Cavity opto-mechanics using an optically levitated nanosphere

Abstract

Recently, remarkable advances have been made in coupling a number of high-Q modes of nano-mechanical systems to high-finesse optical cavities, with the goal of reaching regimes in which quantum behavior can be observed and leveraged toward new applications. To reach this regime, the coupling between these systems and their thermal environments must be minimized. Here we propose a novel approach to this problem, in which optically levitating a nano-mechanical system can greatly reduce its thermal contact, while simultaneously eliminating dissipation arising from clamping. Through the long coherence times allowed, this approach potentially opens the door to ground-state cooling and coherent manipulation of a single mesoscopic mechanical system or entanglement generation between spatially separate systems, even in room-temperature environments. As an example, we show that these goals should be achievable when the mechanical mode consists of the center-of-mass motion of a levitated nanosphere.

Figure 1.

A) Illustration of dielectric sphere trapped in optical cavity. The large trapping beam intensity provides an optical potential U_opt(x) that traps the sphere near an antinode. A second more weakly driven cavity mode with a nonvanishing intensity gradient at the trap center is used to cool the motion of the sphere. B) Energy level diagram of mechanical motion (denoted m) and cavity cooling mode (ph). The mechanical mode has frequency ω_m, while the optical mode has frequency ω₂ and linewidth κ. Photon recoil induces transitions between mechanical states |n_m〉 → |(n ± 1)_m〉 at a rate R_n→n±1 (R_0→1 shown by dashed gray arrow). The cooling beam, with effective optomechanical driving amplitude Ω_m, induces anti-Stokes scattering that cools the mechanical motion and allows for quantum state transfer between motion and light. This beam is also responsible for weaker, off-resonant heating via Stokes scattering. C) Mechanical frequency ω_m as a function of trapping beam intensity. For all numerical results, we take λ = 1 μm, ρ = 2 g/cm³, and ϵ = 2. D) Optical trap depth U₀ (in K) as functions of trapping beam intensity and sphere radius r.

Figure 2.

A) Mean phonon number 〈n_f〉 (black curve) versus cavity finesse () under optimized cooling conditions. The system parameters are given in Table 1. The red curve denotes , the fundamental limit of cooling imposed by sideband resolution. B) Solid blue curve: optimized EPR variance between two levitated spheres, as a function of squeezing parameter e^-2R. System parameters are identical to a). Dashed curve: EPR variance in limit of perfect state transfer, Δ_EPR = e^-2R. Green curve: cavity finesse corresponding to optimal EPR variance. C) Optimized variance (in dB) of squeezed output light from an ideal cavity, as a function of sphere size.