Coherent Control Of Quantum Tunneling For A Spin-orbit Coupled Cold Atom Held In A Double Well

By use of periodic driving fields to manipulate cold atoms has always been a hot topic for researchers.The rapid development of laser technology provides an effective experimental means to manipulate the tunneling dynamics of cold atoms in the experiment.In 2011 the experimental realization of spin-orbit(SO)coupled in Bose-Einstein condensate(BEC)provided a new platform for simulating condensed matter physics.In the last decade,many novel quantum tunneling dynamics phenomena have been revealed by theories and experiments in the SOcoupled cold atom system.However,coherent control of quantum tunneling in non-Hermitic SO-coupled cold atom systems and the search for exact solutions of Hermitic SO-coupled cold atom systems are rarely studied.Therefore,This paper mainly studies the stable control of quantum tunneling of non-Hermitic SOcoupled cold atom system and the precise control of Hermitic SO-coupled cold atom system under periodic driving fields.The structure and main contents of this paper are as follows:In the first chapter,we briefly introduce the types of SO-coupling,experimental realization of SO-coupling cold atoms,some interesting quantum tunneling phenomena under periodic driving external field,and non-Hermitic quantum systems.In the second chapter,we study how to use periodic drive to stabilize spin transport in a non-Hermitian SO-coupled cold atom double well system.Using the high-frequency approximation,the floquet state,quasi-energy,and the non-floquet state of the non-Hermitian drive system are obtained analytically.Based on the stability analysis,we find the stability of spin-dependent dynamics depends on the competition and balance between the effective coupling parameters and the gain-loss coefficients.We have systematically explored how the interplay between periodic driving,dissipation,and other system parameters influences the stability of the spin dependent tunneling in the SO-coupled bosonic junction,by taking into account balanced/unbalanced gain-loss between two wells.Under balanced gain and loss,the stable generalized Rabi oscillations with(without)spin-flipping are found,and stable spin-flipping tunneling is shown to be preferentially suppressed with the increase of gain-loss strength.When the ratio of Zeeman field strength to periodic driving frequency (?)/? is even,continuous stable parameter regions is possible to emerge with subtle domain boundaries.When (?)/? is odd,however,only discrete stable parameter regions are found.Under unbalanced gain and loss,whether (?)/? is even or odd,we also find the equilibrium conditions of parameters for the existence of stable spin tunneling.This result could be useful for the experiments of controlling stable spin transportation in a non-Hermitian SO-coupled system.In the third chapter,we present a simple combination of synchronous and asynchronous modulation,the exact solution of SO-coupling in double well is obtained by applying several common elementary functions.Under synchronous combined modulation,we obtain accurate stationary-like states and obtain some interesting physical phenomena,such as tunneling coherent destruction(CDT),selective tunneling coherent destruction(SCDT),arbitrary population transfer(APT)and complete population inversion(CPI).Under asynchronous combined modulations,the arbitrary population inversion(API)with spin-flipping is realized by analytical and numerical methods respectively.The results obtained in this chapter are of great significance for the preparation of precise entangled states.In the fourth chapter,we summarize the whole paper,and put forward the future research prospect of SO-coupled cold atom system.