Simultaneous cooling and entanglement of mechanical modes of a micromirror in an optical cavity

TL;DR

This paper investigates the simultaneous cooling and entanglement of two mechanical modes in an optical cavity, revealing how their frequency difference influences cooling efficiency and the nature of steady-state entanglement.

Contribution

It demonstrates that the mechanical frequency difference determines whether both modes can be cooled simultaneously and whether the system exhibits tripartite entanglement or a biseparable state.

Findings

Nearby mechanical modes can be cooled simultaneously if their frequency difference exceeds the effective damping.

When the frequency difference is small, destructive interference suppresses cavity cooling.

The steady-state entanglement structure depends critically on the frequency difference, affecting robustness to temperature.

Abstract

Laser cooling of a mechanical mode of a resonator by the radiation pressure of a detuned optical cavity mode has been recently demonstrated by various groups in different experimental configurations. Here we consider the effect of a second mechanical mode with a close, but different resonance frequency. We show that the nearby mechanical resonance is simultaneously cooled by the cavity field, provided that the difference between the two mechanical frequencies is not too small. When this frequency difference becomes smaller than the effective mechanical damping of the secondary mode, the two cooling processes interfere destructively and cavity cooling is suppressed in the limit of identical mechanical frequencies. We show that also the entanglement properties of the steady state of the tripartite system crucially depend upon on the difference between the two mechanical frequencies. If the latter is larger than the effective damping of the second mechanical mode, the state shows fully tripartite entanglement and each mechanical mode is entangled with the cavity mode. If instead the frequency difference is smaller, the steady state is a two-mode biseparable state, inseparable only when one splits the cavity mode from the two mechanical modes. In this latter case, the entanglement of each mechanical mode with the cavity mode is extremely fragile with respect to temperature.