Coherent coupling of fluctuations in mesoscopic systems in optomechanics

Interaction between a quantum and a mesoscopic system has always been intriguing in understanding the quantum-classical interface. In this context, we show how the energy fluctuations can be adiabatically exchanged, by using laser pulses, between two mirrors or between the motional degree of freedom of an ion trapped inside the cavity and that of one of the cavity mirrors. In the former case, two membranes are suspended inside a cavity. The zero-eigenvalue eigenstate of the matrix governing their fluctuation dynamics indicates that a suitable sequence of pulses to drive the cavity modes can lead to a deterministic adiabatic transfer of energy fluctuations from one membrane to the other, in a way akin to stimulated Raman adiabatic passage. Similar results can also be obtained in the later setup, in which a single ion is trapped inside an optical cavity, with one of the mirrors oscillating. Our results show that it is possible to coherently couple the fluctuations of two mesoscopic systems. Interestingly, this also indicates that the motion of a trapped ion (a quantum system) can lead to motional fluctuation in a mesoscopic mirror. This opens up possibilities for an ion-controlled long-distance transfer of fluctuations among mirrors, using more cavities.