Optomechanical trapping and cooling of partially reflective mirrors

M. Bhattacharya, H. Uys, and P. Meystre

Phys. Rev. A 77, 033819 – Published 7 March 2008

Abstract

We consider the radiative trapping and cooling of a partially reflecting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. 99, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick dielectric membrane [J. D. Thompson et al., e-print arXiv:0707.1724v2]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar to that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror-coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially reflective mirrors.

Received 29 August 2007

DOI:https://doi.org/10.1103/PhysRevA.77.033819

Authors & Affiliations

M. Bhattacharya, H. Uys, and P. Meystre

B2 Institute, Department of Physics and College of Optical Sciences, The University of Arizona, Tucson, Arizona 85721, USA

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Vol. 77, Iss. 3 — March 2008

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Images

Figure 1
(Color online). (a) The typical layout for optomechanical cooling and trapping using a two-mirror cavity (2MC). (b) A layout recently suggested by the authors for the same purpose using a three-mirror cavity (3MC) [6] with a perfectly reflecting middle mirror, and implemented experimentally in Ref. [7] using a partially transparent dielectric membrane in place of the middle mirror. In the proposal the 3MC was pumped from both sides; in the experiment the cavity was pumped from one side only, as shown in the figure. (c) A possible arrangement for scaling the technique to more than one mirror. The parameters labeling the figures are defined in the text.Reuse & Permissions
Figure 2
(Color online). Numerical solution of Eq. (5) showing the eigenfrequencies $ω_{n}$ of the full 3MC resonator [Fig. 1b] as a function of middle mirror position $q$ . The solid black seesaw curves are for $T = 0$ and the dashed blue sinusoidal curves are for $T = 0.2$ , chosen exaggeratedly for visibility.Reuse & Permissions
Figure 3
Detuning $Δ_{o}$ (dotted line) [Eq. (21)] and quadratic optomechanical coupling constant $ξ_{Q}$ (solid line) [Eq. (22)] as functions of the middle mirror transmissivity $T$ . The parameter values used to generate these plots are provided in Table .Reuse & Permissions
Figure 4
(Color online) Schematics of the two-color cooling and trapping scheme. The region close to the center of the cavity $(q = 0)$ is shown. The sinusoidal curves correspond to the frequencies of two resonator modes as a function of the middle mirror displacement $q$ from the origin. An odd mode of frequency $ω_{t, o}$ (solid line) excited by a laser of wavelength $λ_{t}$ and an even mode of frequency $ω_{d, e}$ (dotted line) excited by a second laser of wavelength $λ_{d}$ are shown. The equilibrium position $q_{0}$ of the mirror is chosen so as to coincide with a minimum of the $ω_{t, o}$ mode and to be slightly to the right of a maximum of the $ω_{d, e}$ mode. Red-detuning the wavelength $λ_{d}$ of the second laser damps the mirror motion via a linear optomechanical coupling and tuning the wavelength $λ_{t}$ of the trapping field to resonance traps the mirror via a quadratic optomechanical coupling.Reuse & Permissions
Figure 5
Linear optomechanical coupling parameter $ξ_{L}$ as a function of the middle mirror placement $q_{0}$ for various values of the mirror transmission $T$ . The dotted line indicates the position of the mirror at $q_{0} = - λ / 2 + λ / 10$ , allowing $ξ_{L}$ to approach closely the maximum value $ξ$ corresponding to a perfectly reflecting mirror.Reuse & Permissions

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