An Experimental Study Of Phonon Sqeezing Beyond The Limit Of Feedback Cooling In An Optomechanical System

Due to the high mechanical quality and the ability to couple with physical fields of different kinds,micro-mechanical oscillators are widely used in precision measurements,in which physical fields can be transduced into directly measurement mechanical displacement.The measurement precision of mechanical displacement is limited by readout noise(such as shot noise),measurement back-action noise,and thermomechanical noise.Generally,thermomechanical noise is the primary factor that limits the precision of mechanical displacement in room temperature.Therefore,researchers have proposed many schemes to reduce the thermomechanical noise of mechanical resonators.Specifically,in the scheme of feedback cooling,the mechanical resonator is cooled by applying a feedback force according to the measurement of its thermomechanical displacement.And cooling of room-temperature mechanical resonator down to its motional ground state can be realized using the feedback coolling technique,in which the noise level in displacement measurement imposes a fundamental limit to amount cooling.As one of the most intriguing phenomena in quantum mechanics,squeezing can be used to reduce the thermomechanical fluctuation on one motional quadrature even below the zero-point fluctuation of mechanical resonator at the expense of amplifying that on the other orthogonal one.And,in practice,the magnitude of squeezing is limited mainly by the dynamical instability of the amplified quadrature.In this paper,we carry out experimentally study on phonon squeezing beyond the limit of feedback cooling in an optomechanical system.Firstly,we use feedback to cool a mechanical oscillator from room temperature to about 1.4K.Further increasing the gain of cooling feedback,we find that the thermomechanical noise is amplified because the readout noise amplified by the feedback system can act on the mechanical oscillator as feedback force noise.To surpass the limit of feedback cooling,a study on squeezed cooling of mechanical resonator is conducted to combine techniques of phonon squeezing and feedback cooling.By applying parametric squeezing at the feedback cooling limit,the thermomechanical motion is reduced to about-3dB below the limit of feedback cooling.Moreover,we construct a vector feedback system capable of controlling two orthogonal quadrature independently to pre-cool the squeezed motional quadrature and stabilize the parametrically amplified quadrature simultaneously.And,with respect to the fact that the strength of parametric pump is usually limited in practice,we conduct study on optimization of feedback control to realize an optimal squeezed cooling in experiment.Finally,we carry out experimentally study on sympathetic feedback cooling of two coupled cantilevers.The content of our work includes four parts:(1)The construction of cavity optomechanical system.We inset a micro-cantilever into the middle of a cavity formed by two fiber end face to construct a dispersive optomechanical system.In this system,we can not only optical readout cantilever’s displacement with high precision but also modify the cantilever’s frequency through optically trapping.(2)Feedback cooling of the cantilever.We construct a feedback cooling system for the mechanical oscillator.We realize feedback cooling of the cantilever by applying a control force according to the measurement of thermomechanical motion.By measuring the oscillation spectrum of the cantilever,we calculate the effective temperature of the cantilever in different feedback gain.And the influence of feedback phase,frequency and measured noise on feedback cooling is analyzed to realize an optimal feedback cooling.(3)Squeezed cooling of the cantilever.A parametric pump is applied by modulating the power of trapping laser at a frequency twice of the cantilever’s resonant frequency.The measured displacement signal of the cantilever is demodulated and projected to two orthogonal quadrature in a phase space so that the squeezing state of the cantilever can be recorded.By applying the parametric squeezing at the limit of feedback cooling,a squeezed cooling of the cantilever beyond the imprecision limit of feedback cooling is realized.To get a deep squeezing,we construct a vector feedback system to control the conjugate motion quadrature independently.The amount of squeezed cooling is improved obviously by pre-cooling the squeezed motional quadrature and stabilizing the parametrically amplified quadrature simultaneously using the vector feedback system.And the influence of phase mismatch and phase detuning on squeezed cooling is analyzed.Finally,the vector feedback system is optimized in the case that the strength parametric pump is limited.And optimal squeezed cooling of the cantilever is realized experimentally.(4)Sympathetic feedback cooling of two coupled cantilevers.The hybridization of the cantilevers creates two normal modes:symmetric mode and antisymmetric mode.Due to the symmetry of its oscillation shape,antisymmetric mode is unable to be directed cooled by feedback.To cool antisymmetric mode,we provide a parametric pump to couple antisymmetric mode with cooled symmetric mode by modulating trap power.The coherent dynamics of the sympathetic feedback cooling is investigated by changing the strength of feedback cooling.And the strength of mode coupling is enhanced to improve the sympathetic cooling to the limit imposed by the capacity of feedback cooling.