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The Journal of Chemical Physics

Extended system–bath entanglement theorem with multiple baths in the presence of external fields

Hao-Yang Qi, Yu Su, Yao Wang, Rui‐Xue Xu, YiJing Yan

Published Sep 23, 2024• 3 citations
Publisher

Abstract

The system-bath entanglement theorem (SBET) was established in terms of linear response functions [Du et al., J. Chem. Phys. 152, 034102 (2020)] and generalized to correlation functions [Su et al., J. Chem. Phys. 160, 084104 (2024)] in our previous studies. This theorem connects the entangled system-bath properties to the local system and bare-bath ones. In this work, we extend the SBET to field-dressed conditions with multiple baths at different temperatures. As in reality, the external fields may interact with not only the system but also environments. The extended SBET facilitates, for example, photo-acoustic, photo-thermal, pump-probe related studies. The theorem under the field-free condition (multiple baths) and its counterpart in the classical limit is also presented.

DOI
10.1063/5.0226351

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臺灣大學物理研究所學位論文•Jan 1, 2010•0 citations
The system-bath entanglement theorem (SBET) was established in terms of linear response functions [Du et al., J. Chem. Phys. 152, 034102 (2020)] and generalized to correlation functions [Su et al., J. Chem. Phys. 160, 084104 (2024)] in our previous studies. This theorem connects the entangled system-bath properties to the local system and bare-bath ones. In this work, we extend the SBET to field-dressed conditions with multiple baths at different temperatures. As in reality, the external fields may interact with not only the system but also environments. The extended SBET facilitates, for example, photo-acoustic, photo-thermal, pump-probe related studies. The theorem under the field-free condition (multiple baths) and its counterpart in the classical limit is also presented.
The system-bath entanglement theorem (SBET) was established in terms of linear response functions [J. Chem. Phys. 152, 034102 (2020)] and generalized to correlation functions [arXiv: 2312.13618 (2023)] in our previous works. This theorem connects the entangled system-bath properties to the local system and bare bath ones. In this work, firstly we extend the SBET to field-dressed conditions with multiple bosonic Gaussian environments at different temperatures. Not only the system but also environments are considered to be of optical polarizability, as in reality. With the aid of the extended SBET developed here, for the evaluation of the nonlinear spectroscopy such as the pump-probe, the entangled system-bath contributions can be obtained upon reduced system evolutions via certain quantum dissipative methods. The extended SBET in the field-free condition and its counterpart in the classical limit is also presented. The SBET for fermionic environments is elaborated within the transport scenarios for completeness.
In this work, we establish a so-called "system-bath entanglement theorem," for arbitrary systems coupled with Gaussian environments. This theorem connects the entangled system-bath response functions in the total composite space to those of local systems, as long as the interacting bath spectral densities are given. We validate the theorem with direct evaluation via the exact dissipaton-equation-of-motion approach. Therefore, this work enables various quantum dissipation theories, which originally describe only the reduced system dynamics, for their evaluations on the system-bath entanglement properties. Numerical demonstrations are carried out on the Fano interference spectroscopies of spin-boson systems.
We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.
The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.
We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.
The thesis is devoted to the study of the non-Markovian dynamical process in several different physical systems. Specifically, we investigate the non-Markovian entangle- ment dynamics of two quantum bits (qubits) in a thermal squeezed bath, the non-Markovian dynamics of a nanomechanical resonator (NMR) measured by a quantum point contact (QPC) detector and, the non-Markovian evolution of two-time correlation functions (CF’s) of a two-level atom coupled to a thermal bosonic bath. First, in the investigation of the non-Markovian entanglement dynamics of two qubits in a common squeezed bath, we see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics. Second, we also investigate the dynamics of a NMR subject to a measurement by a low-transparency QPC or tunnel junction in the non-Markovian domain. We derive the non-Markovian number-resolved (conditional) and unconditional master equations valid to second order in the tunneling Hamiltonian without making the rotating-wave approximation and the Markovian approximation, generally made for systems in quantum optics. We find considerable difference in dynamics between the non-Markovian cases and its Markovian counterparts. We also calculate the time-dependent transport current through the QPC which contains information about the measured NMR system. We find an extra transient current term proportional to the expectation value of the symmetrized product of the position andmomentum operators of the NMR. This extra term, with a coefficient coming from the combination of the imaginary parts of the QPC reservoir correlation functions, was generally ignored in the studies of the same problem in the literature. But we find that it has a substantial contribution to the total transient current in the Non- Markovian case and differs qualitatively and quantitatively from its Markovian counterpart. Thus it may serve as a witness or signature of non-Markovian features for the coupled NMR-QPC system. Finally, we use the quantum master equation approach to derive, valid to second order in the system-environment interaction Hamiltonian, non-Markovian evolution equations of two-time CF’s of system operators at finite environment temperatures with any initial separable system-environment states (pure or mixed). When applied to a general model of a system coupled to a finite-temperature bosonic environment with a system coupling operator L in the system-environment interaction Hamiltonian, the resultant evolution equations are valid for both Her- mitian and non-Hermitian system coupling operator cases. We then give conditions on which the derived evolution equations reduced to the case of quantum regression theorem (QRT)in the weak system-environment coupling case, and apply the derived evolution equations to a problem of a two-level system (atom) coupled to a bosonic environment (electromagnetic fields) with L=L(＋)L = L^(＋)L=L(＋).