Finite Dissipative Quantum Systems

Yu Pan, Valery Ugrinovskii, M. R. James

Maison Clouâtré, Bünyamin Kartal, Stefano Maranò +2 more

QDE is an emerging paradigm in which an ancillary quantum system is used to remove entropy from a primary quantum system of interest. As a means for entropy reduction, quantum dissipation engineering (QDE) is useful across the domains of quantum sensing, computing, communication, and networking. Whereas most existing approaches concern QDE over an infinite time horizon, this paper studies the use of engineered environments to prepare the primary system in a pure state within finite time. This corresponds to completely transferring the primary system's initial entropy to the engineered environment in finite time. Necessary and sufficient conditions for performing this task are derived. These conditions elucidate the potential of finite-time QDE using real-world quantum systems.

Jae Dong Noh, Takahiro Sagawa, Joonhyun Yeo

The fluctuation-dissipation theorem (FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.

Jing-Dong Bao

The coupling between system and reservoir is considered to be linear in the coordinates of the bath but nonlinear in the system's coordinate. A dissipative threshold is observed at finite temperatures due to nonlinear dissipation. The quantum decay rate of a metastable state including higher-order expanded terms of the coupling form function is proposed, which can be strongly decreased at finite temperatures when the quantum dissipative threshold is added to the saddle point of the potential.