We investigate and characterize the emergence of finite-component dissipative phase transitions (DPTs) in nonlinear photon resonators subject to $n$-photon driving and dissipation. Exploiting a semiclassical approach, we derive general results on the occurrence of second-order DPTs in this class of systems. We show that for all odd $n$, no second-order DPT can occur while, for even $n$, the competition between higher-order nonlinearities determines the nature of the criticality and allows for second-order DPTs to emerge only for $n=2$ and $n=4$. As pivotal examples, we study the full quantum dynamics of three- and four-photon driven-dissipative Kerr resonators, confirming the prediction of the semiclassical analysis on the nature of the transitions. The stability of the vacuum and the typical timescales needed to access the different phases are also discussed. We also show a first-order DPT where multiple solutions emerge around zero, low, and high-photon numbers. Our results highlight the crucial role played by strong and weak symmetries in triggering critical behaviors, providing a Liouvillian framework to study the effects of high-order nonlinear processes in driven-dissipative systems, that can be applied to problems in quantum sensing and information processing.
We calculate the transmission spectra of a flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system constitutes the building block of superconducting circuit QED platforms. The calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the sole influence of the oscillator and of its dissipative environment, an Ohmic heat bath. We find the distinctive features of the qubit-resonator system, namely two-dip structures in the calculated transmission, modified by the presence of the dissipati…
The notion of nonreciprocity, in essence when going forwards is different from going backwards, emerges in all branches of physics from cosmology to electromagnetism. Intriguingly, the breakdown of reciprocity is typically associated with extraordinary phenomena, which may be readily capitalized on in the design of (for example) nontrivial electromagnetic devices when Lorentz reciprocity is broken. However, in order to enable the exploitation of nonreciprocal-like effects in the next generation of quantum technologies, basic quantum optical theories are required. Here we present a versatile mo…
Heralded near-deterministic multi-qubit controlled phase gates with integrated error detection have recently been proposed by Borregaard et al. [Phys. Rev. Lett. 114, 110502 (2015)]. This protocol is based on a single four-level atom (a heralding quartit) and $N$ three-level atoms (operational qutrits) coupled to a single-resonator mode acting as a cavity bus. Here we generalize this method for two distant resonators without the cavity bus between the heralding and operational atoms. Specifically, we analyze the two-qubit controlled-Z gate and its multi-qubit-controlled generalization (i.e., a…
Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, …
A deterministic scheme for generating a macroscopic superposition state of a nanomechanical resonator is proposed. The nonclassical state is generated through a suitably engineered dissipative dynamics exploiting the optomechanical quadratic interaction with a bichromatically driven optical cavity mode. The resulting driven dissipative dynamics can be employed for monitoring and testing the decoherence processes affecting the nanomechanical resonator under controlled conditions.
We present a theoretical treatment for the dissipative two-resonator circuit quantum electrodynamics setup referred to as quantum switch. There, switchable coupling between two superconducting resonators is mediated by a superconducting qubit operating in the dispersive regime, where the qubit transition frequency is far detuned from those of the resonators. We derive an effective Hamiltonian for the quantum switch beyond the rotating wave approximation and study the dissipative dynamics within a Bloch-Redfield quantum master equation approach. We derive analytically how the qubit affects the …
While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implement a reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bo…
A Rabi dimer is used to model a recently reported circuit quantum electrodynamics system composed of two coupled transmission-line resonators with each coupled to one qubit. In this study, a phonon bath is adopted to mimic the multimode micromechanical resonators and is coupled to the qubits in the Rabi dimer. The dynamical behavior of the composite system is studied by the Dirac-Frenkel time-dependent variational principle combined with the multiple Davydov D$_{2}$ ansätze. Initially all the photons are pumped into the left resonator, and the two qubits are in the down state coupled with the …
We present a new approach for deriving exact, closed-form solutions for the steady state of a wide class of driven-dissipative nonlinear resonators that is distinct from more common positive-$P$ function methods. Our method generalizes the coherent quantum absorber approach of Stannigel et al. to include nonlinear driving and dissipation, and relies crucially on exploiting the Segal-Bargmann representation of Fock space. Our solutions and method reveal a wealth of previously unexplored observable phenomena in these systems, including new generalized photon-blockade and anti-blockade effects, a…
We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal invariance violation (TIV) which is induced by two magnetized ferrites. The cavity has the shape of a quarter bowtie billiard of which the corresponding classical dynamics is chaotic. Due to dissipation it is impossible to identify a complete list of resonance frequencies. Based on a random-matrix theory approach we derive analytical expressions for statistical measures of short- and long-rang…
The dispersive regime of circuit QED is the main workhorse for todays quantum computing prototypes based on superconducting qubits. Analytic descriptions of this model typically rely on the rotating wave approximation of the interaction between the qubits and resonators, using the Jaynes-Cummings model as starting point for the dispersive transformation. Here we present analytic results on the dispersive regime of the dissipative Rabi model, without taking the rotating wave approximation of the underlying Hamiltonian. Using a recently developed hybrid perturbation theory based on the expansion…
Driven-Dissipative Dynamics of Measurement-Induced State Transitions
National Taiwan University（台湾大学）；National Tsing Hua University（清华大学）；National Center for Excellence in Quantum Information Science and Engineering, National Tsing Hua University（国家量子信息与工程卓越中心）；National Center for Theoretical Sciences（国家理论科学中心）
Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces. Here we give a theoretical study of a hybrid atom-optomechanical system in which the steady-state squeezing of the mechanical resonator can be generated via the mechanical nonlinearity and cavity cooling process. The validity of the scheme is assessed by simulating the steady-state variance of the mechanical displacement quadrature numerically. The scheme is robust against dissipation of the optical cavity, and the steady-state squeezing can be effecti…
We present theoretical transmission spectra of a strongly driven, damped, flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system, described within a dissipative Rabi model, constitutes the building block of superconducting circuit QED platforms. The addition of a strong drive allows one to characterize the system properties and study novel phenomena, leading to a better understanding and control of the qubit-oscillator system. In this work, the calculated transmission of a weak probe field quantifies the response of the qubit, in freque…
We report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array mod…
Optomechanical system with tunable dissipative and dispersive couplings
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University（山西大学光电研究所量子光学与量子光学器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
We study the unitary time evolution of photons interacting with a dielectric resonator using coherent control pulses. We show that non-Markovianity of transient photon dynamics in the resonator subsystem may be controlled to within a photon-resonator transit time. In general, appropriate use of coherent pulses and choice of spatial subregion may be used to create and control a wide range of non-Markovian transient dynamics in photon resonator systems.
We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories revea…
We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P-representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the mu…
A comparison of different master equations for driven-dissipative dynamics in composite quantum systems: Dispersive readout in structured electromagnetic environments
Sorbonne Université（索邦大学）；Institut des NanoSciences de Paris（巴黎纳米科学研究所）；LPENS, Département de Physique, École Normale Supérieure, Centre Automatique et Systèmes (CAS), MINES ParisTech, Université PSL, Sorbonne Université, CNRS, Inria（物理与能源环境研究实验室，巴黎高等师范学院，自动系统与中央研究院，国立巴黎高等矿业学校，巴黎文理研究大学，索邦大学，法国国家科学研究中心，法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）
We analyze the non-equilibrium behaviour of driven nonlinear photonic resonator arrays under the selective excitation of specific photonic many-body modes. Targeting the unit-filled ground state, we find a counter-intuitive `super bunching' in the emitted photon statistics in spite of relatively strong onsite repulsive interaction. We consider resonator arrays with Kerr nonlinearities described by the Bose Hubbard model, but also show that an analogous effect is observable in near-future experiments coupling resonators to two-level systems as described by the Jaynes Cummings Hubbard Hamiltonia…
Single-photons with high spectro-temporal purity are an essential resource for quantum photonic technologies. The highest reported purity up until now from a conventional silicon photonic device is 92% without any spectral filtering. We have experimentally generated and observed single-photons with 98.0+-0.3 % spectro-temporal purity using a conventional micro racetrack resonator and an engineered dual pump pulse.
Cat states of the microwave field stored in high-Q resonators show great promise for robust encoding and manipulation of quantum information. Here we propose an approach to efficiently prepare such cat states in a Kerr-nonlinear resonator by the use of a two-photon drive. We show that this preparation is robust against single-photon loss. We moreover find that it is possible to remove undesirable phase evolution induced by a Kerr nonlinearity using a two-photon drive of appropriate amplitude and phase. Finally, we present a universal set of quantum logical gates that can be performed on the en…
We propose to generate photon-pair blockade in a Josephson-photonics circuit that consists of a dc voltage-biased Josephson junction in series with a superconducting charge qubit and two nondegenerate microwave resonators. The two-level charge qubit is utilized to create anticorrelations of the charge transport; that is, the simultaneous Cooper pair tunneling events are inhibited. When the Josephson frequency matches the sum of resonance frequencies of the charge qubit and the two resonators, we demonstrate that the two resonators can release their energies in the form of antibunched pairs of …
We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmi…
We study the single photon transfer in a hybrid system where the normal modes of two coupled resonator arrays interact with two transition arms of a ?-type atom localized in the intersectional resonator. It is found that, due to the Fano-Feshbach effect based on the dark state of the ?-type atom, the photon transfer in one array can be well controlled by the bound state of the photon in the other array. This conceptual setup could be implemented in some practical cavity QED system to realize a quantum switch for single photon.
Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-ph…
Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for non-equilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators, coupled nonlinearly by a superconducting quantum interference device (SQUID). We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to…
The coherent nonlinear process where a single photon simultaneously excites two or more two-level systems (qubits) in a single-mode resonator has recently been theoretically predicted. Here we explore the case where the two qubits are placed in different resonators in an array of two or three weakly coupled resonators. Investigating different setups and excitation schemes, we show that this process can still occur with a probability approaching one under specific conditions. The obtained results provide interesting insights into subtle causality issues underlying the simultaneous excitation pr…
High visibility on-chip quantum interference among indistinguishable single-photons from multiples sources is a key prerequisite for integrated linear optical quantum computing. Resonant enhancement in micro-ring resonators naturally enables brighter, purer and more indistinguishable single-photon production without any tight spectral filtering. The indistinguishability of heralded single-photons from multiple micro-ring resonators has not been measured in any photonic platform. Here, we report on-chip indistinguishability measurements of heralded single-photons generated from independent micr…
We study the spectral properties of Markovian driven-dissipative quantum systems, focusing on the nonlinear quantum van der Pol oscillator as a paradigmatic example. We discuss a generalized Lehmann representation, in which single-particle Green's functions are expressed in terms of the eigenstates and eigenvalues of the Liouvillian. Applying it to the quantum van der Pol oscillator, we find a wealth of phenomena that are not apparent in the steady-state density matrix alone. Unlike the steady state, the photonic spectral function has a strong dependence on interaction strength. Further, we fi…
In this work we reproduce the phenomenology of the electromagnetically induced transparency and dynamic Stark effect in a dissipative system composed by two coupled bosonic fields under linear and nonlinear amplification process. Such a system can be used as a quantum switch in networks of oscillators.
The optical scheme is proposed for realization of controlled phase quantum gate based on the off-resonant interaction of photon with three-level atom in single mode QED-cavity. Possible physical implementation of this scheme is discussed.
Quantum thermal transport and two-photon statistics serve as two representative nonequilibrium features in circuit quantum electrodynamics systems. Here, we investigate quantum heat flow and two-photon correlation function at steady-state in a composite qubit-resonator model, where one qubit shows both transverse and longitudinal couplings to a single-mode optical resonator. With weak qubit-resonator interaction, we unravel two microscopic transport pictures, i.e., cotunneling and cyclic heat exchange processes, corresponding to transverse and longitudinal couplings respectively. At strong qub…
Principally, there are two forms of coupling energy when particle(photon) is moving around the micro-ring resonator, which is generated by the construction (creation) and the destruction (annihilation) energies that can disturb the centre nonlinear microring resonator and lead the system unstable from the harmonic motion, from which the squeezing state of the particle can occur. The detected outputs either electrons and their spins or photons can be useful for the new era of electronic devices and circuits, where the classical electronics, plasmonic electronics, spintronic electronics and quan…
We demonstrate that four-wave mixing processes in high-quality non-linear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly anti-bunched photon states.
We give a concrete experimental scheme for engineering the insulator-superfluid transition of light in a one-dimensional (1-D) array of coupled superconducting stripline resonators. In our proposed architecture, the on-site interaction and the photon hopping rate can be tuned independently by adjusting the transition frequencies of the charge qubits inside the resonators and at the resonator junctions, respectively, which permits us to systematically study the quantum phase transition of light in a complete parameter space. By combining the techniques of photon-number-dependent qubit transitio…
We demonstrate time-bin entanglement generation in telecom wavelength using a 7 μm radius Si micro-ring resonator pumped by a continuous wave laser. The resonator structure can enhance spontaneous four wave mixing, leading to a photon pair generation rate of about 90-100 Hz with a laser pump power of as low as -3.92 dBm (0.41 mW). We succeed in observing time-bin entanglement with the visibility over 92%. Moreover, wavelength-tunability of the entangled photon pair is demonstrated by changing the operation temperature.
An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator, and enables to visualize the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.
The future of integrated quantum photonics relies heavily on the ability to engineer refined methods for preparing the quantum states needed to implement various quantum protocols. An important example of such states are quantum-correlated photon pairs, which can be efficiently generated using spontaneous nonlinear processes in integrated microring-resonator structures. In this work, we propose a method for generating spectrally unentangled photon pairs from a standard microring resonator. The method utilizes interference between a primary and a delayed secondary pump pulse to effectively incr…
We study the coherent transport of one or two photons in a 1D waveguide chirally coupled to a nonlinear resonator. Analytic solutions of the one-photon and two-photon scattering is derived. Although the resonator acts as a non-reciprocal phase shifter, light transmission is reciprocal at one-photon level. However, the forward and reverse transmitted probabilities for two photons incident from either the left side or the right side of the nonlinear resonator are nonreciprocal due to the energy redistribution of the two-photon bound state. Hence, the nonlinear resonator acts as an optical diode …
We propose a realizable circuit QED architecture for engineering states of a superconducting resonator off-resonantly coupled to an ancillary superconducting qubit. The qubit-resonator dispersive interaction together with a microwave drive applied to the qubit gives rise to a Kerr resonator with two-photon driving that enables us to efficiently engineer the quantum state of the resonator such as generation of the Schrodinger cat states for resonator-based universal quantum computation. Moreover, the presented architecture is easily scalable for solving optimization problem mapped into the Isin…
We present the dissipative dynamics of the field of two-photon Jaynes-Cummings model (JCM) with Stark shift in dispersive approximation and investigate the influence of dissipation on entanglement. We show the coherence properties of the field can be affected by the dissipative cavity when nonlinear two-photon process is involved.
We experimentally study an optomechanical cavity that is formed between a mechanical resonator, which serves as a movable mirror, and a stationary on-fiber dielectric mirror. A significant change in the behavior of the system is observed when the distance between the fiber's tip and the mechanical resonator is made smaller than about 1 micrometer. The observed effects are attributed to the combined influence of Casimir force, Coulomb interaction due to trapped charges, and optomechanical coupling. The comparison between experimental results and theory yields a partial agreement.
Based on a microwave-photon quantum processor with two superconducting resonators coupled to one transmon qutrit, we construct the controlled-phase (c-phase) gate on microwave-photon-resonator qudits, by combination of the photon-number-dependent frequency-shift effect on the transmon qutrit by the first resonator and the resonant operation between the qutrit and the second resonator. This distinct feature provides us a useful way to achieve the c-phase gate on the two resonator qudits with a higher fidelity and a shorter operation time, compared with the previous proposals. The fidelity of ou…
We propose a tunable nonlinear interaction for the implementation of quantum logic operations on pairs of superconducting resonators, where the two-resonator interaction is mediated by a transmon quantum bit (qubit). This interaction is characterized by a high on-to-off coupling ratio and allows for fast qubit-type and $d$-level system (qudit)-type operations for quantum information processing with multiphoton cavity states. We present analytical and numerical calculations showing that these operations can be performed with practically unit fidelity in absence of any dissipative phenomena, whe…
We investigate the frequency estimation of an optical field suffering from an unavoidable dissipative environment. Generally, dissipative noises greatly reduce the precision. Here, we find that two-photon driving can improve the measurement precision by resisting the noises. Moreover, in long time, the uncertainty of frequency can be close to 0 with a proper magnitude of the parametric two-photon drive, which is in sharp contrast to the uncertainty going to infinity without the two-photon driving. Our results show that two-photon driving can realize the ultrasensitive measurement in dissipativ…
We present a scalable quantum-bus-based device for generating the entanglement on microwave photons (MPs) in distant superconducting resonators (SRs). Different from the processors in previous works with some resonators coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs $r_j$ which are coupled to the quantum bus (another common resonator $R$) in its different positions simply, assisted by superconducting quantum interferometer devices. By using the technique for catching and releasing a MP state in a 1D SR, it can work as an entanglement generator or a node in quant…
We study Landau-Zener-Stückelberg (LZS) interferometry in a cQED architecture under effects of dissipation. To be specific, we consider a superconducting qubit driven by a dc+ac signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for arbitrary amplitude of the drive and different time scales. We unveil important differences in the…
Arrays of coupled photonic cavities driven by external lasers represent a highly controllable setup to explore photonic transport. In this paper we address (quasi)-steady states of this system that exhibit photonic currents introduced by engineering driving and dissipation. We investigate two approaches: in the first one, photonic currents arise as a consequence of a phase difference of applied lasers and in the second one, photons are injected locally and currents develop as they redistribute over the lattice. Effects of interactions are taken into account within a mean-field framework. In th…
We investigate the driven quantum phase transition between the oscillating motion and the classical nearly free rotations of the Josephson pendulum coupled to a harmonic oscillator in the presence of dissipation. We refer to this as the Josephson-Rabi model. This model describes the standard setup of circuit quantum electrodynamics, where typically a transmon device is embedded in a superconducting cavity. We find that by treating the system quantum mechanically this transition occurs at higher drive powers than expected from an all-classical treatment, which is a consequence of the quasiperio…
