Non-Markovian dynamics of quantum open systems embedded in a hybrid environment

Abstract

Quantum systems of interest are typically coupled to several quantum channels (more generally environments). In this paper, we develop an exact stochastic Schrödinger equation for an open quantum system coupled to a hybrid environment containing both bosonic and fermionic particles. Such a stochastic differential equation may be obtained directly from a microscopic model through employing a classical complex Gaussian noise and a non-commutative fermionic noise to simulate the hybrid bath. As an immediate application of our developed stochastic approach, we show that the evolution of the reduced density matrix can be derived by taking the average over both the bosonic noise and the fermionic noise. Three specific examples are given in this paper to illustrate that the hybrid quantum trajectory is fully consistent with the standard quantum mechanics. Our examples also shed new light on the special features exhibited by the fermionic bath and bosnoic bath.

Quantum Entanglement Protection by Utilizing Classical Noises

“…Here, we use the so‐called Ornstein‐Uhlenbeck noises [ 106,107 ] whose correlation functions can be written as $$$$\begin{equation} K_{\beta }(t,s)=\frac{\Gamma _{\beta }\gamma _{\beta }}{2}e^{-\gamma _{\beta }|t-s|},\;(\beta =1,2,Q) \end{equation}$$$$where $$\Gamma _{\beta }$$ represents the global coupling strengths and $$1/\gamma _{\beta }$$ represents the memory time of the noises (the sub‐index $$\beta =1,2$$ corresponds to two classical noises and $$\beta =Q$$ is for the quantized noise). Actually, the correlation function $$K_{\beta }$$ in Equation (14) corresponds to a widely used Lorentzian spectrum density [ 102–105,108 ] $$$$\begin{equation} g_{\beta }(\omega )=\frac{1}{2\pi }\frac{\Gamma _{\beta }\gamma _{\beta }^{2}}{\omega ^{2}+\gamma _{\beta }^{2}},\;(\beta =1,2,Q) \end{equation}$$$$The correlation function $$K_{\beta }$$…”

Quantum coherence protection by noise

“…(ω0−ω) 2 +γ 2 which is widely used [58,59]. Solving equation ( 7) by Laplace transformation, the density matrix of the system can be obtained.…”

Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism

“…Historically, the pioneering works can be traced back to the early attempts of Barnett et al, [94][95][96] Applebaum et al, 97,98 and Rogers, 99 who have derived stochastic dynamical equations to describe fermionic Brownian motion. In recent years, the non-Markovian QSD theory has been extended to address fermionic environments by Yu et al [100][101][102] and others. 103,104 Moreover, the SEOM for fermionic environments has been formally established.…”