We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to
87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.
We present a microscopic analysis and evaluation of the dielectric susceptibility of a dielectric medium consisting of vector-type two-energy-level atoms responding on a weak probe mode when the atoms are driven by a strong coherent field. Each atom, in an environment of others, exists as a quasiparticle further structuring a bulk medium. In a limit of dilute atomic gas, the dynamics of each atom follows the Mollow-type nonlinear excitation regime, and the medium susceptibility collectivizes the individual atomic responses to the probe mode. We outline how the collective dynamics can be interpolated up to a dense medium, and we argue from general positions that in such a medium the optical nonlinearity and, in particular, its parametric part could be significantly magnified by manipulating both the coherent pump and the sample density. That indicates certain limitations for potential capabilities of quantum communication protocols utilizing the entangled photons, created by a parametric process, as a main resource of quantum correlations.
Understanding the effect of strong laser pulses on the evolution of an atomic or molecular wave function is important in the context of coherent control in the strong-field regime, when power broadening and dynamic Stark shifts become comparable with or bigger than the bandwidth of the control field. We experimentally demonstrate the method of complete characterization of a complex-valued amplitude of a quantum state driven by a strong two-photon field. The method is based on coherent scattering of a weak probe pulse from the strong-field-induced atomic coherence, followed by the detection of the time- and frequency-resolved parametric four-wave-mixing signal. We show that the proposed technique corresponds to a cross-correlation frequency-resolved optical gating (XFROG) of the highly perturbed evolution of an atomic quantum state. Utilizing the XFROG retrieval algorithm, we determine both the amplitude and phase of an atomic wave function at any time moment throughout the interaction with the driving field. The direct retrieval of the time-dependent phase of the wave function, rather than the population dynamics only, enables us to observe the strong-field effects with arbitrary time and frequency resolution.