Enhancing Optomechanical Coupling via the Josephson Effect

TLDR

Cavity optomechanics holds promise for probing quantum mechanics in large systems, yet the weak radiation‑pressure coupling limits progress; in certain regimes this coupling can be viewed as qubit‑mediated, and here it arises mainly from a cross‑Kerr interaction that makes the cavity refractive index depend on phonon number. We aim to demonstrate that tuning the Josephson inductance in a single‑Cooper‑pair transistor enables a strong radiation‑pressure‑type coupling between mechanical and microwave resonators. The scheme uses the transistor to adjust the Josephson inductance, creating a cross‑Kerr coupling between the resonators that yields a strong radiation‑pressure‑type interaction. The approach achieves exceptionally large g₀ and enables phonon‑number resolution through cavity measurements.

Abstract

Cavity optomechanics is showing promise for studying quantum mechanics in large systems. However, the smallness of the radiation-pressure coupling is a serious hindrance. Here we show how the charge tuning of the Josephson inductance in a single-Cooper-pair transistor can be exploited to arrange a strong radiation-pressure-type coupling ${g}_{0}$ between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high ${g}_{0}$. Contrary to the recent proposals for exploiting the nonlinearity of a large radiation-pressure coupling, the main nonlinearity in this setup originates from a cross-Kerr type of coupling between the resonators, where the cavity refractive index depends on the phonon number. The presence of this coupling will allow accessing the individual phonon numbers via the measurement of the cavity.