We study the non-Markovian quantum dynamics of an emitter inside an open multimode cavity, focusing on the case where the emitter is resonant with high-frequency cavity modes. Based on a Green's function technique suited for open photonic structures, we study the crossovers between three distinct regimes as the coupling strength is gradually increased: (i) overdamped decay with a time scale given by the Purcell modified decay rate, (ii) underdamped oscillations with a time scale given by the effective vacuum Rabi frequency, and (iii) pulsed revivals. The final multimode strong coupling regime (iii) gives rise to quantum revivals of the atomic inversion on a time scale associated with the cavity round-trip time. We show that the crucial parameter to capture the crossovers between these regimes is the nonlinear Lamb shift, accounted for exactly in our formalism.
We introduce a new multimode cavity QED architecture for superconducting circuits which can be used to implement photonic memories, more efficient Purcell filters, and quantum simulations of photonic materials. We show that qubit interactions mediated by multimode cavities can have exponentially improved contrast for two qubit gates without sacrificing gate speed. Using two-qubits coupled via a three-mode cavity system we spectroscopically observe multimode strong couplings up to 102MHz and demonstrate suppressed interactions off-resonance of 10kHz when the qubits are ~600MHz detuned from the …
We present a novel cavity QED system in which a Bose-Einstein condensate (BEC) is trapped within a high-finesse optical cavity whose length may be adjusted to access both single-mode and multimode configurations. We demonstrate the coupling of an atomic ensemble to the cavity in both configurations. The atoms are confined either within an intracavity far-off-resonance optical dipole trap (FORT) or a crossed optical dipole trap via transversely oriented lasers. Multimode cavity QED provides fully emergent and dynamical optical lattices for intracavity BECs. Such systems will enable explorations…
In-situ Characterization of Light-Matter Coupling in Multimode Circuit-QED Systems
University of Maryland, College Park（马里兰大学帕克分校）；Joint Quantum Institute, NIST/University of Maryland（量子联合研究所，美国国家标准与技术研究院/马里兰大学）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算科学联合中心，美国国家标准与技术研究院/马里兰大学）；Johns Hopkins Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）
Multimode-cavity picture of non-Markovian waveguide QED
Universität Ulm（乌尔姆大学）；NEST, Istituto Nanoscienze-CNR（意大利国家纳米科学技术研究所（NEST））；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
Quantum transmission lines are a central to superconducting and hybrid quantum computing. Parallel to these developments are those of left-handed meta-materials. They have a wide variety of applications in photonics from the microwave to the visible range such as invisibility cloaks and perfect flat lenses. For classical guided microwaves, left-handed transmission lines have been proposed and studied on the macroscopic scale. We combine these ideas in presenting a left-handed/right-handed hybrid transmission line for applications in quantum optics on a chip. The resulting system allows circuit…
Multimode Strong-Coupling Processes in Circuit QED Lattices
University of Maryland, College Park（马里兰大学帕克分校）；Joint Quantum Institute, NIST/University of Maryland（NIST/马里兰大学联合量子研究所）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（NIST/马里兰大学量子信息与计算科学联合中心）；Johns Hopkins Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）
We study an atom-cavity system in which the cavity has several degenerate transverse modes. Mode-resolved cavity transmission spectroscopy reveals well-resolved atom-cavity resonances for several cavity modes, a signature of collective strong coupling for the different modes. Furthermore, the experiment shows that the cavity modes are coupled via the atomic ensemble contained in the cavity. The experimental observations are supported by a detailed theoretical analysis. The work paves the way to the use of interacting degenerate modes in cavity-based quantum information processing, where qubits…
In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are n…
Multimode cavity quantum electrodynamics ---where a two-level system interacts simultaneously with many cavity modes---provides a versatile framework for quantum information processing and quantum optics. Due to the combination of long coherence times and large interaction strengths, one of the leading experimental platforms for cavity QED involves coupling a superconducting circuit to a 3D microwave cavity. In this work, we realize a 3D multimode circuit QED system with single photon lifetimes of $2$ ms and cooperativities of $0.5-1.5\times10^9$ across 9 modes of a novel seamless cavity. We d…
Previous realizations of synthetic gauge fields for ultracold atoms do not allow the spatial profile of the field to evolve freely. We propose a scheme which overcomes this restriction by using the light in a multimode cavity, in conjunction with Raman coupling, to realize an artificial magnetic field which acts on a Bose-Einstein condensate of neutral atoms. We describe the evolution of such a system, and present the results of numerical simulations which show dynamical coupling between the effective field and the matter on which it acts. Crucially, the freedom of the spatial profile of the f…
We propose that condensed matter phenomena involving the spontaneous emergence and dynamics of crystal lattices can be realized in the setting of ultracold Bose-condensed atoms coupled to multimode cavities. Previously, it was shown that in the case of a transversely pumped single-mode cavity, the atoms self-organize at either the even or the odd antinodes of the cavity mode, given sufficient pump intensity, and hence spontaneously break a discrete translational symmetry. Here, we demonstrate that in multimode cavities the self-organization brings the additional feature of continuous translati…
Sign-changing interactions constitute a crucial ingredient in the creation of frustrated many-body systems such as spin glasses. We present here the demonstration of a photon-mediated sign-changing interaction between Bose-Einstein condensed (BEC) atoms in a confocal cavity. The interaction between two atoms is of an unusual, nonlocal form proportional to the cosine of the inner product of the atoms' position vectors. This interaction arises from the differing Gouy phase shifts of the cavity's degenerate modes. Moreover, these Gouy phase anomalies induce an extra pattern of Z_2-symmetry-breaki…
Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic pos…
We address the intrinsic multimode nature of the quantum state of light obtained by pulsed spontaneous parametric downconversion and develop a theoretical model based only on experimentally accessible quantities. We exploit the pairwise entanglement as a resource for conditional multimode measurements and derive closed formulas for the detection probability and the density matrix of the conditional states. We present a set of experiments performed to validate our model in different conditions that are in excellent agreement with experimental data. Finally, we evaluate nonGaussianity of the con…
We study the process of multimode Spontaneous Parametric Down--Conversion (SPDC) in the lossy, one dimensional waveguide. We propose a description using first order Correlation Functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with a complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three wave mixing with ultr…
The study of light-matter interaction has seen a resurgence in recent years, stimulated by highly controllable, precise, and modular experiments in cavity quantum electrodynamics (QED). The achievement of strong coupling, where the coupling between a single atom and fundamental cavity mode exceeds the decay rates, was a major milestone that opened the doors to a multitude of new investigations. Here we introduce multimode strong coupling (MMSC), where the coupling is comparable to the free spectral range (FSR) of the cavity, i.e. the rate at which a qubit can absorb a photon from the cavity is…
Circuit quantum electrodynamics (QED) studies the interaction of artificial atoms, open transmission lines and electromagnetic resonators fabricated from superconducting electronics. While the theory of an artificial atom coupled to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a first-principles model of a multimode resonator coupled to a Josephson junction atom. Studying the model in the absence of any cutoff, in which the coupling rate to mode number $n$ scales as $\sqrt{n}$ for $n$ up to $\infty$, …
Optical cavities can induce photon-mediated interactions among intracavity-trapped atoms. Multimode cavities provide the ability to tune the form of these interactions, e.g., by inducing a nonlocal, sign-changing term to the interaction. By accounting for the Gouy phase shifts of the modes in a nearly degenerate, confocal, Fabry-Perot cavity, we provide a theoretical description of this interaction, along with additional experimental confirmation to complement that presented in the companion paper, Ref. [1]. Furthermore, we show that this interaction should be written in terms of a complex ord…
We study the quantum correlations induced by spontaneous parametric down-conversion (SPDC) of a frequency comb. We derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. After applying it to the relevant example of a spectrally chirped pump, we run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. To assess the adva…
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 show that spontaneous Raman scattering of incident radiation can be observed in cavity-QED systems without external enhancement or coupling to any vibrational degree of freedom. Raman scattering processes can be evidenced as resonances in the emission spectrum, which become clearly visible as the cavity-QED system approaches the ultrastrong coupling regime. We provide a quantum mechanical description of the effect, and show that ultrastrong light-matter coupling is a necessary condition for the observation of Raman scattering. This effect, and its strong sensitivity to the system parameters…
We present a Heisenberg-Langevin formalism to study the effective dynamics of a superconducting qubit coupled to an open multimode resonator, without resorting to the rotating wave, two level, Born or Markov approximations. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the openness of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes. A well-behaved time domain perturbation theory is …
We study the probe spectrum of light generated by spontaneous emission into the mode of a cavity QED system. The probe spectrum has a maximum on-resonance when the number of inverted atoms for an input drive is maximal. For a larger number of atoms N, the maximum splits and develops into a doublet, but its frequencies are different from those of the so-called vacuum Rabi splitting.
We study the light generated by spontaneous emission into a mode of a cavity QED system under weak excitation of the orthogonally polarized mode. Operating in the intermediate regime of cavity QED with comparable coherent and decoherent coupling constants, we find an enhancement of the emission into the undriven cavity mode by more than a factor of 18.5 over that expected by the solid angle subtended by the mode. A model that incorporates three atomic levels and two polarization modes quantitatively explains the observations.
Here we demonstrate generating and storing entanglement in a solid state spin-wave quantum memory with on-demand read out using the process of rephased amplified spontaneous emission (RASE). Amplified spontaneous emission (ASE), resulting from an inverted ensemble of Pr$^{3+}$ ions doped into a Y$_2$SiO$_5$ crystal, generates entanglement between collective states of the praseodymium ensemble and the output light. The ensemble is then rephased using a four-level photon echo technique. Entanglement between the ASE and its echo is confirmed and the inseparability violation preserved when the RAS…
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.
We present results of numerical investigation of a microscopic dynamics of a two-level atom embedded into a ``linear crystal'' of other two-level atoms. These additional atoms play a role of a material media. All atoms interact with a multimode cavity field. We study how the decay of the initially excited atom is affected by the presence of material media and spectral properties of the cavity field.
The electromagnetic field inside an isotropic optically active medium is quantized on the base of Fedorov's model for optical activity. The modified photon propagator is derived. Using this result it is shown that the QED correction to the electron mass contains chiral terms which nevertheless are parity invariant. The spontaneous emission rate of a two-level atom is shown to increase in the medium. The spontaneously emitted radiation is partially polarized.
In this work, we consider atomic spontaneous emission in a system consisting of two identical two-level atoms interacting dispersively with the quantized electromagnetic field in a high-Q cavity. We investigate the destructive effect of the atomic decay on the generation of maximally entangled states, following the proposal by Zheng S B and Guo G C (2000 Phys. Rev. Lett. 85 2392). In particular, we analyze the fidelity of teleportation performed using such a noisy channel and calculatethe maximum spontaneous decay rate we may have in order to realize teleportation.
We utilize high-bandwidth phase quadrature homodyne measurement of the light transmitted through a Fabry-Perot cavity, driven strongly and on resonance, to detect excess phase noise induced by a single intracavity atom. We analyze the correlation properties and driving-strength dependence of the atom-induced phase noise to establish that it corresponds to the long-predicted phenomenon of spontaneous dressed-state polarization. Our experiment thus provides a demonstration of cavity quantum electrodynamics in the strong driving regime, in which one atom interacts strongly with a many-photon cavi…
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.
By placing an atom into a cavity, the electromagnetic mode structure of the cavity is modified. In Cavity QED, one manifestation of this phenomenon is the appearance of a gauge-dependent diamagnetic term, known as the $A^2$ contribution. Although in atomic Cavity QED, the resulting modification in the eigenmodes is negligible, in recent superconducting circuit realizations, such corrections can be observable and may have qualitative implications. We revisit the canonical quantization procedure of a circuit QED system consisting of a single superconducting transmon qubit coupled to a multimode …
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. In that respect, hybrid quantum systems combining circuit QED with ions doped into solids are an attractive platform. There, the ions serve as coherent memory elements and reversible conversion elements of microwave to optical qubits. Among many possible spin-doped solids, erbium ions offer the unique opportunity of a coherent conversion of microwave photons into the telecom C-band at $1.54\,μ$m employed for long distance communication. In…
We investigate spontaneous photon emission processes of two-level atoms in parabolic and ellipsoidal cavities thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms and the energy density of the resulting few-photon electromagnetic radiation field by using semiclassical methods for the description of the multimode scenario. Based on this approach photon path representations are developed for relevant transition probability amplitudes which are valid in the optical frequency regime where the dipole and the rotating-wave app…
We investigate an acoustical analog of circuit quantum electrodynamics that facilitates compact high-Q (${>}20,000$) microwave-frequency cavities with dense spectra. We fabricate and characterize a device that comprises a flux tunable transmon coupled to a $300\,\mathrm{μm}$ long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches $6.5\,\mathrm{MHz}$, exceeding the cavity loss rate ($200\,\mathrm{kHz}$), qubit linewidth ($1.1\,\mathrm{MHz}$), and the cavity free spectral range ($4.8\,\mathrm{MHz}$), placing the device in both the strong coupling and strong multim…
An important challenge in non-Markovian open quantum systems is to understand what information we gain from continuous measurement of an output field. For example, atoms in multimode cavity QED systems provide an exciting platform to study many-body phenomena in regimes where the atoms are strongly coupled amongst themselves and with the cavity, but the strong coupling makes it complicated to infer the conditioned state of the atoms from the output light. In this work we address this problem, describing the reduced atomic state via a conditioned hierarchy of equations of motion, which provides…
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.
Robust and reliable method for reconstructing quasi-distributions of integrated intensities of twin beams generated in spontaneous parametric down-conversion and entangled in photon numbers is suggested. It utilizes the first and second photocount moments and minimizes the declination from experimental photocount histograms. Qualitatively different forms of quasi-distributions for quantum and classical states are suggested in the method. The transition from quantum to classical states caused by an increased detection noise is discussed. Momentum criterion for non-classicality of twin beams is …
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）
We investigate the quantum electrodynamics of a single two-level atom located at the focus of a parabolic cavity. We first work out the modifications of the spontaneous emission induced by the presence of this boundary in the optical regime, where the dipole and the rotating-wave approximations apply. Furthermore, the single-photon state that leaves the cavity asymptotically is determined. The corresponding time-reversed single-photon quantum state is capable of exciting the atom in this extreme multimode scenario with near-unit probability. Using semiclassical methods, we derive a photon-path…
We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations…
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…
Do the wavepacket-size of free-electron wavefunction and its history have physical effect in its interaction with light? Here we answer this problem by analyzing a QED model, considering both spontaneous and stimulated emission of quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission/absorption of photons has a dependence on wavepacket size that decays when it exceeds the interacting radiation wavelength, consistently and complementarily with Schrodinger equation analysis of wavepacket acceleration in classical electromagnetic field. Furthermore…
Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy…
We resolve phonon number states in the spectrum of a superconducting qubit coupled to a multimode acoustic cavity. Crucial to this resolution is the sharp frequency dependence in the qubit-phonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by $\sim40$ acoustic wavelengths. In analogy to double-slit diffraction, the resulting self-interference generates high-contrast frequency structure in the qubit-phonon interaction. We observe this frequency structure both in the coupling rate to multiple cavity modes and in the qubit spontaneous emission…
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…
Based on a multimode multilevel Jaynes-Cummings model and multiphoton resonance theory, a set of universal two- and three-qubit gates, namely the iSWAP and the Fredkin gates, has been realized where dual-rail qubits are encoded in cavities. In this way the information has been stored in cavities and the off-resonant atomic levels have been eliminated by the semi-classical theory of an effective two-level Hamiltonian. A further semi-classical model, namely the spin-$J$ model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multil…
