| Optical nonreciprocal transmission plays an important role in quantum information processing,optical communication technology and quantum devices.This property can be used to control the optical signal and reversed paths of the noise in the research and the development of nonreciprocal devices.Nowadays,plenty of optical nonreciprocal devices have been realized in optical isolator,the circulator and directional amplifier.In order to achieve better on-chip integration of nonreciprocal devices,various low-power and nonmagnetic methods,which satisfies optical nonreciprocity,have been proposed.One typical method is based on cavity optomechanical systems,by which the interaction between the materials can be improved by the optical radiation pressure,and also has the characteristics of high sensitivity and easily manipulable.The nanomechanical oscillator has also provided the conditions for on-chip integration of optical nonreciprocal devices.Based on cavity optomechanical system,this paper mainly presents the perfect optical nonreciprocity by the transmission amplitudes and isolation rate in a double-cavity doubleoptomechanical system,the main results are as follows:(1)The evolution of the operators is obtained by Langevin equation in the doublecavity double-optomechanical system.Meanwhile,the related motion equations are given by the fluctuation and the corresponding average.The transmission amplitudes and isolation rate of the system are also obtained by the standard input-output relation of optical field.Firstly,the parameter range of the stable region is obtained by Routh-Hurwitz steady-state criterion.In whole red-detuned driving,the system is stable,and we plot the distribution of unidirectional isolation rate versus the atom-field coupling strengths and the effective optomechanical coupling strengths.When the phase difference is an integral multiple ofπ2,the nonreciprocity is the most obvious.And the complete isolation can also be achieved under two nanomechanical oscillators.When the other nanomechanical oscillator with a high-quality factor is added,the signal in the resonant frequency can be transmitted and a double-peak spectrum curve of isolation rate is firstly observed.(2)In blue-detuned driving,two specific frequencies noise has been suppressed and the double-peak condition of isolation rate can also be obtained by transmitting amplitudes and the isolation rate spectral curve.Firstly,the difference between the blue-detuned and red-detuned driving is that the direction of the nonreciprocity is completely opposite in the same phase and secondly,the system can realize signal amplification.In the stable region,it appears two kinds of optomechanical synergy,which can be used to realize the complete isolation of the resonance frequency.In addition,rich and varied transmission amplitudes spectrum curves are also depicted.(3)In the standard double-cavity double-optomechanical system,the Hamiltonian is first diagonal by using the unitary matrix under the rotating wave approximation.And then the excitation energy is obtained by the new Bose mode.By adjusting the atom-field coupling strengths and the optomechanical coupling strengths,we can achieve selective energy exchange between the cavity mode and the mechanical mode.And the degree of energy exchange has also been enhanced by adjusting the coupling parameters.In all,based on the double-cavity double-optomechanical system,we discuss the transmission amplitudes and the isolation rate in red--detuned and blue-detuned driving.And we obtain the rich curves of transmission amplitudes spectrum and the isolation rate by adjusting the phase,the atom-field coupling strengths,the different optomechanical coupling strengths and the dissipation rate.These results may exist the potential applications in realizing multi-functional optical nonreciprocal devices,especially the optical isolator because it can prevent the flow of two frequencies noise and realize the reverse transmission of a certain frequency signal. |
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