Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature

Summary form only given. In cavity optomechanics one can manipulate the dynamics of a nanomechanical resonator with light, and at the same time one can control light by tayloring its interaction with one (or more) mechanical resonances. A notable example of this kind of light beam control is provided by the optomechanical analogue of electromagnetically induced transparency (EIT), the so called optomechanically induced transparency (OMIT), which has been recently demonstrated [1-3]. In OMIT, the internal resonance of the medium is replaced by a dipole-like interaction of optical and mechanical degrees of freedom which occurs when the pump is tuned to the lower motional sideband of the cavity resonance. OMIT may offer various advantages with respect to standard atomic EIT: i) it does not rely on naturally occurring resonances and could therefore be applied to previously inaccessible wavelength regions; ii) a single optomechanical element can already achieve unity contrast, which in the atomic case is only possible within the setting of cavity quantum electrodynamics; iii) one can achieve significant optical delay times, since they are limited only by the mechanical resonance lifetime 1/γ_m. Previous OMIT demonstrations have been carried out in a cryogenic setup [1,2]; here we show OMIT in a room temperature optomechanical setup consisting of a thin semitransparent membrane within a high-finesse optical Fabry-Perot cavity [3]. Fig. 1 (left upper panel) shows the phase shift acquired by the probe beam during its transmission through the optomechanical cavity. The derivative of such a phase shift gives the group advance due to causality-preserving superluminal effects which a probe pulse spectrally contained within the transparency window would accumulate in its transmission through the cavity. From the fitting curve we infer a maximum signal time advance τT ≈ -108 ms, which is very close to the theoretical achievable maximum τ- max = -2C/[γm(1 +C)], which is -109 ms in our case where the optomechanical cooperativity is C = 160. The reflected field is instead delayed, and from the corresponding expression for the maximum time delay τRmax = 2/[γm(1 +C)], we can also infer a group delay of the reflected probe field τR ≈ 670 μs [3]. In the left lower panel the transparency frequency window in which the probe is completely reflected by the interference associated with the optomechanical interaction is evident. The width of the transparency window is related to the effective mechanical dampingγeffm ≈ γm(1 +C). Therefore both delay and width can be tuned by changing C which in our case is achieved by shifting the membrane along the cavity axis. This is illustrated in the right panel, where the modulus of the beat amplitude vs Δ is plotted for different positions shifts z0 of the membrane from a field node (see caption).