raman-scattered photons. We observe two-photon interference of photon pairs from a PCF with the help of an unbalanced Mach-Zehnder interferometer. Two-photon interference fringes with 83% visibility, which exceeds the classical limit of 50%, are obtained.
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…
The quantum interface (QI) that generates entanglement between photonic and spin-wave (atomic memory) qubits is a basic building block for quantum repeaters. Realizing ensemble-based repeaters in practice requires quantum memory providing long lifetime and multimode capacity. Significant progresses have been achieved on these separate goals. The remaining challenge is to combine long-lived and multimode memories into a single QI. Here, by establishing multimode, magnetic-field-insensitive and long-wavelength spin-wave storage in laser-cooled atoms that are placed inside a phase-passively-stabi…
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multiparticle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transformati…
Integrated quantum optics has drastically reduced the size of table-top optical experiments to the chip-scale, allowing for demonstrations of large-scale quantum information processing and quantum simulation. However, despite these advances, practical implementations of quantum photonic circuits remain limited because they consist of large networks of waveguide interferometers that path encode information which do not easily scale. Increasing the dimensionality of current quantum systems using higher degrees of freedom such as transverse spatial field distribution, polarization, time, and freq…
We demonstrate controlled entanglement routing between bunching and antibunching path-entangled two-photon states in an unbalanced Mach-Zehnder interferometer (UMZI), in which the routing process is controlled by the relative phase difference in the UMZI. Regarding bunching and antibunching path-entangled two-photon states as two virtual ports, we can consider the UMZI as a controlled entanglement router, which bases on the coherent manipulation of entanglement. Half of the entanglement within the input two-photon state is coherently routed between the two virtual ports, while the other is los…
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）
