Generation of Strong Mechanical-Mechanical Entanglement by Pump Modulation

The implementation of strong quantum entanglement between two macroscopic mechanical oscillators is a longstanding pursued goal in fundamental research or applied science. Here, an effective scheme is proposed to generate strong mechanical-mechanical entanglement in a double-oscillator optomechanical system via only introducing the sole amplitude-modulated pattern into the pump field instead without the requirement of any extra techniques. Based on two mechanical oscillators with identical or different frequencies, a specific kind of amplitude-modulated pump field is respectively designed, which successfully manipulates the mechanical oscillators into the highly entangled two-mode squeezed state. The maximum value of the logarithmic negativity that quantifies the generated entanglement reaches about 9 ebits in the appropriate parameter regime, which greatly surpasses the bound 1 ebits on the maximal stationary entanglement from the two-mode parametric interaction. Moreover, the obtained entanglement can be detected via resorting to an ancillary cavity mode with homodyne detection technique. Compared with the previous congeneric schemes, this scheme involves fewer modulation techniques and may provide a new perspective to effectively manipulate the mechanical quantum states in optomechanical systems utilizing the time-dependent modulation.