A Technique for Measuring Decoherence through Mechanical Interference in Multimode Optomechanics

The process of quantum state swapping allows the preparation and control of hard-to-manipulate quantum systems through more manageable auxiliary systems. This is useful for the study of fundamental physics as it enables us to couple systems in disparate regimes and exploit the advantages of each. We propose an experiment in which a high-frequency resonator prepared in a single-phonon Fock state is coupled to a massive, low-frequency resonator with two-tone pi/2-pulses. Assuming the high-frequency resonator is well isolated from the environment, we can study decoherence of the massive resonator by monitoring the interference pattern in the phonon occupation of the two resonators. The proposed scheme is general and can be implemented in any system with two independently addressable modes. We present fabrication details of one implementation with trampoline resonators. In addition, we report microfabrication goals, challenges and techniques for a different implementation with thin membrane resonators.