Dispersive optomechanics: a membrane inside a cavity

A.M. Jayich, J.C. Sankey, B.M. Zwickl, C. Yang, J.D. Thompson, S.M. Girvin, A.A. Clerk, F. Marquardt, J.G.E. Harris
NJP 10, 095008 (2008)

We present the results of theoretical and experimental studies of dispersively coupled (or ‘membrane in the middle’) optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric membrane. We focus on the cavity’s transmission, reflection and finesse as a function of the membrane’s position along the cavity axis and as a function of its optical loss. We compare these calculations with measurements and find excellent agreement in cavities with empty-cavity finesses in the range 104–105. The imaginary part of the membrane’s index of refraction is found to be ~10−4. We calculate the laser cooling performance of this system, with a particular focus on the less-intuitive regime in which photons ‘tunnel’ through the membrane on a timescale comparable to the membrane’s period of oscillation. Lastly, we present calculations of quantum non-demolition measurements of the membrane’s phonon number in the low signal-to-noise regime where the phonon lifetime is comparable to the QND readout time.