Self-organized Structures Of Laser Field And Their Manipulation In Ultracold Rydberg Atomic Gases

Rydberg atom refers to a kind of atom in which the outermost valence electron transitions to the quantum state with the higher principal quantum number.The atom has the advantages of large radius and electric dipole moment,long lifetime and strong and long-ranged interaction,etc.Especially,the dipole blockade effect contributed by strong Rydberg interaction provides a foot stone for the research in nonlinear and quantum optics,quantum computing,quantum information,quantum many-body sim-ulation,precision spectroscopy and precision measurement,etc.Electromagnetic induced transparency(EIT)effect provides a new research inter-ests for the resonant nonlinear optics.Rydberg-EIT provides a powerful method for the study of Rydberg atoms.In the laser cooled Rydberg atomic system,through Rydberg-EIT,by mapping the strong Rydberg-Rydberg interaction to the photon-photon interac-tion,the optical Kerr nonlinear susceptibility is 5 orders of magnitude larger than that of traditional EIT medium.In recent years,the strong nonlocal self-focusing Kerr nonlinear effect based on Rydberg-EIT has carried out the research on high-dimensional spatiotemporal opti-cal pulses and their storage and retrieval,and has achieved many results.However,Rydberg-EIT can also achieve strong nonlocal self-defocusing Kerr nonlinearity.Based on this,many new physical effects can be obtained,especially the self-organized be-havior of laser field.As we all know,symmetry breaking and the formation of self-organized structure(SOS)are widespread and important phenomena in both nature and human society.The research on the SOS of laser field and their manipulation in Ryd-berg atomic gas is of great significance not only for the in-depth exploration of Rydberg atoms,but also for the study of self-organized behavior.In the dissertation,we shall investigate the SOS of laser field and their manipu-lation in ultracold Rydberg atomic system,which mainly include:(i)Constructing the theoretical model for the interaction between light and atoms,deriving the Maxwell-Bloch(MB)equations,and the nonlocal nonlinear Schr?dinger(NNLS)equation(s)satisfied by the envelope of probe field.(ii)Studying significantly enhanced Kerr non-linear effects.(iii)Studying modulation instability(MI)of the plane-wave state of NNLS.(iv)Exploring the possible SOS of laser field and structural phase transitions.(v)Finally,cloning the SOS by the nonlocal cross-Kerr nonlinearity.The main work contains the following aspects:1.SOS and their manipulation of probe field with microwave controlled Ry-dberg interactions.We propose a scheme to realize optical SOS in a cold Rydberg atomic gas via EIT.We first drive the Hamiltonian,MB equations and(2+1)dimen-sional NNLS equation.The nonlinear parts of the NNLS equation has both the attrac-tive and repulsive interactions.Then,MI analysis is carried out and,subsequently,it is found that the MI can be flexibly manipulated by microwave field in repulsive interaction regime.By manipulating the nonlocality of Kerr nonlinearity,microwave field,and probe field,we obtain not only hexagonal structures,but also two kinds of square structures through solving numerically the NNLS equation with imaginary time method.Further,we theoretically analyze the reasons of the emergence of different structures.In addition,we also obtain nonlocal(2+1)dimensional spatial optical soli-tons when the attractive interaction dominates.Our work opens a way for the study of SOS and structural phase transition of Rydberg gas based on microwave dressing and is expected to be applied to optical information processing and transmission.2.SOS and their manipulation of the circularly polarized light in ultracold Rydberg gases.We investigate the formation and control of SOS in a cold Rydberg atomic gas via double EIT.Based on the Hamiltonian and MB equations,we drive the coupled envelope equations of NNLS for circularly polarized light beyond the mean-field approximation(MFA),which consist of nonlocal self-Kerr nonlinearity and cross-Kerr nonlinearity.We show that,through the MI of plane-wave state of a laser field with two polarization components,the system undergoes a spontaneous symmetry breaking and hence the emergence of plentiful self-organized optical lattice structures,which can be manipulated by the ratio between the cross- and self-Kerr nonlinearities,the nonlocality degree of the Kerr nonlinearities,and the populations initially prepared in the two atomic ground states.Interestingly,a crossover from mixture to separation in space(optical phase separation)of the two polarization components occurs when the ratio between the cross- and self-Kerr nonlinearities exceeds a critical value.We also show that the system supports nonlocal two-component optical solitons and vortices with suitable the parameters of the system.The rich diversity and active controllability of the SOS reported here provide a way for realizing novel optical patterns and solitons and their structural phase transitions based on Rydberg atomic gases.3.Selection and cloning of SOS of probe field in ultracold Rydberg gases.Based on the beyond MFA and assumed the probe field 2 is the weaker than the probe field 1,the(2+1)dimensional NNLS equations are derived firstly,which has the follow-ing characteristics: the fields 1 and 2 have only the nonlocal self-Kerr and cross-Kerr nonlinearities,respectively.The MI analysis and numerical simulation on probe field1 are shown that the ground state has only hexagonal structure.By design the spatially weak modulated control field,we have selected successfully the SOS,including hexag-onal,square,and stripe structures.In addition,we have successfully selected different optical structures through boundary conditions.Finally,by virtue of the cross-Kerr non-linearity,these optical patterns(stripe,square,and hexagon,etc.)prepared in probe 1can be cloned onto probe 2 with very high fidelity.The selection and cloning results of optical SOS reported here are helpful to guide new experimental findings and promising for practical applications in all-optical information processing and transmission.The theoretical model,calculation methods,and some research results proposed here have certain significance for further understanding the relevant nonlinear phenom-ena in ultracold Rydberg atoms.It has the potential application prospect in the design of optical structure and optical information transmission system.