System–bath entanglement theorem with Gaussian environments

Generalized system-bath entanglement theorem for Gaussian environments

The entanglement between system and bath often plays a pivotal role in complex systems spanning multiple orders of magnitude. A system-bath entanglement theorem was previously established for Gaussian environments in J. Chem. Phys. 152, 034102 (2020) regarding linear response functions. This theorem connects the entangled responses to the local system and bare bath properties. In this work, we generalize it to correlation functions. Key steps in derivations involve using the generalized Langevin dynamics for hybridizing bath modes and the Bogoliubov transformation that maps the original finite-temperature reservoir to an effective zero-temperature vacuum by employing an auxiliary bath. The generalized theorem allows us to evaluate the system-bath entangled correlations and the bath mode correlations in the total composite space, as long as we know the bare-bath statistical properties and obtain the reduced system correlations. To demonstrate the cross-scale entanglements, we utilize the generalized theorem to calculate the solvation free energy of an electron transfer system with intramolecular vibrational modes.

Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction

In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics.

Disentanglement Dynamics in Nonequilibrium Environments

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Nonequilibrium work distributions in quantum impurity system-bath mixing processes

The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes, in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation, but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.

A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions

For open quantum systems, 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 a 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.

Nonequilibrium Kondo regime current noise spectrum of quantum dot systems with the single impurity Anderson model

We investigate the nonequilibrium current noise spectrum of single impurity Anderson model quantum dot systems on the basis of the accurate dissipation equation of motion evaluations. By comparing between the equilibrium and nonequilibrium cases and between the non-Kondo and Kondo regimes, we identify the current noise spectrum of the nonequilibrium Kondo features that actually appear in the entire region of ω ∈ [-eV, eV]. It is well known that the primary Kondo characteristics at ω = ±eV = ±(μ_L - μ_R) display asymmetrical upturns and remarkable peaks in S(ω) and dS(ω)/dω, respectively. These features are originated from the Rabi interference of the transport current dynamics, with the Kondo oscillation frequency of |eV|. Moreover, we also identify the minor but very distinguishable inflections, crossing over from ω = -eV to ω = +eV. This uncovered feature would be related to the interference between two Kondo resonance channels.

Correlated vibration-solvent effects on the non-Condon exciton spectroscopy

Excitation energy transfer is crucially involved in a variety of systems. During the process, the non-Condon vibronic coupling and the surrounding solvent interaction may synergetically play important roles. In this work, we study the correlated vibration-solvent influences on the non-Condon exciton spectroscopy. Statistical analysis is elaborated for the overall vibration-plus-solvent environmental effects. Analytic solutions are derived for the linear absorption of monomer systems. General simulations are accurately carried out via the dissipaton-equation-of-motion approach. The resulted spectra in either the linear absorption or strong field regime clearly demonstrate the coherence enhancement due to the synergetic vibration-solvent correlation.