Cavity mode dephasing via the optomechanical interaction with an acoustic environment

TL;DR

This paper investigates how optomechanical interactions with different acoustic environments cause pure dephasing of cavity modes, revealing dependence on environment geometry and size, with implications for quantum coherence preservation.

Contribution

It provides a detailed analysis of cavity mode dephasing due to acoustic environments of various dimensions, highlighting the role of infrared and ultraviolet divergences in these processes.

Findings

Dephasing depends on environment size for 1D and 2D systems.

Dephasing is volume-independent but geometry-dependent in 3D systems.

Infrared divergence affects 1D and 2D environments, ultraviolet divergence affects 3D environments.

Abstract

We consider an optomechanical system comprising a single cavity mode and a dense spectrum of acoustic modes and solve for the quantum dynamics of initial cavity mode Fock (i.e., photon number) superposition states and thermal acoustic states. The optomechanical interaction results in dephasing without damping and bears some analogy to gravitational decoherence. For a cavity mode locally coupled to a one-dimensional (1D) elastic string-like environment or two-dimensional (2D) elastic membrane-like environment, we find that the dephasing dynamics depends respectively on the string length and membrane area--a consequence of an infrared divergence in the limit of an infinite-sized string or membrane. On the other hand, for a cavity mode locally coupled to a three-dimensional (3D) bulk elastic solid, the dephasing dynamics is independent of the solid volume (i.e., is infrared finite), but dependent on the local geometry of the coupled cavity--a consequence of an ultraviolet divergence in the limit of a "pointlike" coupled cavity. We consider as possible respective realizations for the cavity-coupled-1D and 2D acoustic environments, an LC oscillator capacitively coupled to a partially metallized strip and a cavity light mode interacting via light pressure with a membrane.