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Optics and Spectroscopy

Light slowing-down effects caused by nonlinear interactions of radiations in two-level systems

Yu. I. Heller, A. V. Sharypov

Published Feb 1, 2009• 3 citations
Publisher

Abstract

The effect of slowing down pulses of probe radiation in a medium consisting of two-level quantum systems whose longitudinal and transverse relaxation times strongly differ is studied. The conditions for the occurrence of “slow light” in a transparency window are obtained. Regimes are discovered in which the medium becomes transparent or amplifies the probe radiation, with the high dispersion of the refractive index being conserved. The parameters at which the delay time of the probe radiation reaches a maximum or the group velocity of this radiation decreases to a maximal possible value under the condition of exact resonance with the strong field are found.

DOI
10.1134/s0030400x09020179

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Soviet Journal of Quantum Electronics•Sep 30, 1978•0 citations
The effect of slowing down pulses of probe radiation in a medium consisting of two-level quantum systems whose longitudinal and transverse relaxation times strongly differ is studied. The conditions for the occurrence of “slow light” in a transparency window are obtained. Regimes are discovered in which the medium becomes transparent or amplifies the probe radiation, with the high dispersion of the refractive index being conserved. The parameters at which the delay time of the probe radiation reaches a maximum or the group velocity of this radiation decreases to a maximal possible value under the condition of exact resonance with the strong field are found.
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).
Electromagnetically-induced transparency (EIT) of atomic medium interacting with two laser beams can exhibit effects of reciprocal influence of both beams on optical properties of the medium. If the probe beam reaches instantaneous intensity comparable to that of the control beam, considerable energy is transferred to the latter. Resulting increase in the control-beam intensity temporarily modifies EIT conditions and consequently affects propagation of probe-beam pulses. The effect is particularly strong in atomic media exhibiting significant dissipation of radiation energy due to relaxation processes efficiently counteracting the optical pumping. Coherent interaction of atoms with both beams causes reduction of dissipation of the control beam (reciprocal EIT conditions). Our experiments with hot rubidium vapor demonstrate the possibility of dual control over slow propagation of light pulses in such media. Besides the well-known dependence on input control-beam intensity, the delays of output probe pulses depended significantly also on the energy of input probe pulses. Moreover, for relatively short input pulses, very specific shape of output pulses was observed, invariant in wide ranges of input probe pulse energies and control-beam intensities. The shapes of the output pulses were also the same for short input pulses of different shapes as well as for pulses temporarily stored in the medium by switching off the control beam during their propagation.
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.
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.
We consider the propagation of a Gaussian probe pulse in an absorptive, optically dense, two-level medium if a deep, persistent hole is created in advance by another pump field in the inhomogeneously broadened absorption spectrum of this medium. Both fields are well separated in time and the lifetime of the hole is assumed to be long with respect to the delay time between the pump and probe pulses. We show that the group velocity of the Gaussian probe pulse reduces several orders in magnitude, similarly to the reduction of the group velocity for the probe field in electromagnetically induced transparency (EIT) phenomena. In contrast to EIT, the width of the transparency window can be made very wide because of the saturation broadening of the hole.
Numerical integration of a system of equations describing the coherent interaction between radiation and a two-level medium (e.g., a semiconductor) is employed to analyze the effect of relaxation processes on the energy characteristics and dynamics of radiation pulses of duration τpΣ T '2 (T '2 is the irreversible polarization relaxation time). It is shown that the interaction of these pulses with the medium is strongly dependent on their area on entry to the medium and the attenuation of the pulses as a result of relaxation processes decreases with increasing pulse input power. This may be utilized for probing the medium in the resonant absorption range for short polarization relaxation times, in solution 42.65.Gv.