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arXiv:1105.6297 · Journal of Physics B Atomic Molecular and Optical Physics

An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium

Shih-Wei Su, Yi-Hsin Chen, Shih-Chuan Gou, Ite A. Yu

Published Jul 20, 2011• 14 citations
arXivHTMLPDF

Abstract

We model the effects of the atomic thermal motion on the propagation of a light pulse in an electromagnetically induced transparency medium by introducing a set of effectively temperature-dependent parameters, including the Rabi frequency of the coupling field, optical density and relaxation rate of the ground state coherence, into the governing equations. The validity of this effective theory is verified by the close agreement between the theoretical results and the experimental data.

DOI
10.1088/0953-4075/44/16/165504

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We model the effects of the atomic thermal motion on the propagation of a light pulse in an electromagnetically induced transparency medium by introducing a set of effectively temperature-dependent parameters, including the Rabi frequency of the coupling field, optical density and relaxation rate of the ground state coherence, into the governing equations. The validity of this effective theory is verified by the close agreement between the theoretical results and the experimental data.
We present a numerical scheme to study the dynamics of slow light and light storage in an electromagnetically-induced-transparency (EIT) medium at finite temperatures. Allowing for the motional coupling, we derive a set of coupled Schr\"odinger equations describing a boosted closed three-level EIT system according to the principle of Galilean relativity. The dynamics of a uniformly moving EIT medium can thus be determined by numerically integrating the coupled Schr\"odinger equations for atoms plus one ancillary Maxwell-Schr\"odinger equation for the probe pulse. The central idea of this work rests on the assumption that the loss of ground-state coherence at finite temperatures can be ascribed to the incoherent superposition of density matrices representing the EIT systems with various velocities. Close agreements are demonstrated in comparing the numerical results with the experimental data for both slow light and light storage. In particular, the distinct characters featuring the decay of ground-state coherence can be well verified for slow light and light storage. This warrants that the current scheme can be applied to determine the decaying profile of the ground-state coherence as well as the temperature of the EIT medium.
We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.
A number of experiments have been performed on light slowing and stopping in the electromagnetically induced transparency (EIT) media of hot atomic gases where the Doppler-shift may add detunings to the field frequencies in an inhomogeneous fashion. We provide here a theoretical analysis as to the effect of such a Doppler-broadened environment on the dynamics of the system in comparison to a cold atomic medium. We will show that one of the most critical factors in the formation of a stationary light pulse is the enhancement of the excited-state decay rate caused by the collisions between the atoms of the medium and the molecules of the buffer gas.
We present a systematic theoretical study to deal with linear and nonlinear light propagations in a Doppler-broadened three-level $\ensuremath{\Lambda}$ system via electromagnetically induced transparency (EIT), with incoherent population exchange between two lower energy levels taken into account. Through a careful analysis of base state and linear excitation, we show that the EIT condition of the system is given by $|{\ensuremath{\Omega}}_{c}|{}^{2}{\ensuremath{\gamma}}_{31}\ensuremath{\gg}2{\ensuremath{\gamma}}_{21}\ensuremath{\Delta}{\ensuremath{\omega}}_{D}^{2}$, where ${\ensuremath{\Omega}}_{c}$ is half the Rabi frequency of the control field, $\ensuremath{\Delta}{\ensuremath{\omega}}_{D}$ is the Doppler width, and ${\ensuremath{\gamma}}_{\mathit{jl}}$ is the decay rate of the coherence between states $|j\ensuremath{\rangle}$ and $|l\ensuremath{\rangle}$. Under this condition, the effect of incoherent population exchange is insignificant, while dephasing dominates the decoherence of the system. This condition also ensures the validity of the weak nonlinear perturbation theory used in this work for solving the Maxwell-Bloch equations with inhomogeneous broadening. We then investigate the nonlinear propagation of the probe field and show that it is possible to form temporal optical solitons in the Doppler-broadened medium. Such solitons have ultraslow propagating velocity and can be generated in very low light power. The possibility of realizing (1+11+11+1)-dimensional and (2+12+12+1)-dimensional spatial optical solitons in the adiabatic regime of the system is also discussed.
We present a realistic theoretical treatment of a three-level Λ system in a hot atomic vapor interacting with a coupling and a probe field of arbitrary strengths, leading to electromagnetically-induced transparency and slow light under the two-photon resonance condition. We take into account all the relevant decoherence processes including collisions. Velocity-changing collisions (VCCs) are modeled in the strong collision limit effectively, which helps in achieving optical pumping by the coupling beam across the entire Doppler profile. We take into account a dynamic rate of influx of atoms in the two lower levels of the Λ, and an outflux from all the three levels. The steady-state expressions for the atomic density-matrix elements are numerically evaluated to yield the experimentally measured response characteristics. Our predictions are in excellent agreement with the reported experimental results for 4He*. The role played by the VCC parameter is seen to be distinct from that by the transit time or Raman coherence decay rate.
The influence of Kerr nonlinearity and Doppler broadening on the slow light propagation of a dispersive atomic medium is revisited using a four-level ?-type (87Rb) atomic system under the condition of electromagnetically induced transparency (EIT). The medium exhibits an EIT process which is accompanied by normal dispersion, i.e.,?sub-luminal (slow light) pulse propagation. In the presence of Kerr nonlinearity and the Doppler broadening effect the dispersion property of the proposed atomic medium is modified, which leads to enhancement of the positive group index of the medium. The combined effect of Kerr nonlinearity and Doppler broadening on slow light propagation inside the medium is the major motivation for this work.