Spin-orbit Coupling Of Ultracold Atoms In The Cavity

Ultracold atoms can be trapped in the optical lattices to form the crystal-like structure,and the interaction between atoms can be adjusted by Feshbach resonance technology.Therefore,ultracold atomic physics provides an ideal platform for the study of the solid physics and the many-body theory.However,since the ultracold atoms are electrically neutral,it is difficult to simulate the movement of charged particles in an electromagnetic field.The synthetic gauge potential and synthetic spin-orbit coupling achieved in neutral ultracold atoms have solved this problem and led to the study and simulation of the physical properties associated with the gauge field in solid physics by using ultracold atoms in recent years.An important research direction of the quantum optics is to study the coupling system of ultracold atoms and an optical cavity.In this case,the atom's degrees of freedom are coupled with the optical modes of the cavity field,so that the dynamic behavior of the atom is affected by the feedback of the cavity,and the photons scattered by the atom during the dynamic evolution will effectively change the properties of the cavity field.This paper is based on the Raman-induced synthetic spin-orbit coupling and combined with cavity quantum electrodynamics(CQED)to study the spin-orbit coupling of ultracold atoms in the confined space including the Fabry-Pérot(F-P)cavity and the ring cavity,and discuss the effects of the spin-orbit coupling and the cavity feedback on the system.Firstly,the paper studies the spin-orbit coupling of Bose-Einstein condensates(BEC)in a standing wave cavity as the F-P cavity.The single-mode F-P cavity provides the periodic quantized optical lattices for the ultracold atoms,which can be secondarily quantized by using a tight-binding approximation.It is found through calculation that the large effective detuning(35)?_c can be realized by adjusting the cavity parameters.At this time,the Hamiltonian of this system can be effectively and reasonably approximated,and the specific expression of the single atom's dressed energy levels can be obtained.Due to the introduction of spin-orbit coupling,the pseudospin energy levels of the bosonic atom appear to cross,and there are the massless Dirac points which are similar to massless Dirac points in fermions.At this time,adjusting the incident angle of the two Raman lasers can change the value of the energy levels'intersection and the shapes of the dispersion curves.And changing the applied magnetic field can effectively move the positions of the Dirac points in the momentum space.However,it should be noted that in this model the spin-orbit coupling can't be directly affected by the quantized photon field in the cavity.Secondly,this paper studies the spin-orbit coupling of a single cold atom in a traveling wave cavity.Considering that the light field in the ring cavity is transmitted in one direction,the quantized light field can be directly used instead of one Raman laser when the synthetic spin-orbit coupling is implemented in the single ultracold atom.So the model can be solved using the mean field approximation to obtain the atom's dressed state levels and the photon number of the cavity field.When discussing the influences of various parameters on this system,it is found that the atom's dressed state energy levels are separated with the increase of the pumping rate,and a loop structure appears in the separation process.Then we use the dynamics equations to analyze the stability of this system and introduce the decay rate of the unstable state.When the pumping rate is small,the nonlinearity of this system is more obvious.And with the increase of the pumping rate,the dynamic coupling of spin-orbit coupling and the cavity field decreases,thus the nonlinear effect is weakened.