The Optomechanical Response of a Cubic Anharmonic Oscillator

Abstract

The nonlinearity of a mechanical oscillator may lead to the generation of the macroscopic quantum states, which are useful for precision measurement. Measuring the nonlinearity of a mechanical oscillator becomes important in order to effectively assess its performance. In this paper, we study the electromagnetically induced transparency (EIT) in an optomechanical system with a cubic nonlinear movable mirror. In the presence of the nonlinearity of the movable mirror, we show that the intensity of the output probe field exhibits an asymmetric shape with the transparency peak shifted to a frequency lower than the cavity resonance frequency. This shift can be used to measure the nonlinearity strength of the movable mirror. We also show that the mechanical nonlinearity gives rise to the enhancement of the intensity of the second-order upper sideband generation.

Normal Mode Splitting in a Cavity Optomechanical System with a Cubic Anharmonic Oscillator

“…Here we assume the cubic mechanical nonlinearity strength is real and positive (α > 0). It has been estimated that the cubic mechanical nonlinearity strength α can be about 1.2 × 10 8 N/m 2 [32] by coupling a linear movable mirror to a three-level system [28].…”

“…During the last decade, it has been reported that the large mechanical nonlinearity can be engineered by coupling a linear mechanical resonator to a low-dimesional additional system [28], enhancing the intrinsic geometric nonlinearity of the mechanical resonator with the help of electrostatic fields [29], and using the thermal energy of the levitated nanomechanical oscillator [30]. Moreover, it has been shown that the mechanical nonlinearity in a cavity optomechanical system can be measured from the phase change of a cavity field using a four-pulse interaction [31] and the transparency peak shift of a weak coherent probe field [32]. In addition, the mechanical nonlinearity in an optomechanical system can be used to achieve the self-oscillation [33], enhance the second-order generation [32], entangle the two nanomechanical qubits [34], prepare a single-phonon Fock state [35] and the mechanical squeezed state [36].…”

“…Moreover, it has been shown that the mechanical nonlinearity in a cavity optomechanical system can be measured from the phase change of a cavity field using a four-pulse interaction [31] and the transparency peak shift of a weak coherent probe field [32]. In addition, the mechanical nonlinearity in an optomechanical system can be used to achieve the self-oscillation [33], enhance the second-order generation [32], entangle the two nanomechanical qubits [34], prepare a single-phonon Fock state [35] and the mechanical squeezed state [36].…”

Second-Order Sidebands and Group Delays in Coupled Optomechanical Cavity System with a Cubic Nonlinear Harmonic Oscillator

“…Due to its important research value in quantum communication and quantum computing [2] and ultrasensitive force measurement [3], cavity optomechanics has received considerable attention. Recent experiments have proved the possibility of cooling the mechanical oscillator to the quantum ground state in a cavity optomechanical system [4,5], which enables us to explore many nonlinear optical phenomena in optomechanical systems [6][7][8], such as the non-classical correlations between phonons and single photons [9], entanglement between mechanical and optical resonators [10,11], parametric normal-mode splitting [12][13][14], and mechanical compression state below zero point fluctuation [15][16][17]. In addition, electromagnetic induced transparency (EIT) effect has been widely discussed in quantum optics.…”

Kerr-like nonlinearities in an optomechanical system with an asymmetric anharmonic mechanical resonator

“…In the frame of this model in optomechanics, the possibility of precision measuring electrical charge with optomechanically induced transparency [31], Coulomb-interaction-dependent effect of high-order sideband generation [32] as well as force-induced transparency and conversion between slow and fast lights [33] have been studied. Recently, the elec-tromagnetically induced transparency with a cubic nonlinear movable mirror has been considered [34]. Steadystate mechanical squeezing via Duffing and cubic nonlinearities was analyzed [35].…”