Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement

Abstract: Continuous observation on an oscillator is known to result in quantum back-action which limits the knowledge acquired by the measurement. A careful balance between the information obtained and the back-action disturbance leads to a limit known as the standard quantum limit. The means to surpass this limit by modulating the measurement strength with the period proportional to half period of the oscillation has been proposed decades ago (Braginskii et al 1978 JETP Lett. 27 276; Thorne et al 1978 Phys. Rev. Lett. 40 667; Braginskii et al 1980 Science 209 547). Such modulated or stroboscopic observation leading to a squeezed state of one quadrature of the oscillator motion with the quantum noise below that of the zero-point fluctuations has been a long-standing goal. Here, we report on the generation of a quadrature-squeezed state of an oscillator by stroboscopic back-action evading measurement. The oscillator is the collective spin of an atomic ensemble precessing in magnetic field. It is initially prepared in nearly the ground state with an average thermal occupancy number $0.08 \pm 0.01$. The oscillator is coupled to the optical mode of a cavity, and the cavity output field detected with polarization homodyning serves as the meter. A back-action-evading measurement is performed by stroboscopically modulating the intensity of the light field at twice the Larmor frequency, resulting in a squeezed state conditioned on the light-polarization measurement with $2.2 \pm 0.3$ dB noise reduction below the zero-point fluctuations for the measured quadrature. The demonstrated squeezing holds promise for metrological advantage in quantum sensing.