Quantum Optomechanical Heat Engine

We investigate theoretically a quantum optomechanical realization of a heat engine. In a generic optomechanical arrangement the optomechanical coupling between the cavity field and the oscillating end mirror results in polariton normal mode excitations whose character depends on the pump detuning and the coupling strength. By varying that detuning it is possible to transform their character from phononlike to photonlike, so that they are predominantly coupled to the thermal reservoir of phonons or photons, respectively. We exploit the fact that the effective temperatures of these two reservoirs are different to produce an Otto cycle along one of the polariton branches. We discuss the basic properties of the system in two different regimes: in the optical domain it is possible to extract work from the thermal energy of a mechanical resonator at finite temperature, while in the microwave range one can in principle exploit the cycle to extract work from the blackbody radiation background coupled to an ultracold atomic ensemble.

Figure 1

Eigenfrequencies of the normal modes $A$ and $B$, in units of ${\omega }_m$, as functions of the normalized cavity detuning $\mathrm{\Delta }/{\omega }_m$ for the dimensionless optomechanical coupling strength $G/{\omega }_m=0.1$. Dashed lines: noninteracting energies of the phonon and photon modes. ${\mathrm{\Delta }}_i$ and ${\mathrm{\Delta }}_f$ are the initial and final detunings for a generic Otto cycle.

Figure 2

Intuitive physical picture of the Otto cycle for the optomechanical heat engine, see text for details.

Figure 3

Thermal efficiency and total work of the Otto cycle, in units of $\hslash {\omega }_m$, for $T_a=0$ and $T_b=0.1\mathrm{K}$, corresponding to ${\overline{n}}_a=0$, ${\overline{n}}_b=10$, and ${\omega }_m=200\mathrm{MHz}$. In the white region the linearized system is unstable.