Optomechanical Cooling with Generalized Interferometers

The fields in multiple-pass interferometers, such as the Fabry-Pérot cavity, exhibit great sensitivity not only to the presence but also to the motion of any scattering object within the optical path. We consider the general case of an interferometer comprising an arbitrary configuration of generic beam splitters and calculate the velocity-dependent radiation field and the light force exerted on a moving scatterer. We find that a simple configuration, in which the scatterer interacts with an optical resonator from which it is spatially separated, can enhance the optomechanical friction by several orders of magnitude.

Figure 1

(a) The general system consisting of a mobile scatterer $S$ between two sets of generic immobile optical elements (we show a Bragg reflector on the left and a Fabry-Pérot-type cavity on the right as an example). The mobile scatterer can a priori represent anything, e.g., an atom or a mirror. We discuss two specific configurations in this Letter: an atom in front of (b) a two-mirror cavity and (c) a plane mirror [10].

Figure 2

The amplitude of the friction force acting on the scatterer, for various near-mirror transmissivities, is shown as a function of the mirror separation in the cavity. The different curves represent different near-mirror transmissivities: $|t|=0.45$ (dash-dotted curve), $|t|=0.20$ (dotted curve), $|t|=0.10$ (dashed curve), $|t|=0.05$ (solid curve). (Scatterer polarizability $\zeta =1$, scatterer-cavity separation $x\approx 400{\lambda }_0$, $|T|=0.01$, ${\lambda }_0=780\mathrm{nm}$.)

Figure 3

Amplitude of the friction acting on a scatterer of polarizability $\zeta =1$ interacting with a cavity tuned to achieve maximum friction, for varying transmissivity of the near mirror. The friction amplitude (solid curve) approaches that for mirror mediated cooling using the far (dotted line, $t\to 1$) or the near (dash-dotted line, $t\to 0$) mirror only in the appropriate limits. The arrow indicates the point at which the two cavity mirrors have the same reflectivity. Also shown is the intracavity field (dashed curve). ($x\approx 400{\lambda }_0$, $L\approx 2000{\lambda }_0$, $|T|=0.01$, ${\lambda }_0=780\mathrm{nm}$, finesse at peak friction $5.0\times {10}^4$.)

Figure 4

In region (b) of Fig. 3, the friction coefficient amplitude (solid curves) is attenuated due to the attenuation in the field reflected from the cavity (dashed curves). $|T|=0.01$ in every plot; $|t|$ is, from left to right, $6.7\times {10}^{-3}$, $8.3\times {10}^{-3}$, $1.0\times {10}^{-2}$, $1.2\times {10}^{-2}$, and $1.5\times {10}^{-2}$. (Parameters as in Fig. 3.)