We investigate the behaviour of quantum CHSH-nonlocality, $\rm F_3$-steering, and usefulness for teleportation in an interacting two-qubit dissipative system. We show regimes where these three quantum correlations can be extracted by means of local filtering operations, despite them not being displayed in the bare natural time evolution. Moreover, we show the existence of local hidden state (LHS) and local hidden variable (LHV) models for some states during the dynamics and thus, showing that apparently-useless physical systems could still exhibit quantum correlations, which are hidden from us, but that can still be revealed by means of local filtering operations and therefore, displaying the phenomenon of \emph{hidden} quantum correlations. We furthermore show that there actually exists a trade-off between the amount of quantum correlations which can be extracted and the filtering probability with which such protocol can be implemented. From a theoretical point of view, the existence of such trade-off imposes a fundamental limit to the extraction of quantum correlations by local filtering operations. From a practical point of view on the other hand, the results here presented determine the amount of resources that should be invested in order to extract such maximal hidden quantum correlations.
Cavity-optomechanics enables photon-phonon interaction and correlations by harnessing the radiation-pressure force. Here, we realize a ``cavity-in-a-membrane'' optomechanical architecture which allows detection of the motion of lithographically-defined, ultrathin membranes via an integrated optical cavity. Using a dissipative filtering method, we are able to eliminate the probe light in situ and observe photon-phonon correlations associated with the low-frequency membrane mechanical mode. The developed method is generally applicable for study of low-frequency light scattering processes where c…
A longstanding challenge in nonequilibrium thermodynamics is to predict the emergence of self-organized behaviours and functionalities typical of living matter. Despite the progress with classical complex systems, it remains far from obvious how to extrapolate these results down to the quantum scale. Here, we employ the paradigmatic master equation framework to establish that some lifelike behaviours and functionalities can indeed emerge in elementary dissipative quantum systems driven out of equilibrium. Specifically, we find both energy-avoiding (low steady dissipation) and energy-seeking be…
Periodically driven closed quantum many-body systems are known to exhibit prethermal or quasi-steady-state dynamics. In this work, we theoretically show that such prethermal phases can appear in the dynamics of a dipolar two-spin-$1/2$ system coupled to a heat bath if the cross terms between the drive and dipolar interactions are taken into consideration. To this end, we use our recently-reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)], to show that the predicted dynamics can successfully explain the experimentally obs…
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to study driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary reduce the entropy of the many-body sta…
To understand the dynamical origin of the measurement in quantum mechanics, several models have been put forward which have a quantum system coupled to an apparatus. The system and the apparatus evolve in time and the Born rule for the system to be in various eigenstates of the observable is naturally obtained. In this work, we show that the effect of the drive-induced dissipation in such a system can lead to the Born rule, even if there is no separate apparatus. The applied drive needs to be much stronger than the system-environment coupling. In this condition, we show that the dynamics of a …
Quantum Filtering and Stabilization of Dissipative Quantum Systems via Augmented Neural Ordinary Differential Equations
School of Science, Harbin Institute of Technology, Shenzhen（哈尔滨理工大学深圳学院）；Shenzhen Key Laboratory of Advanced Functional Carbon Materials Research and Comprehensive Application（深圳市先进功能碳材料研究与综合应用重点实验室）
We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are du…
Due to growing interest in quantum measurement, control and feedback, we reproduce a manuscript from 1992, presenting a simple physical and mathematical derivation of stochastic differential equations for wave functions of probed quantum systems. V. P. Belavkins seminal quantum filtering theory with similar equations, developed in the 1980es, was not known to the authors at the time of writing of the present manuscript.
We predict the emergence of a time crystal generated by an incoherently driven and dissipative nonlinear optical oscillator, where the nonlinearity also comes from dissipation. We show that a second-order dissipative phase transition of light occurs in the frame rotating at the cavity frequency, while a boundary (dissipative) time crystal emerges in the laboratory frame. We relate these two phenomena by using the Liouvillian superoperator associated with the Lindblad master equation and its symmetries. These results connect the emergence of a second-order dissipative phase transition and a dis…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum trajectories in quantum state diffusion approach. Quantum dynamical manifestation of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement are studied by numerical simulation of ensemble averaged Wigner function and von Neumann entropy.
A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analogue of such a theory. Specifically, we consider local dissipative dynamics preparing a steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes satisfying detailed balance, ther…
We investigate steady-state properties of a two-dimensional incoherent-pumped dissipative Bose-Hubbard model, which describes a photon square lattice. This incoherent pumping exhibits an important environment-induced higher-order fluctuation effect, which induces a strong competition between the driven-dissipative channel, the photon-photon interaction, and the photon hopping in multi-photon processes. This new competition gives rise to a spontaneous breaking of the U(1) symmetry of system. As a result, we predict a many-body steady-state localized-delocalized phase transition and an anti-bloc…
The interaction of a quantum system, which is not accessible by direct measurement, with an external probe can be exploited to infer specific features of the system itself. We introduce a probing scheme based on the emergence of spontaneous quantum synchronization between an out-of-equilibrium qubit, in contact with an external environment, and a probe qubit. Tuning the frequency of the probe leads to a transition between synchronization in phase and antiphase. The sharp transition between these two regimes is locally accessible by monitoring the probe dynamics alone and allows one to reconstr…
We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy contact with an environment. We use the Loschmidt echo and local observables to indicate the presence of a finite sized dissipative time crystal. Starting from the closed Hubbard model we then provide examples of dissipation mechanisms that yield experimentally observable quantum periodic dynamics and allow analysis of the emergence of finite sized dissipative…
Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for the quantum master equation. In both cases, the maximally predictive states for the harmonic oscillator are the coherent states, which is the same result found by Zurek,Habib and Paz for the Calde…
We consider a linear chain made of spins of one half in contact with a dissipative environment for which periodic delta-kicks are applied to the qubits of the linear chain in two different configurations: kicks applied to a single qubit and simultaneous kicks applied to two qubits of the linear chain. In both cases the system reaches a non-equilibrium stationary condition in the long time limit. We study the transient to the quasi stationary states and their properties as function of the kick parameters in the single kicked qubit case and report the emergence of stationary entanglement between…
Recent experiments show that periodic drives on dipolar systems lead to long-lived prethermal states. These systems are weakly coupled to the environment and reach prethermal states in a timescale much shorter than the timescale for thermalization. Such nearly-closed systems have previously been analyzed using Floquet formalism, which shows the emergence of a prethermal plateau. We use a fluctuation-regulated quantum master equation (FRQME) to describe these systems. In addition to the system-environment coupling, FRQME successfully captures the dissipative effect from the various local intera…
Multicritical dissipative phase transitions manipulated by dipole--dipole interactions
College of Physics, Sichuan University（四川大学物理学院）；School of Physics and Hubei Key Laboratory of Gravitation and Quantum Physics, Huazhong University of Science and Technology（华中科技大学物理科学与技术学院）
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a dissipative process. We obtain our results in a random quantum circuit model that is constrained to have a conservation law. We find that a generic spreading operator consists of two parts: (i) a conserved part which comprises the wei…
We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete $\mathbb Z_2$ spatial symmetry which, depending on the strength of the drive, can be broken in the time-crystalline phase or it cannot. An exact semiclassical mean-field analysis, numerical simulations in the quantum regime, and the spectral analysis of the Liouvillian are combined to show the emergence of the time crystal and to prove the robustness of the oscillation period against quantum fluctuations.
We address the problem of spin dynamics in the presence of a thermal bath, by solving exactly the appropriate quantum master equations with continued-fraction methods. The crossover region between the quantum and classical domains is studied by increasing the spin value S, and the asymptote for the classical absorption spectra is eventually recovered. Along with the recognized relevance of the coupling strength, we show the critical role played by the structure of the system-environment interaction in the emergence of classical phenomenology.
In this paper, we explore the emergence of the Wigner entropy production rate in the stationary state of a two-mode Gaussian system. The interacting modes dissipate into different local thermal baths. Also, one of the bosonic modes evolves into the squeezed-thermal state because of the parametric amplification process. Using the Heisenberg-Langevin approach, combined with quantum phase space formulation, we get an analytical expression for the steady-state Wigner entropy production rate. It contains two key terms. The first one is an Onsager-like expression that describes heat flow within the …
We study the influence of short-range quantum correlations and classical spatial correlations on the phase diagram of the dissipative XYZ model by using a Gutzwiller Monte carlo method and a cluster Gutzwiller ansatz for the wave function. Considering lattices of finite size we show the emergence of a ferromagnetic phase, two paramagnetic phases and the possible existence of a phase transition which is entirely quantum in nature. The inclusion of short-range quantum correlations has a drastic effect on the phase diagram but our results show the inclusion of long-range quantum correlations or t…
Procrastinating einselection in non-Markovian quantum dynamics
University of Maryland, Baltimore County（马里兰大学巴尔的摩分校）；Quantum Science Institute, University of Maryland, Baltimore County（马里兰大学巴尔的摩分校量子科学研究所）；Research Center for Quantum Physics, National Research and Innovation Agency（国家研究与创新局量子物理研究中心）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；National Quantum Laboratory（国家量子实验室）
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…
We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as ``quantum phase space contraction rate'' and which is related to a fundamental property of quantum channels: non-unitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attaractor-like structures is displayed.
We apply the Gaussian trajectories approach to the study of the critical behavior of two-dimensional dissipative arrays of nonlinear photonic cavities, in presence of two-photon driving and in regimes of sizable loss rates. In spite of the highly mixed character of the density matrix of this system, the numerical approach is able to provide precise estimations of the steady-state expectation values, even for large lattices made of more than 100 sites. By performing a finite-size scaling of the relevant properties of the steady state, we extrapolate the behavior of the system in the thermodynam…
We investigate theoretically the generation of indistinguishable single photons from a strongly dissipative quantum system placed inside an optical cavity. The degree of indistinguishability of photons emitted by the cavity is calculated as a function of the emitter-cavity coupling strength and the cavity linewidth. For a quantum emitter subject to strong pure dephasing, our calculations reveal that an unconventional regime of high indistinguishability can be reached for moderate emittercavity coupling strengths and high quality factor cavities. In this regime, the broad spectrum of a dissipat…
We exploit the non-dissipative dynamics of a pair of electrons in a large square quantum dot to perform singlet-triplet spin measurement through a single charge detection and show how this may be used for entanglement swapping and teleportation. The method is also used to generate the AKLT ground state, a further resource for quantum computation. We justify, and derive analytic results for, an effective charge-spin Hamiltonian which is valid over a wide range of parameters and agrees well with exact numerical results of a realistic effective-mass model. Our analysis also indicates that the met…
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…
The equivalence between classical epidemic model and nondissipative and dissipative quantum tight-binding model is derived. Classical epidemic model can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be almost entirely simulated by classical statistical model. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of …
We discuss the emergence of spontaneous synchronization for an open spin-pair system interacting only via a common environment. Under suitable conditions, and even in the presence of detuning between the natural precession frequencies of the two spins, they are shown to reach a long-lasting transient behavior where they oscillate in phase. We explore the connection between the emergence of such a behavior and the establishment of robust quantum correlations between the two spins, analyzing differences between dissipative and dephasing effects.
We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from the mean-field equations, we explain the emergence of chaos by way of quasiperiodicity -- presence of two or more incommensurate frequencies. This is known as the Ruelle-Takens-Newhouse route to chaos. The equations of motion have a $\mathbb{Z}_{2}$-symmetry with respect to the interchange of the two ensembles. However, some of the attractors of these equat…
We analyze a modified version of the Coleman-Hepp model, that is able to take into account energy-exchange processes between the incoming particle and the linear array made up of $N$ spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic ($N \rightarrow \infty$) limit. In such a limit and in a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No assumptions are made on the spectrum of the Hamiltonian of the spin syst…
