Feedback Control of Quantum Optomechanical Systems

We show how the performance of a multi-mode optomechanical systems formed by one or more optical cavity modes coupled to a set of high-Q nanomechanical membrane can be controlled and improved both in the classical and in the... [ view full abstract ]

We show how the performance of a multi-mode optomechanical systems formed by one or more optical cavity modes coupled to a set of high-Q nanomechanical membrane can be controlled and improved both in the classical and in the quantum regime by means of phase sensitive feedback loop based on homodyne measurement of the cavity output light. In particular one can beat the quantum back action limit of resolved sideband laser cooling of mechanical resonators, or tailor the cavity response in order to reach the strong coupling regime of normal mode splitting, by amplitude modulation of the driving laser realising an effective "in-loop" cavity with tailored amplified or reduced amplitude fluctuations. By extending the same ideas to the case of more mechanical modes one can engineer the stationary entanglement between mechanical resonators and tailor mechanical squeezing in order to reach quantum-limited sensing of forces.

[1] M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, D. Vitali, "Enhancing Sideband Cooling by Feedback-Controlled Light", Phys. Rev. Lett. 119, 123603 (2017).

[2] M. Rossi, N. Kralj, S. Zippilli, R. Natali, A. Borrielli, G. Pandraud, E. Serra, G. Di Giuseppe, D. Vitali, "Normal-mode splitting in a weakly coupled optomechanical system", Phys. Rev. Lett. 120, 073601 (2018).

Figure Caption (a) A cavity is driven by a coherent field with amplitude quadrature modified by an amplitude modulator fed with the output of the homodyne quadrature detection. (b) The radiation pressure interaction in an optomechanical cavity yields sidebands at mechanical frequencies. (c)–(f) Theoretical results for the phonon number of the cooled resonator at a low temperature (when standard sideband cooling is limited by backaction noise), as a function of the feedback gain amplitude [panels (c) and (e)] and the homodyne phase ϕ [panels (d) and (f)], for the parameters of the experiment of Peterson et al. [panels (c) and (d)] and of J. Clark et al., [panels (e) and (f)]. The light-pink areas indicate results beyond the backaction limit. Red lines are the best up-to-date results obtained for systems operating at the quantum backaction limit.