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arXiv:2304.04223

Effects of non-Markovian squeezed bath on the dynamics of open systems

Arapat Ablimit, Feng-Hua Ren, Run-Hong He, Yang-Yang Xie, Zhao-Ming Wang

Published Apr 9, 2023• 1 citation
arXivHTMLPDF

Abstract

Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity $γ$, the squeezed direction $θ$ and squeezed strength $r$. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller $γ$ or bigger $p$-quadrature. Interestingly, when $0<θ<π/2$, the squeezed quadrature is determined by the combination of $r$ and $θ$, and by numerical simulation we find that the fidelity peak occurs at $r=1-2θ/π$. The fidelities increase with increasing $r$ when $r\in (0,1-2θ/π]$. When $θ\geπ/2$, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.

DOI
10.48550/arxiv.2304.04223

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Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity γγγ, the squeezed direction θθθ and squeezed strength rrr. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller γγγ or bigger ppp-quadrature. Interestingly, when 0<θ<π/20<θ<π/20<θ<π/2, the squeezed quadrature is determined by the combination of rrr and θθθ, and by numerical simulation we find that the fidelity peak occurs at r=1−2θ/πr=1-2θ/πr=1−2θ/π. The fidelities increase with increasing rrr when r∈(0,1−2θ/π]r\in (0,1-2θ/π]r∈(0,1−2θ/π]. When θ≥π/2θ\geπ/2θ≥π/2, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.
We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.
Understanding heat transfer between a quantum system and its environment is of grave importance if reliable quantum devices are to be constructed. Here, the heat transfer between the system and bath in non-Markovian open quantum systems in the process of adiabatic speedup is investigated. Using the quantum state diffusion equation method, the heat current, energy current and the power are calculated during the free evolution and under external control of the system. While the heat current increases with increasing system-bath coupling strength and bath temperature, the non-Markovian nature of the bath can restrict the heat current. Without pulse control, the heat current is nearly equal to energy current. However, with pulse control, the energy current is nearly equal to the power. We show that more non-Markovian baths can be used to better approximate an adiabatic evolution and have a smaller heat current. Our results reveal that the non-Markovian nature of the bath significantly contributes to both the heat transfer rate as well as the effective adiabatic speedup.
High fidelity target control over quantum systems has been realized in noisy environments. However, with the development of quantum science and technology, much higher requirements have been placed on the control precision. Meanwhile, the open system dynamics can also be modulated via engineering the reservoirs. In this work, on a basis of high fidelity control over systems, we investigate the further enhancement of the fidelity via squeezing the reservoirs. Taking the adiabatic evolution of an open spin system as an example, we find that the squeezing direction determines whether the improvement of adiabatic fidelity occurs, while the squeezing strength determines how much the fidelity is improved. Therefore, a significant enhancement in fidelity can be obtained by choosing suitable squeezing parameters. In addition, squeezing is able to slow down the decline trend that the fidelity degrades with a longer evolution time, a larger system–bath interaction strength, or a more pronounced bath Markovianity. Our work shows that squeezing enables the further improvement of high fidelity and uses a combined strategy that simultaneously controls the system and its environment, which will have potential applications in various quantum information processing tasks.
We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir states are considered. Particularly, the squeezed reservoirs coupled to the system through single and two quanta exchange processes are put in the spotlight. We investigate the quantumness conveyed to the system through the bath by computing a nonclassicality measure for different bath properties and when the memory effects are appreciable. The measure of nonclassicality is calculated for projective measurements both in the number state basis and a basis formed by a set of coherent states. Our results show that in both bases the measure exhibits characteristic features for each bath state and the form of its interaction with the system. Some of those features are independent from the measurement scheme (number or coherent), and thus, emergent from the bath and its interaction with the probe system. This allows for fingerprinting and identifying the environmental effects by tracking a given probe with appropriate measurements. Hence, may prove useful for distinguishing different sources of decoherence.
We apply the stochastic Schr\"odinger equation approach to study the non-Markovian dynamics of quantum systems coupled to a squeezed environment. We derive the non-Markovian quantum-state-diffusion equation using coherent-state unraveling and the associated zeroth-order master equation for general models in a microscopic quantum context. Focused on a dissipative optical cavity coupled with a squeezed vacuum, the numerical simulations demonstrate the time evolution of photon numbers in an optical cavity. We observe that the long-time limits of the non-Markovian dynamics are significantly different from those of the Markovian dynamics for various memory factors and squeezing factors. Additionally, non-Markovian dynamics exhibit a distinct pattern of behavior when parameters change. Our work provides a method to study the impact of multiple parameters on the non-Markovian dynamics and long-time limits in a joint manner. The method can be further extended to squeezed finite-temperature environments.
The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the 'spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.