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arXiv:1912.04398 · The Journal of Chemical Physics

System–bath entanglement theorem with Gaussian environments

Peng-Li Du, Yao Wang, Rui‐Xue Xu, Hou-Dao Zhang, YiJing Yan

Published Jan 16, 2020• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.5134745

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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.
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.
For open quantum systems, the Gaussian environmental dissipative effect can be represented by statistical quasi-particles, namely, dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between an important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.
The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.
We consider the hybrid system-bath dynamics, based on the Yan's dissipaton formalism [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)]. This theory provides a unified quasi-particle treatment on three distinct classes of quantum bath, coupled nonperturbatively to arbitrary quantum systems. In this work, to study the entangled system and bath polarization and nonlinear Fano interference, we incorporate further the time-dependent light field, which interacts with both the molecular system and the collective bath dipoles directly. Numerical demonstrations are carried out on a two-level system, with comparison between phonon and exciton baths, in both linear and nonlinear Fano interference regimes.
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hierarchical equations of motion formalism is constructed on the basis of a calculus-on-path-integral algorithm, via the auxiliary influence generating functionals related to the interaction bath correlation functions in a parametrization expansion form. The corresponding continued-fraction Green's functions formalism for quantum dissipation is also presented. Proposed further is the principle of residue correction, not just for truncating the infinite hierarchy, but also for incorporating the small residue dissipation that may arise from the practical difference between the true and parametrized bath correlation functions. The final residue-corrected hierarchical equations of motion can therefore be used practically for the evaluation of arbitrary dissipative quantum systems.
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.