Photon Shot Noise Limited Charge Sensitivity in a Hybrid Quantum System

Hybrid mesoscopic quantum systems serve as essential building blocks for quantum information and metrology devices. One such system that displays a rich variety of behavior in the quantum-classical regime is a Cooper pair transistor embedded in a quarter wave cavity (cCPT). As one application, this device can act as a highly sensitive charge detector, and form the basis for an optomechanical system in the single photon strong coupling regime. We present a theoretical analysis of the photon shot noise limited charge sensitivity of the device, assuming a low average photon number drive. This lower bound is difficult to achieve using conventional detection approaches, owing mainly to the low frequency noise caused by the coupling of thermally activated two-level-fluctuators to the cCPT. The effects of this interaction are observed as 1/f noise in the microwave cavity fundamental resonance frequency. Using careful calibration of a feedback mechanism called Pound-Drever-Hall (PDH) locking, we should be able to observe this noise near the low photon limit. Moreover, a modified PDH scheme may possibly suppress this noise, and achieve charge sensitivity close to our theoretical, minimum shot noise prediction.