Investigation Of Lightwave Mixing And Scattering In Condensed Ultracold Neutral Atomic Gases

Bose-Einstein condensation (BEC) is a phenomenon of macroscopic occupa-tion in one or several quantum states by a large number of identical bosons when the system temperature is below to a critical temperature. BEC is the origin of many kinds of macroscopic quantum phenomena, one of the most important conclusions in quantum statistical physics, and the origin of superconductivity and superfluidity.With the spectacular development of laser cooling and trapping techniques, experimenters chill dilute gases of certain atoms to nano-Kelvin temperatures, which allows the realizations of BEC in weakly interacting bosonic atomic(i.e.87Rb,23Na) gases and quantum degenerate fermionic atomic (i.e.6Li,40K) gases, and using a Feshbach resonance they explore the superfluidity as well as BCS-BCS crossover in quantum degenerate Fermi gases. Ultracold atomic physics has so far been in essence a hot boundary field between atomic and molecular, nonlinear and quantum optics and condensed matter physics, which not only serves as a test-bed for theories developed in matter-wave optics, quantum manipulation, high temperature superconductors, Quark-gluon plasma, and neutron stars, but also leads to new achievements in atom laser, atom interferometers, atom clocks, and light clocks.With the realization of Bose-Einstein condensation (BEC), it is now pos-sible to study the interactions of coherent light with an ensemble of atoms in a single quantum state. The high degree of spatial and temporal coherence of a condensate was confirmed in several experiments, which changes the physical mechanism of the interaction between light and quantum gases. Unlike the Nor-mal gases which passively participate in the light-matter interaction, the coher-ent atom recoil motion in quantum gases actively participates in the light-matter interaction with energy and momentum transfer, which not only changes the density distribution of the condensed matter but also affected the generation and linear/nonlinear propagation of the internal field. Therefore, the study of the interaction between light and quantum gases has great significance for the basic- theory development and the control/manipulation of atomic systems, which is indispensable for the light-matter interaction theory.Theoretical study of the interaction between light and quantum gases can be broadly divided into two categories. One is based on the dynamical evolution of the field, which ignores the condensate/quantum properties of quantum gases, i.e., the classic Collective Atomic Recoil Laser Model (CARL model). The other is based on the condensate properties of quantum gases, ignoring the propagation and evolution of the optical field, i.e., condensed matter model. Due to the different focus of the two methods, one can only get some unilateral results. For this reason, we intend to combine the CARL model with the condensed matter model, derive a basic model for the interaction between light and quantum gases through the secondary quantization theoretical framework and the classical electromagnetic theory. Using the Bogoliubov transformation, we introduce the condensate properties to the dynamic evolution of the optical field. Based on the above aspects, we have studied the light scattering and mixing process in ultracold quantum gases. The main results are as follows:1. We present a theoretical investigation of optical self-focusing effects in light scattering with condensates. Using long (>200μs), red-detuned pulses we show numerically that a non-negligible self-focusing effect is present that causes rapid optical beam width reduction as the scattered field propagates through a medium with an inhomogeneous density distribution. The rapid growth of the scattered field intensity and significant local density feedback positively to further enhance the wave generation process and condensate compression, leading to highly efficient collective atomic recoil motion.2. We present a semiclassical theoretical framework on light-wave mixing and scattering with singlecomponent quantum gases. We show that these optical processes originating from elementary excitations with dominant collective atom-ic recoil motion are stimulated Raman or hyper-Raman in nature. In the forward direction the wave-mixing process, which is the most efficient process in normal gases, is strongly reduced by the condensate structure factor even though the Bo-goliubov dispersion relation automatically compensates the optical-wave phase mismatch. In the backward direction, however, the free-particle-like condensate structure factor and Bogoliubov dispersion result in highly efficient light-wave mixing and collective atomic recoil motion that are enhanced by a stimulated hyper-Raman gain and a very narrow two-photon motional state resonance. In contrast to a normal gas, where the medium "passively" participates in nonlin-ear optical processes, quantum gases "actively" interact with the wave mixing process by enforcing the properties arising from condensed matter physics on the generation and propagation of new light fields. This manifestation of con-densed matter physics leads to intriguing suppression and enhancement effects in directional wave generation and propagation processes that have no counterpart in a normal gas. This opens a new chapter on light-matter-wave mixing and scattering:nonlinear optics with quantum gases.3. We investigate effects of dynamically increasing medium index to optical wave propagation in a rubidium condensate. A long pulsed pump coupling D2line transition results in rapidly growth of an internally-generated field, resulting in a significant optical self-focusing effect and creating a dynamically growing medium index anomaly along the condensate long axis that propagates ultra-slowly with the internally-generated field. When a delay-injected probe pulse catches up with the dynamically increasing index anomaly it is forced to slow down and is prohibited from crossing the index anomaly, realizing an ultra-slow matter-optical wave analogue of a dynamic white-hole even horizon.Furthermore, we have studied the propagation and manipulation of the light field based on the active Raman gain (ARG) configuration in neutral atom gases. The main findings include the following aspects:1. We study optical wave deflection in a three-level active Raman gain medium using a spatially inhomogeneous pump field. Using the Eikonal approx-imation, we derive an analytical expression for the deflection angle and demon-strate more than an order of magnitude increase in deflection when compared to the electromagnetically induced transparency method. Numerical simulations have shown excellent agreement with semi-classical theoretical predictions. We further discuss the concept of light-beam-deflection-based wavelength division multiplexing which may have important applications in integrated circuits for optical telecommunications.2. We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations gov-erning the dynamics of left-and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a fac-tor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an M-type five-state electromagnetically induced transparen-cy (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.3. We demonstrate an all-optical atomic CNOT/polarization gate at very low light intensities in a room-temperature atomic vapor. Using a weak light Polarization-Selective-Kerr-Phase-Shift (PSKPS) technique, we selectively write a π-phase shift to only one of the circularly-polarized components of a linearly-polarized input signal field. At the exit of the medium, a high-fidelity, completely orthogonal linear polarization rotation of the input field is achieved, demonstrat-ing the potential for photonic qubit CNOT/polarization gate operations neces-sary for quantum information processing.