Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols

TL;DR

This paper develops a comprehensive quantum theoretical framework for light coupling with levitating dielectric objects in optical cavities, enabling the generation and detection of non-Gaussian quantum states of mechanical motion.

Contribution

It introduces a general quantum model including elasticity effects and proposes protocols for creating and measuring non-Gaussian mechanical states in levitating dielectric systems.

Findings

Derived the total Hamiltonian and master equation for the system

Designed a protocol for preparing non-Gaussian quantum states

Proposed a tomography scheme for quantum state measurement

Abstract

We provide a general quantum theory to describe the coupling of light with the motion of a dielectric object inside a high finesse optical cavity. In particular, we derive the total Hamiltonian of the system as well as a master equation describing the state of the center of mass mode of the dielectric and the cavity field mode. In addition, a quantum theory of elasticity is used in order to study the coupling of the center of mass motion with internal vibrational excitations of the dielectric. This general theory is applied to the recent proposal of using an optically levitating nanodielectric as a cavity optomechanical system [Romero-Isart et al. NJP 12, 033015 (2010), Chang et al. PNAS 107, 1005 (2010)]. On this basis, we also design a light-mechanics interface to prepare non-Gaussian states of the mechanical motion, such as quantum superpositions of Fock states. Finally, we introduce a direct mechanical tomography scheme to probe these genuine quantum states by time of flight experiments.