Linear response theory for quantum Gaussian processes

Abstract

Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

Charging batteries with quantum squeezing

“…A key ingredient of our proposal is the squeezed nature of the bath being considered. In this case, we can use the linear response theory as developed in [12]. The master equation of a system interacting with a squeezed thermal bath is [7]…”

“…The Lindbladian operators, conversely, can be written in the form Lk = b T k r. Now, given a master equation such as Eq. ( 6), we can write the drift and diffusion matrix as [12]…”

Thermodynamic length and work optimisation for Gaussian quantum states

“…where c n (λ) ∈ C 2N is a vector of complex numbers that may depend on the control parameters. Equations ( 33) and (36) guarantee that dissipative dynamics is Gaussian, that is it maps Gaussian state to Gaussian states [36].…”

“…The goal of this paper is to determine these metrics for a wide class of quantum Gaussian systems and to use this to compute optimal work processes. Gaussian bosonic systems are widely employed in quantum information theory [34][35][36] and quantum thermodynamics [37][38][39] as they are experimentally accessible in current opto-mechanical experiments [40]. It is therefore valuable to understand how to optimise these kind of systems for thermodynamic tasks such as work extraction.…”

Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States

“…The entanglement of m modes with other n modes of a Gaussian multipartite system was treated in [ 17 ]. The linear response for systems close to steady-states under Gaussian processes was obtained in [ 18 ]. The optimal measurement of the fidelity of multimode Gaussian states was studied in [ 19 ].…”