Accelerating relaxation through Liouvillian exceptional point

TL;DR

This paper explores how Liouvillian exceptional points can be used to accelerate the relaxation of open quantum systems, with analytical insights and practical applications in atomic systems and laser cooling.

Contribution

It provides an analytical study of Liouvillian exceptional points, demonstrating how they can be exploited to enhance relaxation rates and optimize dissipative quantum dynamics.

Findings

Degeneracy at LEP increases Liouvillian gap, speeding up relaxation.

Floquet engineering can further widen the gap and accelerate relaxation.

Analytical optimal cooling condition matches experimental and numerical results.

Abstract

We investigate speeding up of relaxation of Markovian open quantum systems with the Liouvillian exceptional point (LEP), where the slowest decay mode degenerate with a faster decay mode. The degeneracy significantly increases the gap of the Liouvillian operator, which determines the timescale of such systems in converging to stationarity, and hence accelerates the relaxation process. We explore an experimentally relevant three level atomic system, whose eigenmatrices and eigenspectra are obtained completely analytically. This allows us to gain insights in the LEP and examine respective dynamics with details. We illustrate that the gap can be further widened through Floquet engineering, which further accelerates the relaxation process. Finally, we extend this approach to analyze laser cooling of trapped ions, where vibrations (phonons) couple to the electronic states. An optimal cooling condition is obtained analytically, which agrees with both existing experiments and numerical simulations. Our study provides analytical insights in understanding LEP, as well as in controlling and optimizing dissipative dynamics of atoms and trapped ions.