The Nonlinear Phenomena In An Optomechanical System With A Cubic Anharmonic Oscillator

Cavity optomechanics explores the interaction between optical and mechanical modes through radiation pressure,and has attracted much attention due to its potential applications in ultrasensitive force measurement and quantum information processing.When the macroscopic mechanical oscillator of the optomechanical system is cooled to its quantum ground state,many quantum optical phenomena can be observed in the system,such as entanglement between optical and mechanical resonators,non-classical correlations between single photons and phonons,normal mode splitting and electromagnetically induced transparency.In this paper,we study the quantum optical phenomena in an optomechanical system with a cubic nonlinear anharmonic oscillator,including electromagnetically induced transparency and normal mode splitting.The main content of this paper is composed of the following aspects:1.We study the electromagnetically induced transparency in a cavity optomechanical system with a cubic nonlinear resonator.We study the propagation of weak detection field in an optomechanical system with a cubic anharmonic oscillator.Through the relevant calculations and analysis,we find that when the optomechanical cavity is driven by a strong red sideband laser,the intensity curve of the output detection field is asymmetric due to the nonlinearity of the movable mirror.The results show that the nonlinear strength of the movable mirror can be detected by measuring the displacement of the transparent peak of the output detection field.2.We study the effect of the nonlinear strength of the mechanical oscillator on the generation of second-order upper sidebands.We have made the relevant calculations and obtained the expression of the generation intensity of the second-order upper sideband.By analyzing the relationship between the generation intensity of the second-order upper sideband in the output field and the nonlinearity of the mechanical oscillator,we find that the nonlinearity of the mechanical oscillator will lead to the enhancement of the generation intensity of the second-order upper sideband.3.We theoretically study the normal mode splitting in optomechanical systems with a cubic anharmonic oscillator.The expression of the displacement spectrum of the mechanical oscillator and the expression of the output spectral density are obtained by the correlation calculation.Through analysis and comparison,we find that the larger the nonlinear strength of the mechanical oscillator will increase the distance between the two peaks in the displacement spectrum of the mechanical oscillator and the output spectral density,and make the two spectra more asymmetric.Therefore,the optomechanical system with a cubic anharmonic oscillator provides another way to produce stronger optomechanical coupling.The results in this paper will be useful in measuring the nonlinearity of a mechanical oscillator,frequency conversion in all-optical communication networks,and the quantum control of the mechanical oscillator.