Nonlocal Nonlinear Optical Effects And Applications Based On Double Rydberg Electromagnetically Induced Transparency

Ultracold Rydberg atoms have attracted great interest in recent years.Rydberg atoms refer to atoms in a highly excited state in which the valence electron is excited to the state with a high principal quantum number n.Rydberg atom has many attractive physical properties,such as large atomic scales,large electric dipole moments,long lifetimes,and great sensitivity to applied electromagnetic fields.In addition,the Rydberg atoms have strong atom-atom interactions and can be actively controlled within more than ten orders of magnitude.These properties make the study of Rydberg atoms important for many applications in fields such as precision spectroscopy and measurement,quantum computing and information,quantum many-body simulation,and nonlinear and quantum optics.Electromagnetically induced transparency(EIT)is a typical quantum interference effect.The destructive interference between the atomic quantum states induced by a control laser field can effectively suppress the resonant absorption of the probe laser field.More importantly,the use of EIT can achieve significant enhancement of nonlinear optical effects in atomic media,and a new avenue of weak-light nonlinear optics has been developed by related pioneering work.The phenomenon of EIT in Rydberg atoms(Rydberg-EIT)has intriguing features.The nonlinear optical effects of the atomic medium can be further enhanced by using Rydberg EIT,and its Kerr nonlinear optical susceptibilities are several orders of magnitude larger than that in the traditional EIT medium.Based on Rydberg EIT,it has experimentally realized the deterministic single-photon sources,high-quality single-photon switches and transistors,singlephoton phase gates,photonic molecules,etc.These key discoveries and advances point to new directions in the research of Rydberg nonlinear optics and quantum optics.In the dissertation,we shall investigate nonlocal nonlinear optical effects and applications in double Rydberg-EIT system,which primarily include:(ⅰ)Solve the MaxwellBloch equations for a probe laser field with two polarized components and an invertedY-type four-level atomic system beyond mean-field approximation based on the reduced density matrix expansion(RDME),and demonstrate that the self-Kerr and cross-Kerr nonlinear optical effects of the system can be enhanced by using double Rydberg EIT,so as to produce significant magneto-optical rotations in the polarized plane of the probe laser field under a weak magnetic field;(ⅱ)Study the formation of two-component light bullets(LBs)and light vortices(LVs)based on the double Rydberg-EIT system,and study the Stern-Gerlach effect on the trajectories of LBs and LVs under weak gradient magnetic fields;(ⅲ)Study the storage and retrieval of LBs,and explore the possibility of new pattern formation in the presence of initial ground state coherence.The main work contains the following aspects:1.Study on giant Kerr nonlinearities and magneto-optical rotations via double EIT in a Rydberg-atom gas.We start by considering a Rydberg-atom gas with an inverted-Y-type four-level atomic configuration via double EIT and derive the MaxwellBloch equations under the rotating wave approximation.And then,the many-body correlations between atoms are treated using RDME and the ground-state approximation to calculate the nonlocal self-Kerr and cross-Kerr nonlinear optical susceptibilities in detail.Our results demonstrate that by using the double EIT,not only the absorption of the probe field can be greatly suppressed,but also the Kerr nonlinear optical effect of the system can be greatly enhanced.The self-Kerr and cross-Kerr nonlinear optical susceptibilities can reach the order of magnitude 10-8 m2V-2,which is very close to the experimental measurement reported recently.We find that using the enhanced Kerr nonlinear optical effect,the polarized plane of the probe laser field in the presence of a weak magnetic field can produce significant magneto-optical rotations.The results contribute to deepening the understanding of the physical properties of Rydberg atoms and can be applied to the measurement of weak magnetic fields and optical information processing and transmission.2.Study on Stern-Gerlach effect of vector light bullets in a nonlocal Rydberg medium.Based on the Maxwell-Bloch equations for the coupling of atoms and the external laser field via double Rydberg-EIT excitation,we derive the(3+1)-dimensional envelope equations(nonlocal nonlinear Schrodinger equations)with diffraction,dispersion,and nonlocal self-and cross-Kerr nonlinearities by using the multiple scales method,which satisfies the propagation of two components of the probe field.We demonstrate that based on the nonlocal self-and cross-Kerr nonlinearities of the system,the dispersion,diffraction,and Kerr nonlinearity effects can be balanced by adjusting the system parameters,thus can form stable(3+1)-dimensional vector LBs and LVs.We also demonstrate that by using a gradient magnetic field,the vector LBs and LVs can have a significant Stern-Gerlach effect,and it can be actively manipulated(including merging together the separate trajectories of such LBs and LVs).Our work not only helps to understand the nonlocal nonlinear optical properties of Rydberg atoms but also can be applied to the measurement of weak gradient magnetic fields.3.Study on the storage and retrieval of LBs and the formation of optical self-organization structures via double EIT in Rydberg gas.Based on the double Rydberg-EIT scheme and the solutions of high-dimensional LBs obtained by solving the nonlocal nonlinear Schr(?)dinger equations,which satisfy the propagation of two polarized components of the probe field,we find that the storage and retrieval of(3+1)dimensional LBs and LVs can be realized by manipulating the control field adiabatically off and on.When the control laser field is turned off,the LB information of the probe laser field is converted to atomic coherence and stored in the atomic medium.When the control laser field is turned on,the LB information is converted into atomic information and retrieval.In addition,the modulation instability analysis of the plane wave light field is carried out under the steady-state approximation.We show that in the presence of initial quantum coherence prepared in the two ground levels,the system can generate several new pattern formations based on the nonlocal Kerr nonlinearities and phase separation phenomenon.Our work can help realize novel optical self-organized structures and can be used in the design of nonlinear-based beam splitters.The theoretical model,calculation approaches,and the obtained results have theoretical value,which is helpful to deepen the understanding of the nonlinear optical properties of the Rydberg system,to obtain greatly enhanced nonlocal Kerr nonlinear susceptibilities,and to realize the stable vector LBs and LVs and their active control.And it has promising prospects for applications,such as precision measurement of weak magnetic fields,optical information processing and transmission.