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Physical Review A

Simplification of the electromagnetically induced transparency system with degenerate Zeeman states

Pei-Chen Guan, Ite A. Yu

Published Sep 18, 2007• 10 citations
Publisher

Abstract

We propose a transformation method that simplifies quantitative analysis in the $\ensuremath{\Lambda}$-type electromagnetically induced transparency (EIT) system containing degenerate Zeeman states. This transformation maps several coupled three-state systems into a simple three-state system. Moreover, we demonstrate that the transformation is an excellent approximation under adiabatic conditions and the calculation results from several coupled systems are in good agreement with those from the simple system. The transformation method is a powerful tool for relevant studies of EIT, slow light, and storage of light.

DOI
10.1103/physreva.76.033817

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We propose a transformation method that simplifies quantitative analysis in the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type electromagnetically induced transparency (EIT) system containing degenerate Zeeman states. This transformation maps several coupled three-state systems into a simple three-state system. Moreover, we demonstrate that the transformation is an excellent approximation under adiabatic conditions and the calculation results from several coupled systems are in good agreement with those from the simple system. The transformation method is a powerful tool for relevant studies of EIT, slow light, and storage of light.
We have studied the role of degenerate Zeeman states in the storage and retrieval of light pulses in the three-level $\ensuremath{\Lambda}$-type system of electromagnetically induced transparency. A probe pulse with the ${\ensuremath{\sigma}}_{+}$ polarization is stored in the medium and subsequently released with the ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarization. However, the manipulation of the retrieved polarization causes an energy loss. Our study shows that the incompatibility between the stored ground-state coherence and the ratio of the probe and coupling Clebsch-Gordan coefficients is responsible for the energy loss. Such energy loss can be avoided as long as all population accumulates in a single Zeeman state. We provide the useful knowledge for the light-storage technique and demonstrate that the degenerate Zeeman states should be considered in the relevant applications.
We have observed various $\ensuremath{\Lambda}$-type electromagnetically induced transparency (EIT) spectra in laser-cooled 87Rb{}^{87}\mathrm{Rb}87Rb atoms of different laser polarization configurations. Unexpected profiles occur in the EIT spectra. We have found the degenerate Zeeman sublevels are responsible for these profiles. The experimental data are in good agreement with the results from the theoretical calculation which takes into account all the 13 Zeeman levels in the $\ensuremath{\Lambda}$ system. Our study demonstrates that Zeeman sublevels play important roles in quantum interference phenomena such as EIT and amplification without population inversion (AWI), and should be taken into account in the analysis of these phenomena.
Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one $\mathrm{\ensuremath{\Lambda}}$ system and retrieving in another $\mathrm{\ensuremath{\Lambda}}$ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a ${\ensuremath{\sigma}}^{+}$-polarized pulse and retrieving with ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.
We report a simplified all-optical scheme that achieves dynamical switching between electromagnetically induced transparency (EIT) and absorption (EIA) in a [Formula: see text]-type atomic system using only two lasers. The switch is controlled via the polarization ([Formula: see text]) and propagation direction of the optical fields. By applying a weak magnetic field, we spectroscopically resolve the degenerate transition into Zeeman-split subsystems and identify an effective N-type pathway as the physical origin of the switching. Theoretical analysis based on dressed-state perturbation theory reveals that the EIT–EIA transition results from constructive quantum interference between secondary dressed states. The scheme also generates tunable dual transparency windows, enabling potential applications in multi-channel signal routing and polarization-controlled slow-light devices.
We analyze electromagnetically induced transparency and light storage in an ensemble of atoms with multiple excited levels (multi-$\ensuremath{\Lambda}$ configuration) which are coupled to one of the ground states by quantized signal fields and to the other one via classical control fields. We present a basis transformation of atomic and optical states which reduces the analysis of the system to that of electromagnetically induced transparency in a regular three-level configuration. We demonstrate the existence of dark state polaritons and propose a protocol to transfer quantum information from one optical mode to another by an adiabatic control of the control fields.
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.