共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived. 相似文献
2.
We investigate what a snapshot of a quantum evolution--a quantum channel reflecting open system dynamics--reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of "Markovianity" is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations. 相似文献
3.
The solutions of the problems related to open quantum systems have attracted considerable interest.We propose a variational quantum algorithm to find the steady state of open quantum systems.In this algorithm,we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation,which can be efficiently evaluated with quantum circuits.We then optimize the parameters of the quantum circuit to find the steady state.Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels.The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%.This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems. 相似文献
4.
We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born–Markov or rotating wave approximations (RWA). This includes master equations of the (asymptotically) stationary, periodic, and time-nonlocal type. We provide proofs on the validity and meaningfulness of the late-time perturbative master equation and on the preservation of complete positivity despite a general lack of Lindblad form. More specifically, we show how the algebraic generators satisfy the theorem of Lindblad and Gorini, Kossakowski and Sudarshan, even though the dynamical generators do not. These proofs ensure the mathematical viability and physical soundness of solutions to non-Markovian processes. Within the same formalism we also expand upon known results for non-Markovian corrections to the quantum regression theorem. Several directions where these results can be usefully applied to are also described, including the analysis of near-resonant systems where the RWA is inapplicable and the calculation of the reduced equilibrium state of open systems. 相似文献
5.
Chuan-Hua Ren Yi-Min Lai Tong-Qiang Song 《International Journal of Theoretical Physics》2009,48(7):2081-2087
We study continuous quantum measurements (CQM) of energy of an open quantum system by Lindblad master equation. It turns out
that the time-dependence of decoherence is identified. We conclude that the CQM of energy accelerate quantum decoherence.
Sponsored by K.C. Wong Magna Fund in Ningbo University. 相似文献
6.
An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula. 相似文献
7.
Quantum operations, are completely positive (CP) and trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of one-qubit open quantum system in layered environment which is a generalized spin star model. The Nakajima-Zwanzig and time-convolutionless projection operators technique are applied for deriving the master equations. Finally, a simple example will be studied to consider the relation between completely positive maps and initial quantum correlation and show that vanishing quantum discord is not necessary for CP maps. 相似文献
8.
In this paper, we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems. The coefficients of the equations are re-evaluated according to the scheme in[(2019), Phys. Rev. A 99, 022118]. They are complex numbers rather than the real numbers obtained from traditional simplified methods. The dynamics of two models(one is an open threelevel quantum system model, and the other is the model of phycoerythrin 545(PE545) in a photosynthesis system) are studied. It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments, but a large distortion of the dynamics in others. These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation. 相似文献
9.
10.
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions. 相似文献
11.
Adrián A. Budini 《Journal of statistical physics》2008,131(1):51-78
Non-Markovian Lindblad rate equations arise from alternative microscopic interactions such as quantum systems coupled to composite
reservoirs, where extra degrees of freedom mediate the interaction between the system and a Markovian reservoir, as well as
from systems coupled to complex structured reservoirs whose action can be well approximated by a direct sum of Markovian sub-reservoirs
(Budini in Phys. Rev. A 74:053815 [2006]). The purpose of this paper is two fold. First, for both kinds of interactions we find general expressions for the system
operator correlations written in terms of the Lindblad rate propagator. Secondly, we find the conditions under which a quantum
regression hypothesis is valid. We show that a non-Markovian quantum regression theorem can only be granted in a stationary
regime, being a necessary condition the fulfillment of a detailed balance condition. This result is independent of the underlying
microscopic interaction, providing a criterion for the validity of the regression hypothesis in non-Markovian Lindblad-like
master equations. As an example, we study the correlations of a two-level system coupled to different kind of reservoirs. 相似文献
12.
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70?years). 相似文献
13.
C. Henkel 《The European physical journal. Special topics》2008,160(1):217-224
We perform a calculation of the linewidth of a micromaser, using
the master equation
and the quantum regression approach. A `dephasing' contribution is
identified from pumping processes that conserve the photon number
and do not appear in the photon statistics. We work out examples for
a single-atom maser with a precisely controlled coupling and for a
laser where the interaction time is broadly distributed.
In the latter case, we also assess the convergence of a
recently developed uniform Lindblad approximation to the master
equation; it is relatively slow. 相似文献
14.
A quantum mechanical model is given which is equivalent to the stochastic dephasing subject to the two-state jump Markovian process. The stochastic variable corresponds to a Hermitian operator of a spin-1/2 system which is embedded in a thermal reservoir, where the time-evolution of the spin-1/2 system is described by the quantum master equation of the Lindblad form. 相似文献
15.
MARKO ŽNIDARIČ 《Pramana》2011,77(5):781-791
We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties.
It is shown that the time-dependent density matrix renormalization method can be used successfully to find a stationary solution
of Lindblad master equation. Furthermore, for a specific model an exact solution is presented. 相似文献
16.
We consider the nonlinear terahertz emission by the system of cavity polaritons in the regime of polariton lasing. To account for the quantum nature of terahertz-polariton coupling, we use the Lindblad master equation approach and demonstrate that quantum microcavities reveal a rich variety of nonlinear phenomena in the terahertz range, including bistability, short terahertz pulse generation, and terahertz switching. 相似文献
17.
《Physics letters. A》2019,383(15):1698-1710
In this work, we present a multiple-scale perturbation technique suitable for the study of open quantum systems, which is easy to implement and in few iterative steps allows us to find excellent approximate solutions. For any time-local quantum master equation, whether markovian or non-markovian, in Lindblad form or not, we give a general procedure to construct analytical approximations to the corresponding dynamical map and, consequently, to the temporal evolution of the density matrix. As a simple illustrative example of the implementation of the method, we study an atom-cavity system described by a dissipative Jaynes-Cummings model. Performing a multiple-scale analysis we obtain approximate analytical expressions for the strong and weak coupling regimes that allow us to identify characteristic time scales in the state of the physical system. 相似文献
18.
In this paper, the theoretical investigation of remote preparation of an entangled state is studied in nonideal conditions. Our studies include two parts. In the first part, we consider the remote state preparation (RSP) of an entangled state through two equally noisy quantum channel states, namely, a mixture of Bell states. Studies show there is a particular mixed-state channel for which all pure entangled states remain entangled after this inexact RSP. In the second part, we suppose that noises which quantum channels suffer from can be expressed as the Lindblad operators.The master equation of the system can be expressed in the Lindblad form. Through solving the master equation, we calculate the fidelity as a function of decoherence rates and parameters of the state to be prepared. For a given entangled state, we investigate the influenceof different types of noises on the fidelity. 相似文献
19.
A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation can be cast into Lindblad form with a single generator for each Cartesian direction. Temperature dependent friction and diffusion coefficients for both position and momentum are expressed in terms of the collision cross section. 相似文献