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 dissipative environment under the long-encoding-time condition.
In this paper, we study the effect of classical driving field on the spontaneous emission spectrum of a qubit embedded in a dissipative cavity. Furthermore, we monitor the entanglement dynamics of the driven qubit with its radiative decay under the action of the classical field. Afterwards, we carry out an investigation on the possibility of entanglement swapping between two such distinct driven qubits. The swapping will be feasible with the aid of a Bell state measurement performing on the photons leaving the cavities. It is demonstrated that the classical driving field has a beneficial effec…
The dynamics of quantum Fisher information (QFI) of the phase parameter in a driven two-state system is studied within the framework of non-Markovian dissipative process. The influences of memory effects, classical driving and detunings on the parameter-estimation precision are demonstrated by exactly solving the Hamiltonian under rotating-wave approximation. In sharp contrast with the results obtained in the presence of Markovian dissipation, we find that classical driving can drastically enhance the QFI, namely, the precision of parameter estimation in the non-Markovian regime. Moreover, the…
Quantum cascaded systems offer the possibility to manipulate a target system with the quantum state of a source system. Here, we study in detail the differences between a direct quantum cascade and coherent/incoherent driving for the case of two coupled cavity-QED systems. We discuss qualitative differences between these excitations scenarios, which are particular strong for higher-order photon-photon correlations: $g^{(n)}(0)$ with $ n>2 $. Quantum cascaded systems show a behavior differing from the idealized cases of individual coherent/incoherent driving and allow to produce qualitatively d…
Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A non-perturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D$_2$ {\it Ansatz} is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the p…
Cat states, which were initially proposed to manifest macroscopic superpositions, play an outstanding role in fundamental aspects of quantum dynamics. In addition, they have potential applications in quantum computation and quantum sensing. However, cat states are vulnerable to dissipation, which puts the focus of cat-state generation on higher speed and increased robustness. Dissipative cat-state generation is a common approach based on the nonlinear coupling between a lossy pump field and a half-frequency signal field. In such an approach, the pump field is usually kept in equilibrium, which…
We analyze Josephson's oscillation of Bose particles in the open (dissipative) Bose-Hubbard dimer. First, we excite the dimer from the vacuum state into a state suitable for observing the oscillation by using a special protocol for external driving. Next, we switch off the driving and observe the oscillation. It is shown that the main mechanism for the decay of Josephson's oscillation is the dephasing due to fluctuating number of particles in open systems. An analytical estimate for the decay time is obtained.
We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such dynamics: 1) the collapse and revival of oscillations in the population difference, 2) the simple exponential decay of the oscillations resulting in their steady state with the finite amplitude, and 3) the steady-state stabilization of the equally populated levels. The nonmonotonic Bessel-function-like dependence on the driving strength is also predicted for th…
Driven-dissipative systems have recently attracted great attention due to the existence of novel physical phenomena with no analog in the equilibrium case. The Keldysh path-integral theory is a powerful tool to investigate these systems. However, it has still been challenge to study strong nonlinear effects implemented by recent experiments, since in this case the photon number is few and quantum fluctuations play a crucial role in dynamics of system. Here we develop a new approach for deriving exact steady states of driven-dissipative systems by introducing the Keldysh partition function in t…
We present a theoretical formalism for resonance fluorescence radiating from a two-level system (TLS) driven by any periodic driving and coupled to multiple reservoirs. The formalism is derived analytically based on the combination of Floquet theory and Born-Markov master equation. The formalism allows us to calculate the spectrum when the Floquet states and quasienergies are analytically or numerically solved for simple or complicated driving fields. We can systematically explore the spectral features by implementing the present formalism. To exemplify this theory, we apply the unified formal…
We study Landau-Zener transitions in a dissipative environment by means of the quasiadiabatic propagator path-integral scheme. It allows to obtain numerically exact results for the full range of the involved parameters. We discover a nonmonotonic dependence of the Landau-Zener transition probability on the sweep velocity which is explained in terms of a simple physical picture. This feature results from a nontrivial competition between relaxation processes and the external sweep and is not captured by perturbative approaches. In addition to the Landau-Zener transition probability, we study the…
We study the dissipative dynamics of a two-level system (TLS) exposed to strong ac driving. By combing Floquet theory with Van Vleck perturbation theory in the TLS tunneling matrix element, we diagonalize the time-dependent Hamiltonian and provide corrections to the renormalized Rabi frequency of the TLS, which are valid for both a biased and unbiased TLS and go beyond the known high-frequency and rotating-wave results. In order to mimic environmental influences on the TLS, we couple the system weakly to a thermal bath and solve analytically the corresponding Floquet-Bloch-Redfield master equa…
We mainly investigate the quantum measurement of Kerr nonlinearity in the driven-dissipative system. Without the dissipation, the measurement precision of the nonlinearity parameter $χ$ scales as "super-Heisenberg scaling" $1/N^2$ with $N$ being the total average number of particles (photons) due to the nonlinear generator. Here, we find that "super-Heisenberg scaling" $1/N^{3/2}$ can also be obtained by choosing a proper interrogation time. In the steady state, the "super-Heisenberg scaling" $1/N^{3/2}$ can only be achieved when the nonlinearity parameter is close to 0 in the case of the sing…
We study the nonequilibrium quantum phase transition of an Ising chain in a dissipative cavity driven by an external transverse light field. When driving and dissipation are in balance, the system can reach a nonequilibrium steady state which undergoes a super-radiant phase transition as the driving strength increases. Interestingly, the super-radiant field changes the effective bias of the Ising chain in return and drives its own transition between the ferromagnetic and paramagnetic phase. We study the rich physics in this system with sophisticated behavior, and investigate important issues i…
Various schemes have been proposed to overcome the drawback of the decoherence on quantum-enhanced parameter estimation. Here we suggest an alternative method, quantum feedback, to enhance the parameter precision of optimal quantum estimation of a dissipative qubit by investigating its dynamics of quantum Fisher information. We find that compared with the case without feedback, the quantum Fisher information of the dissipative qubit in the case of feedback has a large maximum value in time evolution and a smaller decay rate in the long time.
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…
Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the…
Work, moments of work and heat flux are studied for the generic case of a strongly driven twolevel system immersed in a bosonic heat bath in domains of parameter space where perturbative treatments fail. This includes particularly the interplay between non-Markovian dynamics and moderate to strong external driving. Exact data are compared with predictions from weak coupling approaches. Further, the role of system-bath correlations in the initial thermal state and their impact on the heat flux are addressed. The relevance of these results for current experimental activities on solid state devic…
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…
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 study the possibility of enhancing the stationary entanglement achievable with two-qubit dissipating into a common environment by means of feedback. We contrast the effect of Markovian with Bayesian feedback and show that, depending on the initial state, the performance of the latter are from 16% to 33% superior.
We revisit the problem of quantum bi- and multi-stability by considering the dissipative Double Resonance Model. For a large driving frequency, this system has a simpler phase structure than the driven dissipative nonlinear oscillator -- the paradigm model for classical and quantum bistability. This allows us to obtain an analytical estimate for the lifetime of quantum limit cycles. On the other hand, for a small driving frequency, the system is much reacher than the nonlinear oscillator. This allows us to address a novel phenomenon of dissipation- and chaos-assisted tunneling between quantum …
We study a dissipative, mechanically coupled optomechanical system that accommodates gain and loss. The gain (loss) is engineered by driven a purely dispersive optomechanical cavity with a blue-detuned (red-detuned) electromagnetic field. By taking into account the dissipative coupling, the Exceptional Point (EP), which is the $\mathcal{PT}-$symmetry phase transition, occurs at low threshold driving strength compared to the purely dispersive system. In the linear regime, the $\mathcal{PT}-$symmetry is unbroken and the dissipative coupling induces strong coupling between the mechanical resonato…
The multipartite Greenberger-Horne-Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme can be considered as an extension of a recent work [T. M. Wintermantel, Y. Wang, G. Lochead, \textit{et al}, {Phys. Rev. Lett. \textbf{124}, 070503 (2020)}]. By virtue of the polychromatic driving fields and the engineered spontaneous emission, a multipartite GHZ state with odd numbers of atoms are generated with a high effic…
We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks.
Counter-diabatic driving (CD) is a technique in quantum control theory designed to counteract nonadiabatic excitations and guide the system to follow its instantaneous energy eigenstates, and hence has applications in state preparation, quantum annealing, and quantum thermodynamics. However, in many practical situations, the effect of the environment cannot be neglected, and the performance of the CD is expected to degrade. To arrive at general bounds on the resulting error of CD in this situation we consider a driven spin-boson model as a prototypical setup. The inequalities we obtain, in ter…
Gaussian approximation and its corrections for driven dissipative Kerr model
Faculty of Physics, Lomonosov Moscow State University（莫斯科国立大学物理系）；Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所量子技术数学方法系）
We provide a comprehensive study of the energy transfer phenomenon -- populating a given energy level -- in 3- and 4-level quantum systems coupled to two thermal baths. In particular, we examine the effects of an external periodic driving and the coherence induced by the baths on the efficiency of the energy transfer. We consider the Floquet-Lindblad and the Floquet-Redfield scenarios, which both are in the Born-Markov, weak-coupling regime but differ in the treatment of the secular approximation, and for the latter, we develop an appropriate Floquet-type master equation by employing a partial…
Generating robust entanglement among solid-state spins is key for applications in quantum information processing and precision sensing. We show here a dissipative approach to generate such entanglement among the hyperfine coupled electron nuclear spins using the rapid optical decay of electronic excited states. The combined dark state interference effects of the optical and microwave driving fields in the presence of spontaneous emission from the short-lived excited state leads to a dissipative formation of an entangled steady state. We show that the dissipative entanglement is generated for a…
We propose various schemes for the dissipative preparation of a maximally entangled steady state of two atoms in an optical cavity. Harnessing the natural decay processes of cavity photon loss and spontaneous emission, we use an effective operator formalism to identify and engineer effective decay processes, which reach an entangled steady state of two atoms as the unique fixed point of the dissipative time evolution. We investigate various aspects that are crucial for the experimental implementation of our schemes in present-day and future cavity quantum electrodynamics systems and analytical…
The mean-field steady states of a generalized model of $N$ two-state systems interacting with one mode of the radiation field in the presence of external driving and dissipation are surveyed as a function of three control parameters: one governs the interaction strength relative to the resonance frequency, thus accessing the Dicke quantum phase transition, a second the relative strength of counter-rotating to rotating-wave interactions, and a third the amplitude of an external field driving the cavity mode. We unify the dissipative extension of the Dicke quantum phase transition with the recen…
We determine the characteristic of dissipative quantum transport in a coupled qubit network in the presence of on-site and off-diagonal external driving. The work is motivated by the dephasing-assisted quantum transport where noise is beneficial to the transport efficiency. Using Floquet-Magnus expansion extended to Markovian open systems, we analytically derive transport efficiency and compare it to exact numerical results. We find that driving may increase the efficiency at frequencies near the coupling rate. On the contrary, at some other frequencies the transport may be suppressed. We then…
Single-shot qubit readout typically combines high readout contrast with long-lived readout signals, leading to large signal-to-noise ratios and high readout fidelities. In recent years, it has been demonstrated that both readout contrast and readout signal lifetime, and thus the signal-to-noise ratio, can be enhanced by forcing the qubit state to transition through intermediate states. In this work, we demonstrate that the sub-Poissonian relaxation statistics introduced by intermediate states can reduce the single-shot readout error rate by orders of magnitude even when there is no increase in…
We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then, we consider stationary force sensing and study the necessary conditions to minimise the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields, however, the force noise p…
Based on the time-convolutionless master-equation approach, we investigate squeezing of light field in a dissipative Jaynes-Cummings model. The results show that squeezing light can be generated when the atom transits to a ground state from an excited state, and then a collapse-revival phenomenon will occur in the squeezing of light field due to atom-cavity coupling. Enhancing the atom-cavity coupling can increase the frequency of the collapse-revival of squeezing. The stronger the non-Markovian effect is, the more obvious the collapse-revival phenomenon is. The oscillatory frequency of the sq…
We propose a scheme to significantly increase quadratic optomechanical couplings of optomechanical systems with the help of a nonlinear medium and two driving lasers. The nonlinear medium is driven by one laser and the optical cavity mode is driven by a strong laser. We derive an effective Hamiltonian using squeezing transformation and rotating wave approximation. The effective quadratic optomechanical coupling strength can be larger than the decay rate of the cavity mode by adjusting the two optical driving fields. The thermal noise of squeezed cavity mode can be suppressed totally with the h…
Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary driving is increased, this minimal classical model recovers the main features of the "dissipative phase transition" seen experimentally. Between the transmitting and non-transmitting regimes on either side of this transition (which support ballistic and diffusive energy transport respectively), we observe additional dynamical regimes of interest. These include a r…
We study the dissipative dynamics of a single quantum harmonic oscillator subjected to a parametric driving with in an effective Hamiltonian approach. Using Liouville von Neumann approach, we show that the time evolution of a parametrically driven dissipative quantum oscillator has a strong connection with the classical damped Mathieu equation. Based on the numerical analysis of the Monodromy matrix, we demonstrate that the dynamical instability generated by the parametric driving are reduced by the effect of dissipation. Further, we obtain a closed relationship between the localization of the…
We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body $SU(1,1)$ pair coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes…
Dissipative Time Quasicrystals from Multilevel Interference
College of Physical Science and Technology, Central China Normal University（华中师范大学物理科学与技术学院）；School of Science, Hubei University of Technology（湖北工业大学理学院）
We propose an experimentally feasible scheme for dissipative preparation of tripartite entangled state with atoms separately trapped in an array of three coupled cavities. The combination of coherent driving fields and quantum-jump-based feedback control will drive the system into a non-equilibrium steady state, which has a nearly perfect overlap with the genuine three-atom singlet state. Different control strategies are investigated and the corresponding optimal parameters are confirmed. Moreover, the fidelity of target state is insensitive to detection inefficiencies, and it oversteps 90\% f…
We study the performance of a single qubit-laser as a quantum sensor to measure the amplitude and phase of a driving field. By using parameter estimation theory we show that certain suitable field quadratures are optimal observables in the lasing phase. The quantum Fisher information scales linearly with the number of bosons and thus the precision can be enhanced by increasing the incoherent pumping acting on the qubit. If we restrict ourselves to measurements of the boson number observable, then the optimal operating point is the critical point of the lasing phase transition. Our results poin…
The many-body dissipative flow induced by a mobile aussian impurity harmonically oscillating within a cigar-shaped Bose-Einstein condensate is investigated. For very {small and large driving frequencies} the superfluid phase is preserved. Dissipation is identified, for intermediate driving frequencies, by the non-zero value of the drag force whose abrupt increase {signals the spontaneous downstream emission of an array of gray solitons. After each emission event, typically each of the solitary waves formed decays and splits into two daughter gray solitary waves that are found to be robust prop…
Bosons hopping across sites and interacting on-site are the essence of the Bose-Hubbard model (BHM). Inspired by the success of BHM simulators with atoms in optical lattices, proposals for implementing the BHM with photons in coupled nonlinear cavities have emerged. Two coupled semiconductor microcavities constitute a model system where the hopping, interaction, and decay of exciton polaritons --- mixed light-matter quasiparticles --- can be engineered in combination with site-selective coherent driving to implement the driven-dissipative two-site optical BHM. Here we explore the interplay of …
In this work we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimisation. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimise dissipation for slow protocols, …
We study the production of photons in a model of three bosonic atomic modes non-linearly coupled to a cavity mode. In absence of external driving and dissipation, the energy levels at different photon numbers assemble into the steps of an energy staircase which can be employed as guidance for preparing multi-photon states. We consider adiabatic photon production, driving the system through a sequence of Landau-Zener transitions in the presence of external coherent light pumping. We also analyse the non-equilibrium dynamics of the system resulting from the competition of the sudden switch of co…
