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Physical Review A

Direct conversion of slow light into a stationary light pulse

Xiaojun Zhang, Hai-Hua Wang, Chengze Liu, Xingwei Han, Cunbo Fan, Jin‐Hui Wu, Jin-Yue Gao

Published Aug 14, 2012• 6 citations
Publisher

Abstract

Analysis on direct transforming the slow light into the stationary light pulse (SLP) is presented. Without the process of turning the slow light into the coherence between the lower levels, the generation of SLP is more efficient. The Maxwell-Liouville equations are employed to study the light pulse dynamics in the samples coherently driven by a bichromatic standing wave. The solution indicates that the forward and backward components of the SLP approach to each other exponentially. Such property is described by introducing a quantity called characteristic length, which appeared to be the ratio of the optical coherence decay rate and the coefficient of the driving term in Maxwell equation. The necessary length for completing the conversion can be estimated as five times the characteristic length. Several materials are analyzed here, including the ${}^{87}$Rb atoms with different densities, Pr${}^{3+}$-doped yttrium orthosilicate (Pr:YSO), and nitrogen-vacancy color centers in diamond (N-V centers). The values of the characteristic length for the corresponding materials are calculated, as well as the necessary length.

DOI
10.1103/physreva.86.023821

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Analysis on direct transforming the slow light into the stationary light pulse (SLP) is presented. Without the process of turning the slow light into the coherence between the lower levels, the generation of SLP is more efficient. The Maxwell-Liouville equations are employed to study the light pulse dynamics in the samples coherently driven by a bichromatic standing wave. The solution indicates that the forward and backward components of the SLP approach to each other exponentially. Such property is described by introducing a quantity called characteristic length, which appeared to be the ratio of the optical coherence decay rate and the coefficient of the driving term in Maxwell equation. The necessary length for completing the conversion can be estimated as five times the characteristic length. Several materials are analyzed here, including the 87{}^{87}87Rb atoms with different densities, Pr3+{}^{3+}3+-doped yttrium orthosilicate (Pr:YSO), and nitrogen-vacancy color centers in diamond (N-V centers). The values of the characteristic length for the corresponding materials are calculated, as well as the necessary length.
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.
We present a detailed analysis of stationary light pulses (SLP's) for the case of inhomogeneous broadening in both optical and spin transitions, which is normally found in solid materials with long-lived spin coherence. By solving the Langevin equations of motion for the density matrix elements under the integral over the entire range of the inhomogeneous broadenings, the necessary conditions for creating the SLP in a solid are obtained. Then the decay and diffusion processes that the SLP undergoes are analyzed. The characteristics of such processes are studied based on the analytic solution of the SLP with a slowly varying envelope. The dependence of SLP lifetime on inhomogeneous broadenings of spin and optical transitions, which can be regarded as the laser linewidth in the repump scheme, has been discussed.
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counter-propagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. Here, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from0.8 μs0.8\ \mu \mathsf{s}0.8 μsto2.0 μs2.0\ \mu \mathsf{s}2.0 μs. The characteristic dissipation time, obtained by the release efficiency measurement, is1.22 μs1.22\ \mu \mathsf{s}1.22 μs, which corresponds to an effective Q-factor of2.9×1092.9\times 10^{9}2.9×109[1]. As our SLP system reports a large effective N-atom cooperativity of8×1068\times 10^{6}8×106, our work is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multi-mode coherent quantum memory, creation of exotic photonic gas states, etc.
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.
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counterpropagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this Letter, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from 0.8 to 2.0 μs. The characteristic dissipation time, obtained by the release efficiency measurement from the SLP trapping state, is 1.22 μs, which corresponds to an effective Q factor of 2.9×10^{9}. Our Letter is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multimode coherent quantum memory, creation of exotic photonic gas states, etc.
We provide an in-depth numerical study on creation of stationary light pulses (SLP) in a cold atomic medium, locating the optimal parameter space for experimental realization. We visualize the dynamics of the atoms and the field inside the medium. We find that as the coupling field strength increases, the light slowing effect is actually diminished. It also turns out that the spatial profile of the pulse inside the medium is indeed not symmetric around its apex, and we point out that this asymmetry causes the energy imbalance between the two signals retrieved into the opposite directions, in addition to such extrinsic reasons as the disparity between the coupling field strengths or the imperfect centering of the pulse in the medium at the time of “writing”.