Theoretical Research Of Quantum Optomechanical Gyroscope

An important part of inertial navigation system is gyroscope,which is used to detect the angular velocity of its carrier.The performance of inertial navigation system depends on gy-roscope deeply.Nowadays,some kinds of gyroscopes,such as spinning mass gyroscope,op-tical gyroscope,and micro-electromechanical gyroscope,are widely used in different cases with their proper advantages.Spinning mass gyroscope has much higher accuracy than other kinds of gyroscopes.Optical gyroscope can work very stably with medium accuracy.Micro-electromechanical gyroscope is very cheap and can be miniaturized easily.People improve gyroscope not only by technology,but also by inventing new principle.Emerging gyroscopes based on nuclear magnetic resonance,superfluid,atom interference.On the other hand,in recent years quantum optomechanics makes great progress with benefit of micro and nano fabrication technologies.Applications based on optomechanics have been investigated deeply in many aspects,such as quantum state preparation and controlling,information transmission,mechanical mode cooling.For precision measurement,optomechan-ics is used to detect displacement,mass,temperature,acceleration,gravitational wave,and so on.Optomechanical detection for displacement has high accuracy.People propose that,one can transform the angular velocity of the platform to a displacement which can be detected by the optomechanical method,then it constitutes optomechanical gyroscope.Some fundamental researches about optomechanical gyroscope have been proposed recently and we give further discussion about optomechanical gyroscope in this thesis.The main content of this thesis comes in three parts.The first part contains first and second chapters.In first chapter,we introduce the back-ground and current situation of gyroscope and optomechanics.It also include the introduction of previous work about optomechanical gyro-scope.Then we present the basic theory about optomechanical gyroscope and optomechanics in second chapter.For optomechanics,we give the standard model and Hamiltonian,Langevin equation,steady state and linearize,fluctuation and homodyne detection.We also give the dy-namic description of the tow-mode mechanical oscillator in rotating frame,with both classical and quantum forms.Third and forth chapters constitute the second part of this thesis.The content of third chapter is optomechanical gyroscope with external mechanical driving.One mode of the t-wo tow-mode oscillator is driven coherently,then the other mode will experience a sinusoidal oscillation induced by Coriolis force.The amplitude of this oscillation can be detected by op-tomechanical method,and one can deduce the angular velocity of the platform.An other work in this chapter is that,we use coherent quantum noise cancellation(CQNC)to improve optome-chanical gyroscope.CQNC is a mature process in optomechanics field and it aims to cancel the back-action noise from cavity to the mechanical oscillator.We present the optomechanical gyroscope without mechanical driving in forth chapter.The Coriolis force induced by the ro-tating of the platform provides coupling between the tow modes of the mechanical oscillator.This lead two effects:The fluctuation spectrum of the displacement is modified by the Coriolis force;this coupling induces splitting of normal mode frequencies.Both these two effects can be detected in experiment,and can be used as principle of gyroscope.Third part is fifth chapter,which contains the work about ground state sideband cooling with electromagnetically-induced-transparency-like approach in double-cavity optomechanical system.Cooling for mechanical mode maybe useful to improve optomechanical gyroscope.Generally,contribution of thermal noise mainly dominates in the total noise spectrum.So,mechanical mode cooling may be useful to increase the accuracy of optomechanical gyroscope.After the main main content,we present the conclusion and outlook of this thesis in sixth chapter.