Study On Nonadiabatic Non-Abelian Geometric Gates In Cavity Optomechanical System

By interacting mechanical resonators with different physical systems,various physical fields can be transferred to the mechanical vibration,which can be coherently transmitted on the mechanical resonators to construct signal processing units for different physical systems.As a fundamental unit,logic gate,which is essential for both classical and quantum information processing,has been realized in mechanical systems.A primary challenge in further developing of the mechanical logic gates includes realizing non-Abelian geometric gates,which can be used to implement universal logic gates.In this letter,by using the method of constructing nonadiabatic non-Abelian geometric gate in quantum systems,we demonstrate nonadiabatic non-Abelian geometric gates in an optomechanical system.The followings are the chief content of the dissertation:Chapter 1:Introduction of the coherent control scheme and its application in mechanical systems.And we introduce the research background of cavity optomechanical system and some typical cavity optomechanical systems.Chapter 2:Study on parametric coupling between two mechanical modes.We carried out the experiment studies on parametric coupling of two modes in a coupled two cantilevers based two-mode optomechanical system,in which the influence of the mode frequency difference on the coupling strength is investigated.In our experiment,we constructed a tunable two-mode system by trapping one of the cantilevers optically.By applying a parametric drive through periodically modulating the trapping power,we realized parametric coupling between the two modes.Furthermore,we studied the parametric coupling under different frequency differences between two modes and obtained the relationship experimentally.Chapter 3:Study on nonadiabatic non-Abelian geometric gates in an optomechanical system.By applying two parametric drives simultaneously,we realized the parametric coupling between three mechanical modes in a three-mode optomechanical system and observed the formation of a mechanical dark mode.Then,we studied the energy transfer between modes under the condition of three-mode coupling,and realized a purely geometric energy transfer between modes by controlling the strengths and operation time of the two parametric drives.By adjusting the strengths of two parametric drives,we realized geometric gates of different functions,and further verified the non-Abelian character by applying two different logic gates continuously.Chapter 4:Conclusion and outlook of the experiment.We reviewed our work and further pointed out its possible applied direction.