A general method is developed which enables the exact treatment of the non-Markovian quantum dynamics of open systems through a Monte Carlo simulation technique. The method is based on a stochastic formulation of the von Neumann equation of the composite system and employs a pair of product states following a Markovian random jump process. The performance of the method is illustrated by means of stochastic simulations of the dynamics of open systems interacting with a Bosonic reservoir at zero temperature and with a spin bath in the strong coupling regime.
The dynamics of two interacting spins coupled to separate bosonic baths is studied. An analytical solution in Born approximation for arbitrary spectral density functions of the bosonic environments is found. It is shown that in the non-Markovian cases concurrence "lives" longer or reaches greater values.
The time evolution of occupation number is studied for fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of characteristics of thermal reservoirs of different statistics on the non-stationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.
The quantum dynamics of a spin chain interacting with multiple bosonic baths is described in a mixed Wigner-Heisenberg representation. The formalism is illustrated by simulating the time evolution of the reduced density matrix of two coupled spins, where each spin is also coupled to its own bath of harmonic oscillators. In order to prove the validity of the approach, an analytical solution in the Born-Markov approximation is found. The agreement between the two methods is shown.
The evolution of a quantum system towards thermal equilibrium is usually studied by approximate methods, which have their limits of validity and should be checked against analytically solvable models. In this paper, we propose an analytically solvable model to investigate the energy transfer between a bosonic bath and a fermionic chain which are nonlinearly-coupled to each other. The bosonic bath consists of an infinite collection of non-interacting bosonic modes, while the fermionic chain is represented by a chain of interacting fermions with nearest-neighbor interactions. We compare behavior…
We summarize our recent results for the induced exchange interaction due to thermal bosonic environment (bath) which also generates quantum noise. Our focus here is on the onset of the interaction. We demonstrate that the induced interaction can be used to manipulate and create entanglement over time scales sufficiently large for controlling the two-qubit system for quantum computing applications, though ultimately the noise effects will dominate.
We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theore…
Exact dynamics of first-order system-bath coherence in bilinear bosonic models
Ocean University of China（中国海洋大学）；University of the Basque Country UPV/EHU（巴斯克大学）；Dalian Nationalities University（大连民族大学）；University of Toronto（多伦多大学）；Shanghai Jiao Tong University（上海交通大学）
The finite coupled bosonic model of reservoir introduced by Vasile et al. [1] to characterize non-Markovianity, is used to study the different dissipative behaviors of a harmonic oscillator coupled to it when it is in resonance, close to resonance or far detuned. We show that information and energy exchange between system and heat bath go hand in hand because phonons are the carriers of both: in resonance free propagation of excitations is achieved, and therefore pure dissipation, while when far detuned the system can only correlate with the first oscillator in the bath's chain, leading to alm…
Understanding dynamics of localized quantum systems embedded in engineered bosonic environments is a central problem in quantum optics and open quantum system theory. We present a formalism for studying few-particle scattering from a localized quantum system interacting with an bosonic bath described by an inhomogeneous wave-equation. In particular, we provide exact relationships between the quantum scattering matrix of this interacting system and frequency domain solutions of the inhomogeneous wave-equation thus providing access to the spatial distribution of the scattered few-particle wave-p…
The energy of the bosonic bath and the flow of quantum information are analyzed over short and long times in local dephasing channels for special correlated or factorized initial conditions, respectively, which involve thermal states. The continuous distribution of frequency modes of the bosonic bath exhibits a spectral gap over low frequencies. The bath energy shows oscillatory behaviors around the asymptotic value and information is alternatively lost and gained by the open system. Due to the low-frequency gap, the damped oscillations become regular over long times and the frequency of the o…
Non-Markovian dynamics of two interacting two-level qubits coupled to a bosonic bath was previously studied using the quantum-state-diffusion (QSD) equation, where a stochastic state is used to describe the system. In this study, we provide another perspective on this system by deriving the analytic form of the master equation, which describes the system with a reduced density matrix. Then, we validate the master equation by examining entanglement generation and state purity. In addition, with the master equation, we observe the effects from first-order noise and notice that a good asymptotic …
Engineering non-Markovianity from spectral shaping of bosonic and fermionic baths
Fudan University（复旦大学）；University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory（合肥国家实验室）；University of California San Diego（加利福尼亚大学圣迭戈分校）
We consider a surface code suffering decoherence due to coupling to a bath of bosonic modes at finite temperature and study the time available before the unavoidable breakdown of error correction occurs as a function of coupling and bath parameters. We derive an exact expression for the error rate on each individual qubit of the code, taking spatial and temporal correlations between the errors into account. We investigate numerically how different kinds of spatial correlations between errors in the surface code affect its threshold error rate. This allows us to derive the maximal duration of e…
The counter rotating-wave term (CRT) effects from the system-bath coherence on the dynamics of quantum correlation of two qubits in two independent baths and a common bath are systematically investigated. The hierarchy approach is extended to solve the relevant spin boson models with the Lorentzian spectrum, the exact dynamics for the quantum entanglement and quantum discord (QD) are evaluated, and the comparisons with previous ones under the rotating-wave approximation are performed. For the two independent baths, beyond the weak system-bath coupling, the CRT essentially changes the evolution…
We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold probabilities in this system. The full quantum mechanical system-bath dynamics is computed exactly over one quantum error correction cycle. Since all physical qubits interact with the bath, space-time correlations between errors are taken into account. We compute the fidelity of the surface code as a function of the quantum error correction time. The calculation all…
We derive the exact out-of-equilibrium Wigner function of a bosonic mode linearly coupled to a bosonic bath of arbitrary spectral density. Our solution does not rely on any master equation approach and it therefore also correctly describes a bosonic mode which is initially entangled with its environment. It has been recently suggested that non-Markovian quantum effects lead to dissi- pationless dynamics in the case of a strong coupling to a bath whose spectral density has a support bounded from below. We show in this work that such a system undergoes a quantum phase transi- tion at some critic…
We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of (i) a qubit coupled to a bosonic bath with power-law spectral density, and (ii) a qubit coupled to a single harmonic oscillator that dissipates energy into a bosonic bath, which embodies an example of a structured bath for the qubit. We then model the influence of random time jitter in the UDD protocol by sorting pulse-application times from Gaussian distributions centered at appropriate values dictated by…
The character of evolution of an open quantum system is often encoded in the correlation function of the environment or, equivalently, in the spectral density function of the interaction. When the environment is heterogeneous, e.g. consists of several independent subenvironments with different spectral functions, one of the subenvironments can be considered auxiliary and used to control decoherence of the open quantum system in the remaining part of the environment. The control can be realized, for example, by adjusting the character of interaction with the subenvironment via suitable paramete…
Within a generalized Caldeira-Leggett model we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance $r$. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a {\em microscopic} distance that is of order of the cut-off wavelength $λ$ of the system-bath interaction. At larger distances the maximal entanglement is exponentially suppressed with a decay length of order $λ$. We conclude that entanglement generation via a heat bath is not suitable …
We study the limitations on coherence evolutions under the constraints of thermodynamic laws, and focus on the optimal thermal operations (TO) reaching the bounds. For qubit case, we find a thermal operation involving only a single-mode reservoir (STO) which maintains the maximum coherence allowed by general TO. For higher dimensions, we derive general bounds on coherence merging under TO, and find STO to reach the bounds. By applying the bound to a two-qubit system, we prove that erasing correlations while preserving the marginal states is not free in the resource theory of thermodynamics. Du…
We analyze an entangling protocol to generate tripartite Greenberger-Horne-Zeilinger states in a system consisting of three superconducting qubits with pairwise coupling. The dynamics of the open quantum system is investigated by taking into account the interaction of each qubit with an independent bosonic bath with an ohmic spectral structure. To this end a microscopic master equation is constructed and exactly solved. We find that the protocol here discussed is stable against decoherence and dissipation due to the presence of the external baths.
The presence of symmetries in a closed many-body quantum system results in integrability. For such integrable systems, complete thermalization does not occur. As a result, the system remains non-ergodic. On the other hand, a set of non-interacting atoms connected to a regular bosonic bath thermalizes. Here, we show that such atoms in a spatially-correlated thermal bath can show both the behavior depending on the temperature. At zero temperature, the bath has a large correlation length, and hence it acts as a common environment. In this condition, a set of weak symmetries exist, which prevent t…
We investigate the generation of quantum mechanical entanglement of two remote oscillators that are locally coupled to a common bosonic bath. Starting with a Lagrangian formulation of a suitable model, we derive two coupled Quantum Langevin Equations that exactly describe the time evolution of the two local oscillators in presence of the coupling to the bosonic bath. Numerically obtained solutions of the Langevin Equations allow us to study the entanglement generation between the oscillators in terms of the time evolution of the logarithmic negativity. Our results confirm and extend our previo…
We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths the truncation of both, the number of modes and the local Hilbert-space dimensions is necessary. We derive super-exponential Lieb--Robinson-type bounds on the error when restricting the bath to finitely-many modes and show how the error introduced by truncating the local Hilbert spaces may be efficiently monitored numerically. In this way we give error bounds for approximating the infinite system by a…
An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling $α<α_c$. Then $α_c$ is the quantum critical point of a transition from non-degenerate to degenerate ground state and our ca…
We study a system-bath description in the strong coupling regime where it is not possible to derive a master equation for the reduced density matrix by a direct expansion in the system-bath coupling. A particular example is a bath with significant spectral weight at low frequencies. Through a unitary transformation it can be possible to find a more suitable small expansion parameter. Within such approach we construct a formally exact expansion of the master equation on the Keldysh contour. We consider a system diagonally coupled to a bosonic bath and expansion in terms of a non-diagonal hoppin…
In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study dependence of the steady states of the two-level…
We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalizat…
Majorana mode based topological qubits are potentially subject to diabatic errors that in principle can limit the utility of topological quantum computation. Using a combination of analytical and numerical methods we study the diabatic errors in Majorana-based topological Y-junction that are coupled to a Bosonic bath in the Markovian approximation. From the study we find analytically that in the absence of a bath, the error rate can be made exponentially small in the braiding time only for completely smooth pulse shapes. Thus, pristine topological systems can reach exponentially small errors e…
Grid-state deformation in a no-jump non-Hermitian bosonic dimer
Universidad Politécnica Metropolitana de Hidalgo（伊达尔戈大都会理工大学）；University of Texas Rio Grande Valley（德克萨斯大学里奥格兰德河谷分校）；Technical University of Munich（慕尼黑工业大学）
We investigate the quantum evolution speed of a qubit in two kinds of finite-temperature environments. The first environment is a bosonic bath with Ohmic-like spectrum. It is found that the high temperature not only leads to the speed-up but also speed-down processes in the weak-coupling regime, which is different from the strong-coupling case where only exhibits speed-up process, and the effects of Ohmicity parameter of the bath on the quantum evolution speed are also different in the strong-coupling and weak-coupling regimes. Furthermore, we realize the controllable and stationary quantum ev…
Quantum systems in contact with an environment display a rich physics emerging from the interplay between dissipative and Hamiltonian terms. Here we focus on the role of the geometry of the coupling between the system and the baths. In the specific we consider a dissipative boundary driven ladder in presence of a gauge field which can be implemented with ion microtraps arrays. We show that, depending on the geometry, the currents imposed by the baths can be strongly affected by the gauge field resulting in non-equilibrium phase transitions. In different phases both the magnitude of the current…
Induced interactions and bound states of charge carriers immersed in a quantum medium are crucial for the investigation of quantum transport. Ultracold atom-ion systems can provide a convenient platform for studying this problem. Here, we investigate the static properties of one and two ionic impurities in a bosonic bath using quantum Monte Carlo methods. We identify three bipolaronic regimes depending on the strength of the atom-ion potential and the number of its two-body bound states: a perturbative regime resembling the situation of a pair of neutral impurities, a non-perturbative regime t…
The spin-boson model is studied by means of flow equations for Hamiltonians. Our truncation scheme includes all coupling terms which are linear in the bosonic operators. Starting with the canonical generator $η_c=[H_0,H]$ with $H_0$ resembling the non-interacting bosonic bath, the flow equations exhibit a universal attractor for the Hamiltonian flow. This allows to calculate equilibrium correlation functions for super-Ohmic, Ohmic and sub-Ohmic baths within a uniform framework including finite bias.
A $D$-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states. Here we show that, for any ergodic master equation, one can expect to find an {\em adaptive} monitoring scheme on the bath that can confine the system state to jumping between only $K$ states, for some $K \geq (D-1)^2+1$. For $D=2$ we explicitly construct a 2-state ensemble for any ergodic…
A model for a quantum register dissipatively coupled with a bosonic thermal bath is studied. The register consists of $N$ qubits (i.e. spin ${1/2}$ degrees of freedom), the bath is described by $N_b$ bosonic modes. The register-bath coupling is chosen in such a way that the total number of excitations is conserved. The Hilbert space splits allowing the study of the dynamics separately in each sector. Assuming that the coupling with the bath is the same for all qubits, the excitation sectors have a further decomposition according the irreducible representations of the $su(2)$ spin algebra. The …
We study the energy exchange between two bosonic systems that interact via bilinear transformations in the mode operators. The first mode is considered as the thermodynamic system, while the second is regarded as the bath. This work finds its roots in a very recent formulation of quantum thermodynamics [1] which allows to consider baths that are not described by the usual Boltzmann-Gibbs canonical form. Baths can possess quantum properties, such as squeezing or coherence, and can be initially correlated with the system, even through entanglement. We focus mainly on the case of Gaussian states,…
Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schrödinger equation, as introduced by Diósi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $Ω$) two-level atom coupled linearly to a three mode optical bath, with a cent…
We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general non-perturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless tran…
Asymptotic Entanglement across Dynamical Regimes of a Dissipative Bosonic Dimer
Peking University（北京大学）；Hefei National Laboratory（合肥国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Shanxi University（山西大学）
By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state and a variational approach à la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagnetically interacting with each other, with strength $J$, and coupled to a common bath of bosonic oscillators, with strength $α$. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for $J=0$ the critical value of $α$ decreases asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns …
We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a one-dimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For double-well and triple-well systems with non-interacting particles, the steady state is found to be an exact thermal state, which is attributed to the fact that the transfer rates between all pairs of coupled eigenstates satisfy detailed balance condition. The scenario changes when ther…
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures $T_1 > T_2$. For \textit{constant bilinear inter-oscillator coupling} studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary te…
We consider two identical and non-interacting harmonic oscillators coupled to either two independent bosonic baths or to a common bosonic bath. Under the only assumption of weak coupling, we analyze in details the non-Markovian short time-scale evolution of intensity correlations, entanglement and quantum discord for initial two-mode squeezed-thermal vacuum states. In the independent reservoirs case we observe the detrimental effect of the environment for all these quantities and we establish a hierarchy for their robustness against the environmental noise. In the common reservoir case, for in…
Single-photon cooperative dynamics of an assembly of two-level quantum emitters coupled by a bosonic bath are investigated. The bosonic bath is general and it can be anything as long as the exchange of excitations between quantum emitters and bath is present. In these systems, it is found that the population on the excited emitter keeps a simple and universal trapping law due to the existence of system's dark states. Different from the trapping regime caused by photonemitter dressed states, this type of trapping is only associated with the number of quantum emitters. According to the trapping …
The exact form of quantum propagator of a quantum oscillator interacting with a bosonic bath consisting of $N$ distinguished quantum oscillators with different frequencies is obtained in the Heisenberg picture. Reduced density matrix for oscillator is obtained. The kernel or Green's function connecting the initial density matrix of the oscillator to the density matrix in an arbitrary time is obtained and its connection to Feynman-Vernon influence functional is discussed. Weak coupling regime and squared mean values for position, momentum and energy of the oscillator are obtained in equilibrium…
The solution of the quantum Zermelo navigation problem is applied to the non-Markovian open system dynamics of a set of quantum systems interacting with a common environment. We consider a case allowing an exact time-optimal realization of environment-mediated non-local system unitaries. For a linear coupling to a harmonic bosonic bath, we derive a speed limit for the implementation time in terms of the fundamental frequency of the bath modes. As a product of two exponentials of the local free wind and the pairwise system-coupling, the Zermelo unitary forms a natural building block for reachin…
We study quantum annealing of pure and random transverse Ising chains that are coupled to boson baths, using a novel numerical method based on the combination of the quasi-adiabatic propagation path integral (QUAPI) and the matrix product state (MPS) formalisms. We present numerical results on systems up to 64 spins and conclude that the baths disturb quantum annealing of pure and random Ising chains. The numerical method to compute the reduced density matrix is described in detail.
