Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion

Abstract

We present a quantum-mechanical theory of the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the optomechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good-cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.

Controllability of optical bistability, cooling and entanglement in hybrid cavity optomechanical systems by nonlinear atom–atom interaction

“…(5), the two so-called mechanical modes of the system with damping rates γ m = 2 × 10 −5 κ and γ c = 10 −3 κ are driven by the radiation pressure force with the effective frequency ∆ and damping rate κ = 0.5ω m . It is well-known that if the frequency difference of the two mechanical modes ∆ω = ω B −ω m is larger than the band width of the driven force κ, then the two modes can be cooled down to their ground states at two distinct ranges of effective detuning ω j − κ < ∆ < ω j + κ, where the index j refers to m and B for the mechanical and Bogoliubov modes, respectively [15,[34][35][36]. On the other hand, if ∆ω < κ, then both modes can be excited simultaneously by the radiation pressure at a fixed effective detuning ∆.…”

Optomechanics

“…(4)]. One finds (Marquardt et al, 2007;Wilson-Rae et al, 2007) a simple limit on the minimal occupation number,n O M = [κ/(4ω M )] 2 , which can be reached for optimal detuning ∆ = −ω M in the resolved-sideband limit ω M κ, for Γ opt Γ M . In general, the reachable occupation numbern M of the mechanical mode will depend on the initial occupationn T M (hence, starting from cryogenically precooled samples is advantageous) and the mechanical and optical damping rates,…”

“…The power spectrum S FF is directly related (Marquardt et al, 2007) to the spectrum of photon number fluctuations due to shot-noise (see Fig. 3).…”

“…The strong coupling regime, where Γ opt > κ, needs a more sophisticated analysis and gives rise to new features (Marquardt et al, 2007;Marquardt et al, 2008). …”

Macrorealism inequality for optoelectromechanical systems

“…However one cannot easily distinguish the resultant effective low-temperature state of two coupled quantum oscillators from two coupled classical oscillators 19,20 . It is well known from quantum optics that the linear response spectral properties one observes are similar for both theories 18,21,22 , though spectral properties can strongly infer cooling to the mechanical ground state 15,16,19,23 . In addition, the observation of asymmetry between spectral peaks due to absorption and emission of quanta is purely a quantum effect 22 , and has been recently observed in experiment 24 .…”