The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.
Due to its myriad applications in many fields of science and technology, novel light diffraction from specially designed optical gratings is a subject of great interest. Here, we propose a scheme to realize the linear and nonlinear Bragg diffractions from an electromagnetically induced grating (EIG) with parity-time
(PT) symmetry in a cold Rydberg atomic gas, where the Rydberg-Rydberg interaction between atoms are mapped to strong and long-range interaction between photons, characterized by a giant nonlocal Kerr nonlinearity. We show that a probe laser beam with very low light intensity incident upon the
PT-symmetric EIG can display distinctive asymmetric diffraction patterns, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG and the input power of the laser beam. We also show that the intensity distribution among different diffraction orders depends significantly on the
PT-symmetry property of the EIG and on the magnitude and nonlocality degree of the Kerr nonlinearity. In addition, we demonstrate that such Bragg diffraction patterns can be controlled by an external gradient magnetic field, which provides a different way of diffraction control. The research results reported here are not only useful for understanding the unique properties of linear and nonlinear Bragg diffractions by
PT-symmetric gratings but may also be promising for designing optical devices applicable in optical information processing and transmission.
For the first time, we investigate the nonreciprocal generation of six-wave mixing (SWM) in an inverted-Y type four-level system with spatially uniform distribution of atoms. The nonreciprocity results from a moving electromagnetically induced grating (EIG) which is formed by two coupling beams with different frequencies. We demonstrate that the nonreciprocity can be controlled by the frequencies of the coupling fields and the powers of the dressing beams. As the distribution of atoms is uniform, the atomic density cannot affect the nonreciprocity, but it will affect the formation of the photonic band gap structure of the moving EIG. This research can be used to make optical diodes or optical isolators, because the moving EIG, the speed of which is related to the frequency difference of the two coupling beams, can break time-reversal symmetry. We also demonstrate that the nonreciprocal SWM can form a nonreciprocal light droplet when it propagates in atomic vapors with third- and fifth-order nonlinear susceptibilities.