Ground-state Cooling And Squeezing Effect Of Mechanical Oscillator In Cavity Optomechanical System

Cavity optomechanics is an emerging subject studying the interaction between optical(microwave)cavity field and mechanical motion.In recent years,due to the great success in the frontier fundamental researches and the potential value in the practical applications,cavity optomechanics attracts increasing research interest.So far,cavity optomechanical system can be simulated in various experimental platforms and it is becoming an ideal system to investigate the macroscopic quantum effects.It is well known that,to realize the effective quantum manipulation of a macroscopic mechanical oscillator based on the cavity optomechanical system,the precondition is effectively suppressing the detrimental effect of the thermal noise arising from the environment so that the mechanical oscillator can be successfully cooled to ground state.Currently,a lot of schemes have implemented extensive study on the ground-state cooling of a single mechanical oscillator and the ideal cooling results have been made accordingly.But the simultaneous ground-state cooling of the multimode mechanical oscillators,especially the largely detuned multimode mechanical oscillators,is still the long-standing problem and challenge.Meanwhile,generation of strong single-mode and two-mode mechanical squeezing in cavity optomechanical system utilizing relatively simple dynamical manipulation technique is of great significance in many aspects,including macroscopic quantum effect demonstration,quantum information processing,and ultraprecise measurement.In this dissertation,we study the ground-state cooling of double-mechanical oscillators,generation of single-mode and two-mode mechanical squeezing based on the cavity optomechanical system.The main research contents of this dissertation are as follows:We study the double-mechanical-oscillator ground-state cooling in a compound threemode cavity optomechanical system and discuss the simultaneous cooling of a pair of resonant and largely-detuning coupled mechanical oscillators,respectively.As to the resonant case,we introduce the frequency modulation technique to completely suppress the nearest resonant Stokes sideband,which leads to the cooling results of double mechanical oscillators successfully break the quantum backaction cooling limit in the case of without modulation.While for a pair of largely-detuning coupled mechanical oscillators,we further introduce the bias gate voltage modulation to construct the effective beam-splitter type interaction between two mechanical modes,which provides the cooling channel for the second mechanical oscillator.Resorting to the dynamical modulation technique,we successfully realize the simultaneous cooling of two largely-detuning mechanical oscillators.This scheme can be achievable in a much wider parameter zone,i.e.,ranging from weak coupling to ultrastrong coupling and from the resolved-sideband regime to the unresolved-sideband regime.We design the two-layer graphene-membrane experimental system model,which provides the sufficient theoretical guidance for the experimental realization of this scheme.This scheme is very meaningful for the potential practical applications involving large size multimode mechanical systems.In the standard cavity optomechanical system,by introducing the periodic modulation into the single-tone driving field to effectively cool down the mechanical Bogoliubov mode,we study the generation of far beyond 3 d B strong mechanical squeezing.We find that the amount of mechanical squeezing is not simply dependent on the order of magnitude of the effective optomechanical coupling,but is closely related to the ratio of sideband strengths for it.To maximize the mechanical squeezing,we numerically and analytically optimize this ratio in the steady regime.In addition,we also discuss the influence of the environment thermal noise on the mechanical squeezing and find that the generated mechanical squeezing effect is very robust against the thermal noise.This scheme can be expected to simplify some existing dynamical modulation schemes based on the two-tone pump driving technique.We study how to generate the beyond 3 d B limit strong mechanical squeezing via the joint effect between mechanical nonlinearity and parametric pump driving.We find that the reasonable choice of the parametric pump frequency can modulate the effective optomechanical interaction between cavity mode and mechanical mode as a beamsplitter-type interaction in the squeezing transformation frame,which contributes to that the squeezing of the cavity mode created by the optical parametric amplifier can be further transferred into the squeezed mechanical mode induced by the mechanical nonlinearity.Based on this kind of joint effect,we generate the beyond 3-d B strong mechanical squeezing.However,the two respective independent squeezing components are permitted below3 d B.We find that,as to the ideal mechanical bath system,the joint squeezing effect just is the superposition of the two respective independent squeezing components.In addition,we discuss the detection of the joint mechanical squeezing effect,which can be achievable by directly measuring the quadrature fluctuation squeezing spectrum of the output field via the homodyne detection technique instead without the need of introducing an additional ancillary cavity mode.The joint idea in this scheme can be generalized to study other quantum effects.Based on the double-oscillator cavity optomechanical system,through implementing the specific periodic modulation acted on the amplitude of the single-tone pump field,we study the generation of two-mode mechanical squeezing.When the frequencies of the two mechanical oscillators are identical,we make use of a large-detuning laser field with sinusoidal amplitude modulation to drive system and the dynamics of the superposition mode of these two nonlocal mechanical modes is mapped into a parametric oscillator,which successfully induces strong two-mode mechanical squeezing.While for the two mechanical oscillators with different frequencies,we design a specific kind of sidebandmodulation technique to exert on the amplitude of the laser driving field and precisely obtain the desired form of the effective optomechanical coupling for the two-mode mechanical squeezing generation.Since the two-mode mechanical squeezing effect corresponds to quantum entanglement between two mechanical oscillators,we also characterize the mechanical-mechanical entanglement in terms of the logarithmic negativity.No matter to resonant or non-resonant mechanical oscillators,the strong mechanical-mechanical entanglement always can be achievable.This scheme has important application prospect in continuous-variable quantum information processing tasks involving quantum entanglement based on the cavity optomechanical systems.