Trajectory tracking for non-Markovian quantum systems

非马尔可夫量子跃迁方法用于驱动耗散双态系统

Non-Markovian Quantum Jump Method for Driven-Dissipative Two-Level Systems

本文提出了一种改进的非马尔可夫量子跃迁方法，用于高效研究驱动耗散双态系统的动态行为，通过减少计算资源消耗并观察到相干与纠缠的复兴效应。

Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment

Quantum feedback can stabilize a two-level atom against decoherence (spontaneous emission), putting it into an arbitrary (specified) pure state. This requires perfect homodyne detection of the atomic emission, and instantaneous feedback. Inefficient detection was considered previously by two of us. Here we allow for a non-zero delay time $τ$ in the feedback circuit. Because a two-level atom is a nonlinear optical system, an analytical solution is not possible. However, quantum trajectories allow a simple numerical simulation of the resulting non-Markovian process. We find the effect of the tim…

马尔可夫动力学不同量子轨迹解缠中的量子轨迹纠缠

Quantum trajectory entanglement in various unravelings of Markovian dynamics

本文研究开放量子系统主方程的不同量子轨迹解缠中的纠缠，提出自适应贪心算法生成低纠缠轨迹，定位面积律到体积律转变点，并证明随机轨迹模拟成本可指数级低于矩阵乘积算子方法。

Coalescence of non-Markovian dissipation, quantum Zeno effect and non-Hermitian physics, in a simple realistic quantum system

Diagonalization of the effective Hamiltonian describing an open quantum system is the usual method of tracking its exceptional points. Although, such a method is successful for tracking EPs in Markovian systems, it may be problematic in non-Markovian systems where a closed expression of the effective Hamiltonian describing the open system may not exist. In this work we provide an alternative method of tracking EPs in open quantum systems, using an experimentally measurable quantity, namely the effective decay rate of a qubit. The quantum system under consideration consists of two non-identical…

nuHOPS：一种面向非马尔可夫开放量子动力学中高激发环境的量子轨迹方法

nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics

针对非马尔可夫开放量子动力学中的高激发环境模拟难题，提出改进的nuHOPS量子轨迹方法，规避密度矩阵二次缩放、利用轨迹局域化特性，可实现最多1000个辐射体的Dicke模型数值精确求解。

Non-Markovian waiting time distribution

Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time distribution (WTD) of quantum jumps for non-Markovian systems. We generalize Markovian quantum trajectory methods in the sense of deriving an exact analytical WTD for non-Markovian quantum dynamics and show explicitly how to construct this distribution for certain commonly used quantum optical systems.

Pure-state quantum trajectories for general non-Markovian systems do not exist

Since the first derivation of non-Markovian stochastic Schrödinger equations, their interpretation has been contentious. In a recent Letter [Phys. Rev. Lett. 100, 080401 (2008)], Diósi claimed to prove that they generate "true single system trajectories [conditioned on] continuous measurement". In this Letter we show that his proof is fundamentally flawed: the solution to his non-Markovian stochastic Schrödinger equation at any particular time can be interpreted as a conditioned state, but joining up these solutions as a trajectory creates a fiction.

Non-Markovian Quantum Jump with Generalized Lindblad Master Equation

The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. In this paper, we extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Mar…

The non-Markovian stochastic Schrödinger equation for the position unraveling

An important and well established area of quantum optics is the theory of Markovian stochastic Schrödinger equations (or by another name quantum trajectory theory). Recently stochastic Schrödinger equations have been developed for non-Markovian systems. In this paper we extend the current known stochastic Schrödinger equations for non-Markovian systems to include the position unraveling. We also discuss and illustrate that this stochastic Schrödinger equation can have an interpretation under both the orthodox and the de Broglie-Bohm hidden variable interpretation of quantum mechanics. We concl…

Non-Markovian Particle Dynamics in Continuously Controlled Quantum Gases

For a quantum gas, being subject to continuous feedback of a macroscopic observable, the single-particle dynamics is studied. Albeit feedback-induced particle correlations, it is shown that analytic solutions are obtained by formally extending the single-particle Hilbert space by an auxiliary degree of freedom. The particle's motion is then fed by colored noise, which effectively maps quantum-statistical correlations onto the single particle. Thus, the single particle in the continuously controlled gas follows a non-Markovian trajectory in phase-space.

Quantum trajectories under frequent measurements in non-Markovian environment

In this work we generalize the quantum trajectory (QT) theory from Markovian to non-Markovian environments. We model the non-Markovian environment by using a Lorentzian spectral density function with bandwidth ($Λ$), and find perfect "scaling" property with the measurement frequency ($τ^{-1}$) in terms of the scaling variable $x=Λτ$. Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to $x\to\infty$ and $x\to 0$, respectively. This $x$-dependent criterion improves the idea of using $τ$ alone, and quantitatively identif…

多体非马尔可夫动力学的图解方法：记忆效应与纠缠相变

Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions

提出基于量子跳跃和图解结构的方法解析多体非马尔可夫动力学，发现记忆效应相当于马尔可夫动力学的微扰，且非马尔可夫性可稳定随机酉电路中测量诱导纠缠相变的体积律相。

马尔可夫系统和量子电路中的内在量子迈佩姆巴效应

Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits

本文提出内在量子迈佩姆巴效应，通过轨迹长度度量量子态距离，揭示马尔可夫系统和量子电路中反直觉的动态行为。

非马尔可夫性的本质

The Hidden Nature of Non-Markovianity

本文研究了非马尔可夫性在单条轨迹下的不可见性，通过比较马尔可夫与非马尔可夫演化轨迹，揭示了非马尔可夫性在特定条件下无法被观测到的本质。

Operator equality on entropy production in quantum Markovian master equations

An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be still interpreted as a consequence of time-reversal asymmetry of the nonequilibrium processes of the systems. In contrast with the classical case, however, the first order expansion of the equality does not directly related to the mean entropy production, which arises from noncommute property of operators in quantum physics.