Determination Of Nonlinear Nanomechanical Resonator-qubit Coupling Coefficient In A Cavity Electoamagnetical System

Cavity optomechanics,which studies the coupling between the electromagnetic mode of the cavity and the mechanical motion of the nanomechanical resonator via radiation pressure force,has been a field undergoing rapid development.The most common use of cavity optomechanics is for measurement,for example,the Fabry-Perot cavity,has been used in LIGO for detecting the gravitational wave.On the other hand,demonstrations of ground state cooling,manipulation and the detection of mechanical states at the quantum level require strong coupling,where the rate of energy exchange between mechanical oscillator and cavity field exceeds the rates of dissipations of energy from either system.This has been exceedingly difficult to experimentally demonstrate in cavity optomechanic schemes.An alternative approach is to use the electromagenetic elements instead of the optical elements,called cavity electromechanical systems.Electromagnetically induced transparency is an important effect(EMIT).In an EMIT process,the cavity is driven by a strong driving field and a weak probe field,the frequency of the driving field is redshifted from the frequency of the cavity by the frequency of the mechanical resonator.It makes a peak in the spectrum of the transmission rate of the probe field.In this article,we will add a charge qubit to the cavity electromechanical system,investigate its influence to the EMIT.This article has two chapters.In Chapter One,we discuss the history and the recent development of cavity optomechanics.As well we introduce the notions of EMIT,charge qubit and transmission microwave cavity.In Chapter Two,we add a charge qubit,which couples to the mechanical resonator,to the cavity electromechanical system,and investigate its influence to the EMIT.We found that the peak in EMIT is split,the width of the splitting is proportional to the strength of the nonlinear interaction between the qubit and the nanomechanical oscillator.By using this result,we can determine the nonlinear nanomechanical oscillator-qubit coupling coefficient by measuring the splitting of the transmission rate spectrum.