Realizing Einstein’s Mirror: Optomechanical Damping with a Thermal Photon Gas

Abstract

Einstein described the damping and thermalization of the center-of-mass motion of a mirror placed inside a blackbody cavity by collisions with thermal photons. While the time for damping even a microscale or nanoscale object is so long that it is not experimentally viable, we show that this damping is feasible using the high-intensity light from an amplified thermal light source with a well-defined chemical potential. We predict this damping of the center-of-mass motion will occur on timescales of tens of seconds for small optomechanical systems.

Measurement of the motional heating of a levitated nanoparticle by thermal light

“…At any time only one light beam is used for trapping. For this larger particle the recoil heating rates are larger than those of the 55 nm particle as the scattering cross section scales as r 6 . The gas damping has a smaller effect as it scales with radius as r −1 .…”

“…If the particle can be held at lower pressures, where gas heating is not significant and where other sources of heating are not important, the particle should come to an equilibrium temperature determined by the thermal light, in this case the bulk temperature of the SLD [6,16]. Damping of the particle motion occurs via the Doppler effect.…”

“…The particle has mass M and oscillation frequency ω q . The damping rate due to the gas molecules at a temperature T g is γ g while γ q ph and T q ph are the damping rate and temperature of the photon bath [6,16,20]. Due to the directional nature of photon scattering, γ q ph is axis dependent [20,21].…”

“…The variance of the photon number in a mode [18] is N 2 = G(ω)A pn cM d n 2 . The total energy gained [6,16,18] by the particle of polarizability α and scattering cross section σ s = α 2 ω 4 6π 2 0 c 4 due to the fluctuation in the photon number along q is…”

“…The effectiveness of such interactions are, however, eventually limited by the discrete nature of the light. For example, fluctuations in the photon number lead to measurement noise and recoil heating [3][4][5][6]. However, the optomechanical effects of squeezed light, Bose-Einstein condensate of photons [7,8], or the light of different photon statistics such as the Bose-Einstein (BE) on levitated systems have not been explored experimentally yet, although squeezed light sources have now been proposed for reducing the recoil heating of such oscillators [9].…”