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Physical Review A

Decay of stationary light pulses in ultracold atoms

Jin‐Hui Wu, M. Artoni, Giuseppe Carlo La Rocca

Published Mar 11, 2010• 35 citations
Publisher

Abstract

We develop a general scheme for studying the optical response of ultracold atoms driven into a regime of standing-wave electromagnetically induced transparency. We rely on full numerical solutions of the Maxwell-Liouville equations without invoking secular and adiabatic approximations and arbitrary initial state assumptions. These approximations and assumptions can conceal, e.g., significant loss and diffusion responsible for the decay of stationary light pulses in cold atomic samples. The complex decay dynamics of a stationary light pulse is here analyzed in terms of higher-order spin and optical coherences that arise from nonlinear interactions of the stationary light pulse with the two counterpropagating components of a standing-wave driving field. Specific results for stationary light pulses in cold $^{87}\mathrm{Rb}$ atoms have been discussed for temperature regimes where the residual Doppler broadening is negligible.

DOI
10.1103/physreva.81.033822

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We develop a general scheme for studying the optical response of ultracold atoms driven into a regime of standing-wave electromagnetically induced transparency. We rely on full numerical solutions of the Maxwell-Liouville equations without invoking secular and adiabatic approximations and arbitrary initial state assumptions. These approximations and assumptions can conceal, e.g., significant loss and diffusion responsible for the decay of stationary light pulses in cold atomic samples. The complex decay dynamics of a stationary light pulse is here analyzed in terms of higher-order spin and optical coherences that arise from nonlinear interactions of the stationary light pulse with the two counterpropagating components of a standing-wave driving field. Specific results for stationary light pulses in cold 87Rb^{87}\mathrm{Rb}87Rb atoms have been discussed for temperature regimes where the residual Doppler broadening is negligible.
Fourier-expanded Maxwell-Liouville equations are employed to study the light pulse dynamics in atomic samples coherently driven by a standing-wave light field. Solutions are obtained by a suitable truncation of the Maxwell-Liouville equations that contain the number of spin and optical Fourier coherence components appropriate to the sample temperature. This approach is examined here for cold but thermal atoms where the Doppler broadening is still not negligible and familiar secular approximations no longer hold. In this temperature regime higher-order momentum Fourier coherence components are shown to be important for achieving excellent agreement with a recent experiment done in cold 87Rb^{87}\mathrm{Rb}87Rb clouds at several hundred microkelvins.
We discuss stationary light created by a pair of counterpropagating control fields in $\ensuremath{\Lambda}$-type atomic gases with electromagnetically induced transparency for the case of negligible Doppler broadening. In this case, the secular approximation used in the discussion of stationary light in hot vapors is no longer valid. We discuss the quality of the effective light-trapping system and show that in contrast to previous claims it is finite even for vanishing ground-state dephasing. The dynamics of the photon loss is in general nonexponential and can be faster or slower than in hot gases.
We systematically study stationary light pulses formed in cold atomic media based on the effect of electromagnetically induced transparency (EIT) with counterpropagating laser fields. In contrast to hot media, the formation of stationary light in cold media is not straightforward. Detrimental coherences of high spatial frequencies can be excited which are naturally suppressed in hot media. We demonstrate numerically that these excitations prevent the formation of stationary light in cold media. We further present numerical and experimental results which show that these excitations can be dynamically suppressed in a medium of nonstationary atoms by reducing the width of the EIT transparency window below the typical Doppler shifts present in the medium. This provides an increased interaction time of the light pulses with the medium and enhances the efficiency of nonlinear optical interactions.
An analytical method based on a two-mode approximation is here developed to study the optical response of a periodically modulated medium of ultracold atoms driven into a regime of standing-wave electromagnetically induced transparency. A systematic comparison with the usual approach based on the coupled Maxwell-Liouville equations shows that our method is very accurate in the frequency region of interest. Our method, in particular, explains in a straightforward manner the formation of a well-developed photonic bandgap in the optical Bloch wave vector dispersion. For ultracold 87Rb atoms nearly perfect reflectivity may be attained and a light pulse whose frequency components are contained within the gap is seen to be reflected with little loss and deformation.
We present a detailed theoretical description of the generation of stationary light pulses by standing-wave electromagnetically induced transparency in media comprised of stationary atoms such as ultracold gasses and solids. We show that, contrary to thermal gas media, the achievable storage times are limited only by the ground state dephasing rate of the atoms, making such media ideally suited for nonlinear optical interactions between stored pulses. Furthermore, we find significant quantitative and qualitative differences between the two types of media, which are important for quantum-information processing schemes involving stationary light pulses.
We present a detailed theoretical description of the generation of stationary light pulses by standing wave electromagnetically induced transparency in media comprised of stationary atoms. We show that, contrary to thermal gas media, the achievable storage times are limited only by the ground state dephasing rate of the atoms, making such media ideally suited for nonlinear optical interactions between stored pulses. Furthermore, we find significant quantitative and qualitative differences between the two types of media, which are important for quantum information processing schemes involving stationary light pulses.