Theoretical Investigation On Several Quantum Nonlinear Optical Effects In Rydberg Atomic Lattices And Ensembles

As an effective carrier of quantum manipulation,Rydberg atoms have many unique properties like long radiative lifetimes,strong dipole-dipole interactions(DDIs),and large electric dipole moments,which have resulted in wide applications in quantum information,quantum optics,quantum simulation,etc.It is of particular interests that long range DDIs can result in the so-called Rydberg blockade effect,prohibiting the simultaneous excitations of two or more Rydberg atoms in a mesoscopic volume.These nontrivial properties of Rydberg atoms have been explored to realize quantum logical gates,single photon sources,non-equilibrium phase,et al.Note,however,that Rydberg atoms are not easy to deal with in theoretical simulation as a many-body system in the presence of DDIs.As the distance between two atoms is large enough,the DDI can be described as a van der Waals(vd W)potential of long-range characteristics,which will be under consideration in this thesis.Compared to other traditional methods for making many-body system calculations,the Monte Carlo(MC)method has the advantages of less resource occupation,fast calculation speed,and high calculation accuracy.This is why we aim in this thesis,with a suitable MC method,to study the electromagnetically induced transparency(EIT)spectra of absorption and the anti-ferromagnetic(AFM)non-equilibrium phases using controlled dark states in a finite square lattice of Rydberg atoms.In addition,we have adopted the Newton iteration method(NIM)with random initial values to examine the bistability of Rydberg excitations in a sample of four-level Y-type Rydberg atoms with double Rydberg states.Firstly,we briefly introduce the research background and theoretical foundation.In chapter 1,we review the Rydberg atomic system involving properties,applications,and calculation methods.In chapter 2,we explain the Rydberg blockade effect,discuss the complex vd W interactions with atomic system including double Rydberg states,and present the briefs about phenomenon of EIT,AFM phase,and excitation bistability in many-body Rydberg system.In chapter 3,we study the steady optical response of a square lattice in which all trapped atoms are driven by a probe and a coupling field into the ladder configuration of EIT.It turns out to be a many-body problem in the presence of vd W interactions among atoms in the high Rydberg state,so the MC method has been used to calculate the density matrix equations(DMEs),of a very high dimension exponentially increasing with the atomic number,by introducing a sufficiently large cutoff radius.Numerical calculations show that the EIT spectra of absorption and dispersion depend critically on a few key parameters including lattice dimension,unitary vd W shift,probe Rabi frequency,and coupling detuning.That means,by modulating these parameters,it is viable to change symmetries of the absorption and dispersion spectra and control the depth and position of the transparency window on demand.To conclude,we have discussed in this chapter the nonlinear EIT phenomenon in a square lattice of Rydberg atoms with complex vd W interactions by combining the MC method with DMEs.In chapter 4,we study the collective Rydberg excitation of a square atomic lattice driven by a pumping and a coupling field into the ladder configuration via MC simulations based on DMEs.Single-atom Rydberg population can be close to unit benefiting from the formation of a dark state such that the AFM phase have been observed at finite two-photon detunings owing to moderate vd W interactions.We note in particular that the pumping Rabi frequency is more important than the coupling Rabi frequency in manipulating the AFM phase to occur for specific pumping detunings,coupling detunings,and nearest-neighbor vd W potentials.It is also found that the AFM phase enters a saturation regime as the boundary effect of vd W interactions is negligible for a large enough lattice size.To conclude,we have shown in this chapter some new aspects of the AFM phase in terms of collective Rydberg excitation,which is instructive to further explore new non-equilibrium phases in Rydberg atoms.In chapter 5,we study the bistable and multistable behaviors of Rydberg excitations in an ensemble of randomly distributed cold atoms by adopting NIM with random initial values to solve many-body DMEs.Self vd W interactions as well as direct and swapping effects of cross vd W interactions are taken into account as these atoms are driven into the four-level Y-type configuration with double Rydberg states.It is found that Rydberg excitations against relevant detunings can exhibit bistability and even multistability as a result of the cooperative nonlinearity.More importantly,such bistability and multistability can be well manipulated by modulating the pumping Rabi frequency to change the cooperative nonlinearity,and it is viable to control the bistable or multistable Rydberg excitation on one transition path via a suitable modulation of the coupling Rabi frequency on the other transition path.To conclude,a numerical iterative algorithm has been developed in this chapter to explore some new aspects of the nonlinear bistability and multistability of Rydberg excitation.Finally,the conclusions and prospects are given.