Quantum optomechanics with a high-frequency dilational mode in thin dielectric membranes

TL;DR

This paper theoretically explores the interaction of a high-frequency dilational mode in thin dielectric membranes with optical cavity fields, proposing a new platform for quantum optomechanics with potential for ground state cooling and quantum information applications.

Contribution

It introduces a multi-mode optomechanical Hamiltonian for GHz-frequency membrane dilational modes coupled to optical cavities, highlighting their potential for quantum control and measurement.

Findings

The dilational mode frequency is in the GHz range for micron-thick membranes.

Coupling can resonantly connect cavity modes at different frequencies.

Optomechanical effects are observable with realistic parameters.

Abstract

The interaction between a high-frequency dilational mode of a thin dielectric film and an optical cavity field is studied theoretically in the membrane-in-the-middle setup. A derivation from first principles leads to a multi-mode optomechanical Hamiltonian where multiple cavity modes are coupled by the thickness variation of the membrane. For membrane thicknesses on the order of one micron, the frequency of this dilational mode is in the GHz range. This can be matched to the free spectral range of the optical cavity, such that the mechanical oscillator will resonantly couple cavity modes at different frequencies. Furthermore, such a large mechanical frequency also means that the quantum ground state of motion can be reached with conventional refrigeration techniques. Estimation of the coupling strength with realistic parameters suggests that optomechanical effects can be observable with this dilational mode. It is shown how this system can be used as a quantum limited optical amplifier. The dilational motion can also lead to quantum correlations between cavity modes at different frequencies, which is quantified with an experimentally accessible two-mode squeezing spectrum. Finally, an explicit signature of radiation pressure shot noise in this system is identified.