Configurable and scalable continuous variable quantum networks for measurement-based quantum information protocols or multipartite quantum communication schemes can be obtained via parametric down conversion (PDC) in non-linear waveguides. In this work, we exploit symmetric group velocity matching (SGVM) to engineer the properties of the squeezed modes of the PDC. We identify type II PDC in a single waveguide as the best suited process, since multiple modes with non-negligible amount of squeezing can be obtained. We explore, for the first time, the waveguide dimensions, usually only set to ensure single-mode guiding, as an additional design parameter ensuring indistinguishability of the signal and idler fields. We investigate here potassium titanyl phosphate (KTP), which offers SGVM at telecommunications wavelengths, but our approach can be applied to any non-linear material and pump wavelength. This work paves the way towards the engineering of future large-scale quantum networks in the continuous variable regime.
A scheme for spatial multimode quantum memory is developed such that spatial-temporal structure of a weak signal pulse can be stored and recalled via cavity-assisted off-resonant Raman interaction with a strong angular-modulated control field in an extended $Λ$-type atomic ensemble. It is shown that effective multimode storage is possible when the Raman coherence spatial grating involves wave vectors with different longitudinal components relative to the paraxial signal field. The possibilities of implementing the scheme in the solid-state materials are discussed.
Schemes for generation and protocols for network teleportation of multimode entangled cat-states are proposed. Explicit expressions for probability of successful teleportation are derived for both symmetric and asymmetric networks.
We compare phase matching for four-wave mixing using one, two, three, and four waveguide modes. For the comparison, we use numerical optimizations and an estimate of the generated idler power. We present results for few-mode fibers and nano-rib waveguides and show that for both waveguide types, four-wave mixing bandwidths and idler powers are best for one- and two-mode operation and that four-mode four-wave mixing is not feasible at all. Some nano-rib waveguides support three-mode four-wave mixing, albeit with much reduced bandwidth and reduced idler power.
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…
We are motivated by tripartite entanglement for fermions. While GHZ or W states involve 3-fold intrication, we consider here piecewise intrication of 3 fermions in ${\bf C}^2$, namely of type $ab+bc+ca$. Before interaction with Stern-Gerlach apparatus, qu-bits are distinguishable; at the output however they turn into un-distinguishable particles, whose anti-symmetric wave function is of the form $\det(b-a,c-a)$ (affine determinant). More generally, $d+1$ intricated fermions in ${\bf C}^d$ can be represented by the anti-symmetric wave function $\det(a_1-a_0,a_2-a_0,\cdots,a_d-a_0)$. We investig…
We extend the generalize conservation law of light propagating in a one-dimensional $\cal PT$-symmetric system, i.e., $|T-1|=\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\cal PT$ or $\cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first tim…
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…
We report experimental determination of the phase-matching function for type-II three-wave mixing in a periodically poled KTiOPO_4 waveguide in the 792-815 nm spectral region. The measurement was performed by sum-frequency generation of spectrally tuned fundamental components. Strong dependence of the observed signal on the excited spatial modes in the waveguide has been observed and fully interpreted. These results indicate a route to employ the waveguide for spontaneous parametric down-conversion producing photon pairs in well-defined spatial modes.
We present a multimode theory of non-Gaussian operation induced by an imperfect on/off-type photon detector on a splitted beam from a wideband squeezed light. The events are defined for finite time duration $T$ in the time domain. The non-Gaussian output state is measured by the homodyne detector with finite bandwidh $B$. Under this time- and band-limitation to the quantm states, we develop a formalism to evaluate the frequency mode matching between the on/off trigger channel and the conditional signal beam in the homodyne channel. Our formalism is applied to the CW and pulsed schemes. We expl…
We analyze homodyne detection of macroscopically bright multimode nonclassical states of light and propose their application in quantum communication. We observe that the homodyne detection is sensitive to a mode-matching of the bright light to the highly intense local oscillator. Unmatched bright modes of light result in additional noise which technically limits detection of Gaussian entanglement at macroscopic level. When the mode-matching is sufficient, we show that multimode quantum key distribution with bright beams is feasible. It finally merges the quantum communication with classical o…
Wavevector quasi-phase matching was devised in the 1960s as a way to boost nonlinear interactions with efficient quantum noise squeezing as one outstanding outcome. In the era of quantum technologies, we propose a new coupling quasi-phase matching for efficient generation of multimode downconverted quantum light in nonlinear waveguide arrays. We highlight this technique achieving multimode quantum entanglement and Einstein-Podolsky-Rosen steering buildup. We discuss the feasibility of this method with current technology and demonstrate its competitiveness as a resource for continuous variables…
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…
Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT-symmetric dynamics and unidirectional coupling
We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. We demonstrate its advantages using high-gain parametric down conversion (PDC) as an example. By generating the sum frequency in the near-surface region of a nonlinear crystal, we increase the SFG efficiency and get rid of the modulation caused by chromatic dispersion, known as Maker fringes. The obtained results interpreted in terms of the Schmidt mode formalism reveal the sensitivity of the SFG spectrum to the number of frequency modes. Furthermore, we demonstrate efficient n…
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…
Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides. We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks. Our protocol is…
Single-photon addition to multimode quantum fields at telecom wavelengths using lithium niobate and its doped variants
School of Quantum Technology, Defence Institute of Advanced Technology（国防先进技术研究院量子技术学院）；Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France（卡斯勒·布罗塞尔实验室，索邦大学，法国国家科学研究中心，巴黎文理研究大学，法兰西学院）
We experimentally demonstrate the conversion of a Gaussian beam to an approximate Bessel-Gauss mode by making use of a non-collinear four-wave mixing process in hot atomic vapor. The presence of a strong, spatially non-Gaussian pump both converts the probe beam into a non-Gaussian mode, and generates a conjugate beam that is in a similar non-Gaussian mode. The resulting probe and conjugate modes are compared to the output of a Gaussian beam incident on an annular aperture that is then spatially filtered according to the phase-matching conditions imposed by the four-wave mixing process. We find…
Discrete PT-symmetric square wells are studied. Their wave functions are found proportional to classical Tshebyshev polynomials of complex argument. The compact secular equations for energies are derived giving the real spectra in certain intervals of non-Hermiticity strengths Z. It is amusing to notice that although the known square well re-emerges in the usual continuum limit, a twice as rich, upside-down symmetric spectrum is exhibited by all its present discretized predecessors.
The existence of vacuum fluctuations is one of the most important predictions of modern quantum field theory. In the vacuum state, fluctuations occurring at different frequencies are uncorrelated. However, if a parameter in the Lagrangian of the field is modulated by an external pump, vacuum fluctuations stimulate spontaneous downconversion processes, creating squeezing between modes symmetric with respect to half of the frequency of the pump. Here we show that by double parametric pumping of a superconducting microwave cavity, it is possible to generate another fundamental type of correlation…
We demonstrate an unseeded, multimode four-wave mixing process in hot $^{85}$Rb vapor, using two pump beams of the same frequency that cross at a small angle. This results in the simultaneous fulfillment of multiple phase-matching conditions that reinforce one another to produce four intensity-stabilized bright output modes at two different frequencies. Each generated photon is directly correlated to exactly two others, resulting in the preferred four-mode output, in contrast to other multimode four-wave mixing experiments. This provides significant insight into the optimal configuration of th…
We investigate the action of local unitary operations on multimode (pure or mixed) Gaussian states and single out the minimal number of locally invariant parametres which completely characterise the covariance matrix of such states. For pure Gaussian states, central resources for continuous-variable quantum information, we investigate separately the parametre reduction due to the additional constraint of global purity, and the one following by the local-unitary freedom. Counting arguments and insights from the phase-space Schmidt decomposition and in general from the framework of symplectic an…
Squeezing measurement with spectrally broadened in microstructured fiber local oscillator
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；M.V.Lomonosov Moscow State University（莫斯科国立大学）；Dianov Fiber Optics Research Center（季阿诺夫光纤研究中心）
We investigate localization of entanglement of multimode Gaussian states into a pair of modes by local Gaussian measurements on the remaining modes and classical communication. We find that for pure states and for mixed symmetric states maximum entanglement between two modes can be localized by local homodyne detections, i.e. projections onto infinitely squeezed states. We also show that non-Gaussian measurements allow to localize more entanglement than Gaussian ones.
In fiber based Fabry-Pérot Cavities (FFPCs), limited spatial mode matching between the cavity mode and input/output modes has been the main hindrance for many applications. We have demonstrated a versatile mode matching method for FFPCs. Our novel design employs an assembly of a graded-index and large core multimode fiber directly spliced to a single mode fiber. This all-fiber assembly transforms the propagating mode of the single mode fiber to match with the mode of a FFPC. As a result, we have measured a mode matching of 90\% for a cavity length of $\sim$400 $μm$. This is a significant impro…
We present a feasible scheme to use trapped ions Cavity QED system to implement optimal $1\to N$ cloning machine of coherent state. In present scheme, as the ouput of the clone machine, the copies of the cavity mode emerge at the vibrational modes and cavity modes is acted as the ancilla mode in the implementation of the cloning. We further show that such system can be used to generated multimodes quantum state, which can realize optimum symmetric $1\to N$ telecloning of coherent state of distant cavity.
Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their con…
Polarisation-resolved identification of spontaneous four-wave mixing processes in a multimode fused tapered fibre coupler
University of Ottawa（渥太华大学）；National Research Council of Canada（加拿大国家研究委员会）；Nexus for Quantum Technologies, Department of Physics, University of Ottawa（渥太华大学物理系量子技术联盟）；Département de physique et astronomie, Université de Moncton（蒙克顿大学物理与天文学系）；Quantinuum；Corning Incorporated（康宁公司）
In a PT symmetrically complexified square well, bound states are constructed by the matching technique. Their energies prove real in a domain of weak non-Hermiticity, and continuous in the Hermitian limit. At a sequence of certain strong-Hermiticity thresholds, the lowest two energies merge and disappear.
Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. Therefore, it is important to have control over the generation of these resonances. In this work, we show through ab initio simulations of coupled light-matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to …
In this paper, we focus on the quantum communication complexity of functions of the form $f \circ G = f(G(X_1, Y_1), \ldots, G(X_n, Y_n))$ where $f: \{0, 1\}^n \to \{0, 1\}$ is a symmetric function, $G: \{0, 1\}^j \times \{0, 1\}^k \to \{0, 1\}$ is any function and Alice (resp. Bob) is given $(X_i)_{i \leq n}$ (resp. $(Y_i)_{i \leq n}$). Recently, Chakraborty et al. [STACS 2022] showed that the quantum communication complexity of $f \circ G$ is $O(Q(f)\mathrm{QCC}_\mathrm{E}(G))$ when the parties are allowed to use shared entanglement, where $Q(f)$ is the query complexity of $f$ and $\mathrm{Q…
We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such a modal phase matching paves the way …
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then an…
We present a theoretical method to determine the multipartite entanglement between different partitions of multimode, fully or partially symmetric Gaussian states of continuous variable systems. For such states, we determine the exact expression of the logarithmic negativity and show that it coincides with that of equivalent two--mode Gaussian states. Exploiting this reduction, we demonstrate the scaling of the multipartite entanglement with the number of modes and its reliable experimental estimate by direct measurements of the global and local purities.
