Detection of anisotropic particles in levitated optomechanics

Abstract

We discuss the detection of an anisotropic particle trapped by an elliptically polarized focused Gaussian laser beam. We obtain the full rotational and translational dynamics, as well as, the measured photo-current in a general-dyne detection. As an example, we discuss a toy model of homodyne detection, which captures the main features typically found in experimental setups.

Optimal control for feedback cooling in cavityless levitated optomechanics

“…The optically levitated nanoparticle undergoes continuous monitoring of its motion by the trapping laser [39,47]. Specifically, we consider the experimental situation when the translational and rotational degrees of freedom are decoupled, and a single translation degree of freedom can be identified in the detected signal [48].…”

“…In order to emulate the system and to generate an output homodyne current J we use the following dynamical model. We will write the update term due to the detected photons as a stochastic back-action term and we will include additional stochastic terms to account for the undetected photons as well as gas collisions [47,49,52]. This is fully analogous to a classical emulation of the system: loosely speaking, each scattering event due to photons (even if undetected) or to gas particles makes the particle recoil, and this is modelled by noise terms.…”

Precession Motion in Levitated Optomechanics

“…The expressions denote estimates for the variance of momentum (angular momentum) fluctuations per unit time for translations (rotations), induced by gas collisions and photon scattering. Note that this expressions are good estimates for a system that is not highly anisotropic, while for a highly anisotropic objects, the moment of inertia and electric susceptibility tensors have to be taken into account [36]. M and R denote an effective radius and mass of the nanoparticle, Γs and Γc denote photon scattering and gas collision rate, respectively, T is the temperature of the gas, and λ is the laser wavelength (see supplementary material A).…”

“…In this supplementary section we list the terms obtained in [35,36]. We start by specifying the conservative terms.…”

“…1(a) [34]. This experimental situation has been analyzed theoretically using a quantum model [35], as well as numerically, using an approximate classical model [36]. We now summarize the dynamics referring to the latter, where we assume that we are at relatively high pressure, such that we can neglect photon-recoil heating terms.…”