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arXiv:0804.4792 · Physical Review A

Slowing light through Zeeman coherence oscillations in a duplicated two-level system

F. A. Hashmi, M. A. Bouchène

Published May 20, 2008• 16 citations
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Abstract

We present the theory of a method to slow a linearly polarized probe pulse as it propagates through a duplicated two-level system driven by an orthogonally polarized control field. The method makes use of Zeeman coherence oscillations that arise in the atomic system because of the spatial and temporal modulation of the total polarization. This method exhibits properties similar to those that rely on electromagnetically induced transparency but without the existence of any trapping dark state. We demonstrate also the propagation of a polariton in the medium.

DOI
10.1103/physreva.77.051803

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arXiv:1305.4015•Physical Review A•Aug 30, 2013•11 citations
We present the theory of a method to slow a linearly polarized probe pulse as it propagates through a duplicated two-level system driven by an orthogonally polarized control field. The method makes use of Zeeman coherence oscillations that arise in the atomic system because of the spatial and temporal modulation of the total polarization. This method exhibits properties similar to those that rely on electromagnetically induced transparency but without the existence of any trapping dark state. We demonstrate also the propagation of a polariton in the medium.
We consider a double two-level system in which each single two-level system is driven by a strong linearly polarized pulse. The system is probed by a weak pulse orthogonally polarized. We study the distortion experienced by the probe temporal envelope when the relative phase between the pump and the probe is varied. We show that pulse behavior oscillates between two regimes that correspond to transparency and amplification respectively. Interpretation of this effect is given within adiabatic representation.
We study the influence of a lossless material medium on the coherent storage and quantum-state transfer of a quantized probe light in an ensemble of $\ensuremath{\Lambda}$-type atoms. The medium is modeled as uniformly distributed two-level atoms with the same energy level spacing, coupling to a probe light. This coupled system can be simplified to a collection of two-mode polaritons which couple to one transition of the $\ensuremath{\Lambda}$-type atoms. We show that, when the other transition of $\ensuremath{\Lambda}$-type atoms is controlled by a classical light, electromagnetically induced transparency can also occur for the polaritons. In this case the coherent storage and quantum transfer for photon states are achievable through novel dark states with respect to the polaritons. By calculating the corresponding dispersion relation, we find that the ensemble of three-level atoms with $\ensuremath{\Lambda}$-type transitions may serve as quantum memory for it slows or even stops light propagation through the mechanism of electromagnetically induced transparency.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
This paper shows that it is theoretically possible for a medium to generate two copies of an incoming probe pulse as a result of the successive action of two control pulses under conditions of electromagnetically induced transparency. The medium is treated in the model of two-level atoms with threefold degeneration of the lower level (tripod configuration). The three laser-radiation pulses differ in polarization, and the propagation directions of the probe pulse and the two control pulses are orthogonal. The calculation uses a semiclassical approach, the slow-amplitude approximation, and the fixed-field approximation of the control pulses.
For the known, experimentally realized conditions, the detailed analysis of the field-induced transparency and formation of exceptionally low group velocity of probe light is performed. The secondary fields being due to the atomic polarization induced by the two propagating light pulses - coupling (or dressing) and probe ones, resonant to the adjoining transitions in a three-level scheme, are explicitly taken into account. Partly linear (relative to the probe pulse field) and completely non-linear regimes are considered. Particularly, the outputting coupled wave is shown to be slightly amplified, when the probe light pulse “disappears” inside the medium.
We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization, temporal (frequency), and spatial dispersions. The method is based on the reduced Maxwell equation, atomic density matrix formalism, and adiabatic approximation. In order to demonstrate the efficiency of our method we investigate in detail the case of propagation of the pulses under conditions of coherent population trapping in a medium of two-level atoms with degenerate energy levels. Equations describing the evolution of various field parameters are derived. It is shown that pulses of ellipticity and spatial orientation of polarization ellipse propagate with slowing. Analytical expressions for the slowing factor are obtained. Previously unknown effects of the stimulated phase modulation and the generation of a phase pilot pulse by the variation of spatial orientation of the polarization ellipse are predicted.