Mechanical quadrature squeezing beyond the 3dB limit via quantum learning control

The preparation of mechanical quadrature-squeezed states holds significant importance in cavity optomechanics because the squeezed states have extensive applications in elucidating fundamental quantum mechanics and exploiting modern quantum technonogy. Here, we propose a reliable scheme for generating mechanical quadrature squeezing in a typical cavity optomechanical system via seeking for optimal cavity-field driving pulses using a quantum-learning-control method. We realize strong quadrature squeezing exceeded the 3 dB steady-state limit in the mechanical resonator subjected to thermal noise with one hundred thermal phonons. Furthermore, the mechanical squeezing can be ultrafastly created within one mechanical oscillation period. We also obtain the optimal pulsed drivings associated with the created mechanical squeezings and analyze the mechanism for mechanical squeezing generation. This work will motivate succeeding applications of optimal quantum control in quantum optics and quantum information science.