Hayato Goto, Yasuo Yanagihara, Haibo Wang, Tomoyuki Horikiri, Takayoshi Kobayashi
An oscillatory correlation function has been observed by the coincidence counting of multimode two-photon pairs produced with a degenerate optical parametric oscillator far below threshold. The coherent superposition of the multimode two-photon pairs provides the oscillation in the intensity correlation function. The experimental data are well fitted to a theoretical curve.
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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.
For one-mode and multimode light, the photon-number tomograms of Gaussian quantum states are explicitly calculated in terms of multivariable Hermite polynomials. Positivity of the tomograms is shown to be necessary condition for positivity of the density matrix.
We experimentally analyze the complete photon number statistics of parametric downconversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes.
Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.
We report the first demonstration of quantum interference in multimode interference (MMI) devices and a new complete characterization technique that can be applied to any photonic device that removes the need for phase stable measurements. MMI devices provide a compact and robust realization of NxM optical circuits, which will dramatically reduce the complexity and increase the functionality of future generations of quantum photonic circuits.
We address the reconstruction of the full photon distribution of multimode fields generated by seeded parametric down-conversion (PDC). Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood (MaxLik) estimation and does not involve photon counting. We present a novel constrained MaxLik method that incorporates the request of finite energy to improve the rate of convergence and, in turn, the overall accuracy of the reconstruction.
We consider theoretically how to extract mode dependent single photons from a time/frequency multimode non-classical beam. To achieve this task, we calculate the properties of sum frequency generation with a pulse shaped pump, taking into account both temporal and spatial degree of freedom. We show that using a non-collinear configuration it is possible to achieve a mode dependent weakly reflective beam splitter, with Schmidt number compatible with photon extraction for continuous variable regime tasks. We explicit the possible application to the degaussification of highly multimode squeezed f…
Advances in photonics require photon-number resolved simulations of quantum optical experiments with Gaussian states. We demonstrate a simple and versatile method to simulate the photon statistics of general multimode Gaussian states. The derived generating functions enable simulations of the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics of Gaussian states as well as of multimode photon-added and photon-subtracted Gaussian states. Numerical results are obtained by automatic differentiation of these generating functions by employin…
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.
We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-gaussian states are produced conditionally. These are useful states for continuous-variable quantum information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric downconversion, thereby improving the analysis of existing experimental results. The ma…
Genuine multimode entanglement in continuous variable systems can be quantified by exploring the geometry of the state-space, namely via the generalized geometric measure (GGM) which is defined as the shortest distance of a given multimode state from a nongenunely multimode entangled state. For multimode Gaussian states, we derive a closed form expression of GGM in terms of the symplectic invariants of the reduced states. Following that prescription, the characteristics of GGM for typical three- and four-mode Gaussian states are investigated. In the non-Gaussian paradigm, we compute GGM for ph…
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.
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…
Exploring Photon Blockade in Multimode Jaynes-Cummings Models with Two-Photon Dissipation
本文研究多模Jaynes-Cummings模型中光子阻塞现象，通过两光子耗散和外部驱动分析单模与多模情况下的二阶相关函数，揭示传统与非传统光子阻塞条件及多模的控制优势。
Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalised center-of-mass tomographies are discussed. Examp…
Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the Type-II collinear down conversion, while single-mode cond…
We investigate the coupling efficiency of parametric downconversion light (PDC) into single and multi-mode optical fibers as a function of the pump beam diameter, crystal length and walk-off. We outline two different theoretical models for the preparation and collection of either single-mode or multi-mode PDC light (defined by, for instance, multi-mode fibers or apertures, corresponding to bucket detection). Moreover, we define the mode-matching collection efficiency, important for realizing a single-photon source based on PDC output into a well-defined single spatial mode. We also define a mu…
Quantum interfaces (QIs) that generate entanglement between a multimode atomic memory and a photon forms a multiplexed repeater node and hold promise to greatly improve quantum repeater rates. Recently, the temporal multimode spin-wave memory that is entangled with a photon has been demonstrated with cold atoms. However, due to additional noise generated in multimode operation, the fidelity of spin-wave-photon entanglement significantly decreases with the mode number. So far, the improvement on temporal-multimode entanglement fidelity via suppressing the additional noise remains unexplored. He…
Multimode ion-photon entanglement over 101 kilometers of optical fiber
该研究构建基于囚禁离子的三量子比特量子网络节点，实现各量子比特与经过101公里光纤的光子纠缠，并证明多模方案可提高远程纠缠分发速率。
Nonlinear squeezing generation via multimode PDC and single photon measurement
该研究利用多模 PDC 与单光子添加技术，在弱非高斯条件下实现双模同时非线性压缩，并给出依赖模态结构及本地振荡器配置的最优测量策略。
We report the generation of a type-I multimode two-photon state on a rubidium D$_2$ line (780 nm) using periodically poled KTiOPO$_4$ crystals. With a degenerate optical parametric oscillator far below threshold, we observe an oscillatory correlation function, the cross-correlation between two photons shows a cavity bandwidth of about 7.8 MHz. We also use a Fabry-P$\acute{\rm{e}}$rot etalon to filter its most longitudinal modes and observe its time correlation function. The experimental data are well fitted to theoretical curves. This system could be utilized for demonstrating storage and retr…
Characterization of the multimode nature of single-photon sources based on spontaneous parametric down conversion
该研究针对自发参量下转换预示单光子源，建立了基于精确Bogoliubov处理的多模描述及微扰有效方法，解析估计成功概率与纯度，并揭示短泵浦下单模描述准确、长泵浦或连续泵浦下需多模描述，为量子信息协议设计提供指导。
Quantum correlations between long lived quantum memories and telecom photons that can propagate with low loss in optical fibers are an essential resource for the realization of large scale quantum information networks. Significant progress has been realized in this direction with atomic and solid state systems. Here, we demonstrate quantum correlations between a telecom photon and a multimode on-demand solid state quantum memory. This is achieved by mapping a correlated single photon onto a spin collective excitation in a Pr$^{3+}$:Y$_2$SiO$_5$ crystal for a controllable time. The stored singl…
We implement a direct detection scheme based on hybrid photodetectors to experimentally investigate high-order correlations for detected photons by means of quantities that can be experimentally accessed. We show their usefulness in fully characterizing a multimode twin-beam state in comparison with classical states and, in particular, we introduce a nonclassicality criterion based on a simple linear combination of high-order correlation functions. Our scheme is self-consistent, allowing the estimation of all the involved parameters (quantum efficiency, number of modes and average energy) dire…
We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong-Ou-Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information.
The sources, which generate atom-photon quantum correlations or entanglement based on quantum memory, are basic blocks for building quantum repeaters (QRs). For achieving highly entanglement-generation rates in ensemble-based QRs, spatial-, temporal- and spectral-multimode memories are needed. The previous temporal-multimode memories are based on rephrasing mechanisms in inhomogeneous-broadened media. Here, by applying a train of multi-direction write pulses into a homogeneous-broadened atomic ensemble to induce Duan-Lukin-Cirac-Zoller-like Raman processes, we prepare up to 19 pairs of modes, …
Photon catalysis for general multimode multi-photon quantum state preparation
本文提出了一种基于光子催化机制，利用多端口干涉仪等设备实现任意多模式多光子态的精确制备，并验证了其在不同态类上的100%保真度。
Multimode Strong-Coupling Processes in Circuit QED Lattices
研究多模强耦合在电路量子电动力学晶格中的新现象，包括电路拉格朗日分析和强波混叠共振实验，揭示了新特征如带隙、抬高退化、展宽平面带和频率依赖的跃迁。
The generation and distribution of quantum correlations between photonic qubits is a key resource in quantum information science. For applications in quantum networks and quantum repeaters, it is required that these quantum correlations be stored in a quantum memory. In 2001, Duan, Lukin, Cirac, and Zoller (DLCZ) proposed a scheme combining a correlated photon-pair source and a quantum memory in atomic gases, which has enabled fast progress towards elementary quantum networks. In this letter, we demonstrate a solid state source of correlated photon pairs with embedded spin-wave quantum memory,…
We propose and theoretically study a method for the stochastic realization of arbitrary quantum channels on multimode single-photon qudits. In order for our method to be undemanding in its implementation, we restrict our analysis to linear-optical techniques, vacuum ancillary states and non-adaptive schemes, but we allow for random switching between different optical networks. With our method it is possible to deterministically implement random-unitary channels and to stochastically implement general, non-unital channels. We provide an expression for the optimal probability of success of our s…
We present a detailed analytic framework for studying multimode non-Gaussian states that are conditionally generated when few modes of a multimode Gaussian state are subject to photon-number-resolving detectors. From the output state Wigner function, we deduce that the state factorizes into a Gaussian gate applied to a finite Fock-superposition non-Gaussian state. The framework provides an approach to find the optimal strategy to generate a given target non-Gaussian state. We explore examples, such as the generation of cat states, weak cubic phase states, and bosonic code states, and achieve i…
Entanglement between photons at telecommunication wavelengths and long-lived quantum memories is one of the fundamental requirements of long-distance quantum communication. Quantum memories featuring on-demand read-out and multimode operation are additional precious assets that will benefit the communication rate. In this work we report the first demonstration of entanglement between a telecom photon and a collective spin excitation in a multimode solid-state quantum memory. Photon pairs are generated through widely non-degenerate parametric down-conversion, featuring energy-time entanglement …
We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single photon sources, strong coherent laser beams, and photodetectors with single-photon resolution. The efficiency of this setup may be greatly enhanced if, in addition, a quantum memory is available.
Multimode Photon-Photon Coupling
本研究通过仿真与实验，在由三个互补开口谐振环组成的平面系统中观察到多光子模式间的强耦合，并提出理论框架定量描述模式杂化与耦合强度，为可调光子相互作用平台设计提供指导。
We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.
Multiplexed quantum memories capable of storing and processing entangled photons are essential for the development of quantum networks. In this context, we demonstrate the simultaneous storage and retrieval of two entangled photons inside a solid-state quantum memory and measure a temporal multimode capacity of ten modes. This is achieved by producing two polarization entangled pairs from parametric down conversion and mapping one photon of each pair onto a rare-earth-ion doped (REID) crystal using the atomic frequency comb (AFC) protocol. We develop a concept of indirect entanglement witnesse…
Multimode Qubit-Conditional Operations via Generalized Cross-Resonance
本文提出一个基于广义交叉共振的通用框架，用于生成单模和多模量子比特条件操作，包括条件位移、压缩、分束器及联合操作，对玻色子量子纠错、相位估计和量子模拟至关重要。
The resonant interaction between two two-level atoms and m- electromagnetic modes in a cavity is considered. Entanglement dynamics between two atoms is examined. In particular we compare dynamical variations for different cavity modes as well as for different cavity photon numbers. The collapse and revival of entanglement is exhibited by varying the atom-photon interaction times.
The subtraction of a single photon from a multimode quantum field is analyzed as the conditional evolution of an open quantum system. We develop a theory describing different subtraction schemes in a unified approach and we introduce the concept of subtraction modes intrinsic to the process. The matching between the subtraction modes and the modes of the field defines different possible scenarios for the photon subtraction. In particular, our framework identifies: the conditions of pure photon subtraction, the quantum states of the field modes conditioned to the photon subtraction, the mode wi…
Photons occupying multiple spatial modes hold a great promise for implementing high-dimensional quantum communication. We use spontaneous four-wave mixing to generate multimode photon pairs in a few mode fiber. We show the photons are correlated in the fiber mode basis using an all-fiber mode sorter. Our demonstration offers an essential building block for realizing high-dimensional quantum protocols based on standard, commercially available fibers, in an all-fiber configuration.
We investigate the entanglement patterns of photon-added and -subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the "player" modes, the others being "spectators." We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast of the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state …
General solutions to the quantum Rabi model involve subspaces with unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for arbitrary number of qubits and photon modes. Unlike the Juddian solution, ours exists for arbitrary single qubit-photon coupling strength with constant eigenenergy. This corresponds to a horizontal line in the spectrum, while still being a qubit-photon entangled state. As a possible application, we propose an adiabatic scheme for the fast generation of arbitrary single-photon multimode W states with non…
Multiphoton, multimode state classification for nonlinear optical circuits
本文提出了一种基于齐次多项式可分解性的多模态多光子状态分类方法，并设计了多层干涉仪以实现不同类别状态的生成，为状态鲁棒性提供了基准。
The generation and distribution of entanglement are key resources in quantum repeater schemes. Temporally multiplexed systems offer time-bin encoding of quantum information which provides robustness against decoherence in fibers, crucial in long distance communication. Here we demonstrate the direct generation of entanglement in time between a photon and a collective spin excitation in a rare earth ion doped ensemble. We analyze the entanglement by mapping the atomic excitation onto a photonic qubit and by using time-bin qubits analyzers implemented with another doped crystal using the atomic …
With advanced micro- and nano-photonic structures, the vacuum photon-photon coupling rate is anticipated to approach the intrinsic loss rate and lead to unconventional quantum effects. Here, we investigate the classical-to-quantum transition of such photonic nonlinear systems using the quantum cluster-expansion method, which addresses the computational challenge in tracking large photon number states of the fundamental and harmonic optical fields involved in the second harmonic generation process. Compared to the mean-field approximation used in weak coupling limit, the quantum cluster-expansi…
Coherent temporal filtering of multimode parametric down-conversion using a quantum pulse gate
本研究利用量子脉冲门（QPG）对多模参量下转换（PDC）源进行相干时域滤波，其产生的预示光子纯度高于0.90，优于传统强度滤波，可用于量子网络应用。
Few-photon transport via waveguide-coupled local quantum systems has attracted extensive theoretical and experimental studies. Most of the study has focused on atomic or atomic-like local quantum systems due to their strong light-matter interaction useful for quantum applications. Here, we study few-photon transport via a waveguide-coupled multimode optical cavity with second-order bulk nonlinearity. We develop a Feynman diagram approach and compute the scattering matrix of the one- and two-photon transport. Based on the calculated scattering matrix, we show highly nonclassical photonic effect…
The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involves maximising the interference visibility whilst maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include large numbers of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong--Ou--Mandel interference visibility of parametric photon sources, considering both threshold and number re…
Thermal states of light are widely used in quantum optics for various quantum phenomena testing. Particularly, they can be utilized for characterization of photon creation and photon annihilation operations. During the last decade the problem of photon subtraction from multimode quantum states become of much significance. Therefore, in this work we present a technique for statistical parameter estimation of multimode multiphoton subtracted thermal states of light, which can be used for multimode photon annihilation test.
Cavity-enhanced and spatial-multimode spin-wave-photon quantum interface
本文基于费马光学定理构建支持6个TEM00模式的环形腔，利用冷原子DLCZ过程实现12模空间复用的自旋波–光子量子接口，获得70%零延迟本征读取效率和0.6 ms有效存储时间。
We present a method for computing the action of conditional linear optical transformations, conditioned on photon counting, for arbitrary signal states. The method is based on the Q-function, a quasi probability distribution for anti normally ordered moments. We treat an arbitrary number of signal and ancilla modes. The ancilla modes are prepared in an arbitrary product number state. We construct the conditional, non unitary, signal transformations for an arbitrary photon number count on each of the ancilla modes.
Single-photon addition to multimode quantum fields at telecom wavelengths using lithium niobate and its doped variants
本研究通过理论分析和数值模拟，探讨了在电信波长下使用铌酸锂及其掺杂晶体对多模量子场进行单光子加法，确定了最佳实验条件和相位匹配参数，为非高斯量子态工程提供了平台。
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…
The total mass of noncollinear photons forming diverging light pulses is defined and found explicitly. Both classical and quantum derivations are presented. The quantum derivation is based on the use of multimode coherent states, and links between parameters of these states and those of the classical field strength are established.
Multi-photon propagation in connected structures - a quantum walk - offers the potential for simulating complex physical systems and provides a route to universal quantum computation. Increasing the complexity of quantum photonic networks where the walk occurs is essential for many applications. Here, we implement a quantum walk of indistinguishable photon pairs in a multimode fiber supporting 380 modes. Using wavefront shaping, we control the propagation of the two-photon state through the fiber in which all modes are coupled. Excitation of arbitrary output modes of the system is realized by …
We report generation of near-infrared photon pairs in fundamental spatial modes via type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide supporting multiple transverse modes. This demonstrates experimentally a versatile scheme for controlling the spatial characteristics of the produced nonclassical light based on exploitation of intermodal dispersion. The down-converted photons are characterized by the measurement of the beam quality factors in the heralded regime.
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…
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…
Hyperentangled photonic states - exhibiting nonclassical correlations in several degrees of freedom - offer improved performance of quantum optical communication and computation schemes. Experimentally, a hyperentanglement of transverse-wavevector and spectral modes can be obtained in a straightforward way with multimode parametric single-photon sources. Nevertheless, experimental characterization of such states remains challenging. Not only single-photon detection with high spatial resolution - a single-photon camera - is required, but also a suitable mode-converter to observe the spectral/te…
Multimode photon-subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous-variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the pay-off for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equat…
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