Coupling rotational and translational motion via a continuous measurement in an optomechanical sphere

TL;DR

This paper explores a continuous measurement technique on a nano-optomechanical sphere that couples its rotational and translational motions, revealing quantum properties and testing a new numerical simulation method.

Contribution

It introduces a novel measurement approach that links orientation and position, and demonstrates an efficient numerical method for simulating quantum measurement processes.

Findings

The measurement couples rotational and translational degrees of freedom.

The new numerical method is simpler and more efficient than previous approaches.

The measurement reveals quantum correlations in optomechanical spheres.

Abstract

We consider a measurement of the position of a spot painted on the surface of a trapped nano-optomechanical sphere. The measurement extracts information about the position of the spot and in doing so measures a combination of the orientation and position of the sphere. The quantum back-action of the measurement entangles and correlates these two degrees of freedom. Such a measurement is not available for atoms or ions, and provides a mechanism to probe the quantum mechanical properties of trapped optomechanical spheres. In performing simulations of this measurement process we also test a numerical method introduced recently by Rouchon and collaborators for solving stochastic master equations. This method guarantees the positivity of the density matrix when the Lindblad operators for all simultaneous continuous measurements are mutually commuting. We show that it is both simpler and far more efficient than previous methods.