On the time optimal thermalization of single mode Gaussian states

TL;DR

This paper investigates the optimal control strategies to accelerate the relaxation of a single-mode Gaussian quantum system towards its steady state under Markovian dissipation, with potential applications in quantum optics and nanotechnology.

Contribution

It analytically derives the optimal relaxation time for Gaussian control of a bosonic quantum system, assuming ideal instantaneous Gaussian operations.

Findings

Derived the optimal relaxation time under ideal control conditions.

Identified Gaussian operations as sufficient for time-optimal control.

Applicable to electromagnetic modes and levitated nanospheres.

Abstract

We consider the problem of time optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e. arbitrary phase rotations, bounded squeezing and unlimited displacements. In the ideal ansatz of unconstrained quantum control (i.e. when the unitary phase rotations, squeezing and displacement of the mode can be performed instantaneously), we study how control can be optimized for speeding up the relaxation towards the fixed point of the dynamics and we analytically derive the optimal relaxation time. Our model has potential and interesting applications to the control of modes of electromagnetic radiation and of trapped levitated nanospheres.