Published on: Sat Jan 08 2011

Notes on “Cavity optomechanics using an optically levitated nanosphere” by D.E. Chang, C.A. Regal, S.B. Papp, D.J. Wilson, J. Ye, O. Painter, H.J. Kimble, P. Zoller

The reason for optically levitating a nanosphere is to minimize contact of other materials with the sphere, so that the sphere can be kept cold, with less effort. This means quantum effects can be observed for a longer time.

The paper talks about reducing thermalization and decoherence rates of nano and micro-mechanical systems. Thermalization is the process of returning the temperature to equilibrium and decoherence is the appearance of wave function collapse, (decoherence post) The reason to reduce these two things is to study whether or not quantum coherence and entanglement can be observed at mesoscopric or macroscopic scales. Mesoscipic is the size range between atomic and macroscopic.

When a sphere is optically levitated in a vacuum, it can be cooled, and quantum behavior emerges even in room temperature environments. (*The paper say’s the CM can be self-cooled to the ground state. How does self-cooling work?)* Since the CM has a long coherence time, more exotic quantum states can be observed. The paper gives two states. One exotic state is to map a squeezed motional state onto light leaving the cavity. (*What is initially squeezed? The sphere?*) The other state is to show entanglement originally shared between two modes of light can be transferred onto the motion of two spheres trapped in spatially separate cavities, creating EPR correlations. (EPR post)

The main point of the paper is to talk about the mechanics of the CM of the sphere. I do not know what exactly the sphere is made out of, but the radius of the sphere is much less than the wavelength of the optical modes that are levitating it. The sphere is like a point dipole. The first thing to do is to optically levitate the sphere. This is done using two standing-wave optical modes. One mode provides an optical dipole trap for the sphere (The sphere is dielectric). The second mode is weaker and has a non-zero intensity gradient at the center of the trap. The non-zero intensity gradient cools the sphere.

The sphere has a dipole moment and optical potential. The position of the point is the center of mass. It has a polarizability, volume and density. Epsilon, the electric permittivity affects the sphere. The optical field has field intensity. I think the sphere is oscillating back and forth slightly in the trap. The trap depth is a function of intensity, volume and the real part of electric permittivity. The oscillation frequencies are a function of the wave number, intensity, density and the real part of electric permittivity. The sphere is subject to noise forces due to collisions with background gas and momentum recoil from scattered photons. The noise forces lead to warming of the sphere.

(*Why does the electric permittivity have a real and imaginary component?)*

The collision rate, R, between the sphere and gas molecules, tells about how quickly the sphere will become to warm. It is a function of the radius of the sphere, along with other factors. Because of this the ideal radius for a sphere to levitate can be determined.