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Physical Review A

Two types of adiabatons in electromagnetically induced transparency

R. N. Shakhmuratov, J. Odeurs

Published Oct 5, 2006• 13 citations
Publisher

Abstract

We analyze the energy transformation of light propagating with slow group velocity in a three-level medium. Depending on the excitation scheme, the energy of the probe can be transformed into the coupling field or into the atomic excitation. As a result a zero-energy adiabaton develops for the lambda scheme or an energy carrying adiabaton is formed for the ladder scheme. In both cases slow light is produced by the atoms, also feeding this light by the energy stored in the metastable state (ladder scheme) or borrowing the energy from the coupling field (lambda scheme).

DOI
10.1103/physreva.74.043807

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We analyze the energy transformation of light propagating with slow group velocity in a three-level medium. Depending on the excitation scheme, the energy of the probe can be transformed into the coupling field or into the atomic excitation. As a result a zero-energy adiabaton develops for the lambda scheme or an energy carrying adiabaton is formed for the ladder scheme. In both cases slow light is produced by the atoms, also feeding this light by the energy stored in the metastable state (ladder scheme) or borrowing the energy from the coupling field (lambda scheme).
We analyze the energy storage process of light propagating with slow group velocity in a sample where electromagnetically induced transparency (EIT) is created by a strong coupling field. We compare the formation of slow light in EIT and in self-induced transparency (SIT). For SIT, soliton-like propagation of light with essentially reduced group velocity takes place because of the temporary storage of an appreciable part of the pulse energy in the atoms. For EIT, no energy of the probe is stored in the atoms. This energy is transformed to the coupling field and leaves the sample with phase velocity c without absorption. Slow light is formed by a low frequency coherence induced at the input by the probe and coupling fields in a two-quantum excitation process. This coherence propagates as a “spin wave” with small group velocity, and at a large distance from the input, the coherence rules the process of the energy transformation from the coupling field to the probe, reproducing exactly the temporal profile of the probe at the input.
We investigate the weak probe pulse propagation through the atomic medium, in the presence of the strong control laser field, under the regime of the electromagnetically induced transparency (EIT). These fields couple to the medium by forming the 3-level ladder configuration. We focus on two distinct cases: closed system, which is a non-degenerate, and open system, where the middle level is 3-fold degenerate, and the additional levels are coupled to the other levels only via spontaneous emission. The spatio-temporal profile of the probe pulse envelope is obtained by using the formalism of Maxwell-Bloch equations with the help of the Fourier transform method. We study the influence of the control field Rabi frequency, the spectral half-width of the initial pulse and decay rates on the propagation of the probe pulse. Several important pulse parameters are also calculated and discussed. It is shown that the group velocity of light can be controlled in such a manner that one can switch from slow to fast light and vice versa when changing the control Rabi frequency and spectral pulse half-width. Moreover, the possibility of replacing the open with an effective closed system is also discussed.
Abstract We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N -type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell–Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.
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 present the results of numerical simulation of the adiabaton emergence process in the lambda scheme of degenerate energy levels with the quantum number of the total angular momentum, J = 0, 2, 1. In the case of linear polarisation of the input highfrequency field and circular polarisation of the input low-frequency field, the energy of the high-frequency component of the adiabaton is shown to focus in two or more pulses: in one of the pulses the field is circularly polarised in a direction opposite to that of the low-frequency input field, whereas in other pulses it is circularly polarised in the same direction as that of the field. This effect is caused by the specific character of electromagnetically induced transparency in the lambda scheme under study and by the trends introduced by self-induced transparency in it.
We studied the electromagnetically induced transparency, where the three-level atom of Λ-type is put in two statistically independent squeezed vacuums. We start from the master equation containing the decay of the atom to the squeezed vacuums, and solve the non-diagonal density matrix element analytically, finding that it is strongly dependent on the squeezing degree and the phase of the squeezed vacuum. There is also a dependence on the intensity and phase of the probe beam, which would not appear in the normal vacuum case. By coupling with squeezed vacuums, the atom would not only experience electromagnetically induced transparency and slow group velocity, but also induce a fast group velocity,backward group velocity and a gain in the probe light field. Besides, the absorption and gain can be modulated by the intensity of probe light.