Cooperatively Enhanced Precision Of Hybrid Light-Matter Sensors

We consider a hybrid system of matter and light as a sensing device and quantify the role of cooperative effects. The latter generically enhance the precision with which modifications of the effective light-matter coupling constant can be measured. In particular, considering a fundamental model of N qubits coupled to a single electromagnetic mode, we demonstrate that the ultimate bound for the precision shows double-Heisenberg scaling: Delta theta proportional to 1/(Nn), with N and n the number of qubits and photons, respectively. Moreover, even using classical states and measuring only one subsystem, a Heisenberg-times-shot-noise scaling, i.e., 1/(N root n) or 1/(n root N), is reached. As an application, we show that a Bose-Einstein condensate trapped in a double-well optical lattice within an optical cavity can in principle be used to detect the gravitational acceleration g with the relative precision of Delta g/g similar to 10(-4) Hz(-1/2). The analytical approach presented in this study takes into account the leakage of photons through the cavity mirrors, and allows one to determine the sensitivity when g is inferred via measurements on atoms or photons.