Optical Bistability In Rydberg Atomic Ensemble With Doppler Broadening

Quantum coherence and interference resulted by atom-field interaction can produce a lot of interesting optical phenomena in an atomic system.Such as electromagnetically induced transparency(EIT),coherent population trapping(CPT),lasing without inversion(LWI),optical bistability(OB)and so on.Optical bistability has been widely studied both theoretically and experimentally due to its applications in all-optical switches,optical transistors and optical storage.With the optical bistability phenomenon was deeply studied,the realization mechanism of optical bistability was also expanded.Lately,the study of optical bistability has been extended to the Rydberg atomic system.The Rydberg atom with the large main quantum number has many special properties different from ordinary atoms.Such as huge dipole moments,long lifetimes and dipole blockade effect due to dipole-dipole interaction of Rydberg state,et al.We can use these special properties of Rydberg atoms to study the nonequilibrium phase transition in quantum multi-body physics,to realize single photon storage in quantum information processing,to realize quantum entanglement and quantum communication,et al.These special properties also provides the possibility to realize optical bistability in Rydberg atomic system.In recent years,optical bistability has been widely studied in therm Rydberg atomic system,but the influence of Doppler effect did not take into consideration.It is known that Doppler effect induced by atomic thermal motion will influence atomic optical response.So the influence of Doppler effect can not be ignored.In this paper,We mainly study the effect of Doppler effect caused by atomic thermal motion on optical bistability in Rydberg atomic ensembles.Here,we extend the theoretical study of optical bistability in two-level Rydberg atomic ensembles with Doppler effect of Maxwell distribution.We use a mean-field theory to deal with the dipole-dipole interaction between Rydberg atoms,and then we take the temperature into account.In order to accurately consider the influence of Doppler effect on the steady-state optical response of Rydberg atomic ensemble,we should not only integrate the Rydberg population,but also consider the influence of the average van der Waals potential based on the average Rydberg population.To solve this difficulty,we adopt an asymptotic iteration method to solve the final Rydberg population with the Doppler effect.We find that by numerical analysis,for fixed Rabi frequency and the van der Waals potential,the width of the bistable region varies with the temperature,until the temperature exceeds the critical value,the bistability will be destroyed.In addition,we also find that the characteristic temperature of bistable disappearance is related to the value of the van der Waals potential.Then we consider a three-level ladder atomic structure,which can be adiabatically eliminated into an equivalent two-level structure under the condition of the large single-photon detuning and two-photon resonance.Through a two-photon excitation structure,the Doppler effect can be partially eliminated,in this way,the influence of the Doppler effect on optical bistability can be reduced.