Quantum noise in photothermal cooling

We study the problem of cooling a mechanical oscillator using the photothermal (bolometric) force. Contrary to previous attempts to model this system, we take into account the noise effects due to the granular nature of photon absorption. We achieve this by developing a Langevin formalism for the motion of the cantilever, valid in the bad-cavity limit, which includes both photon absorption shot noise and the noise due to radiation pressure. This allows us to tackle the cooling problem down to the noise-dominated regime and to find reasonable estimates for the lowest achievable phonon occupation in the cantilever.

Figure 1

Schematic diagram of an optomechanical system. The mechanical system, or cantilever, is fixed on the (blue) left edge, and operates as a movable mirror (right side, in orange) forming one half of an optical cavity (shown by the red constriction). The gray disk is a nonmovable (i.e., fixed) half-mirror. The optical and mechanical modes are coupled via both radiation-pressure and photothermal forces. The optical cavity (bounded by the fixed gray disk and the (orange) right edge of the cantilever) has equilibrium frequency ${\omega }_c$, quality factor $Q_c$, equilibrium length $L_c$, photon lifetime ${\Gamma }_c$, and is pumped by an external laser with power $P$ and frequency ${\omega }_p$. The cantilever has thermal conductivity $\kappa$, length $L_m$, and surface area $s$. The cantilever mode we consider for cooling has frequency ${\omega }_m$, effective mass $m$, and quality factor $Q_m$. The right edge of the cantilever absorbs photons at the rate $\alpha$, and has a thermal deformation coefficient $\chi$.