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arXiv:1301.6264 · Laser Physics

Electromagnetically induced transparency with degenerate atomic levels

V A Reshetov, I V Meleshko

Published Aug 15, 2014• 3 citations
arXivHTMLPDF

Abstract

For the coherently driven Λ -type three-level systems the general expression for the susceptibility tensor at the frequency of the weak probe field is obtained for the arbitrary polarization of the strong coupling laser field and arbitrary values of the angular momenta of resonant atomic levels. The dependence of the relative difference in the group velocities of the two polarization components of the probe field on the polarization of the coupling field is studied.

DOI
10.1088/1054-660x/24/9/094011

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For the coherently driven Λ -type three-level systems the general expression for the susceptibility tensor at the frequency of the weak probe field is obtained for the arbitrary polarization of the strong coupling laser field and arbitrary values of the angular momenta of resonant atomic levels. The dependence of the relative difference in the group velocities of the two polarization components of the probe field on the polarization of the coupling field is studied.
Abstract The general expression for the transformation matrix of the two input weak arbitrarily polarized probe fields passing through the medium under the conditions of double-Λ electromagnetically induced transparency is obtained for arbitrary values of the amplitudes, phases and polarizations of the control fields and arbitrary values of the angular momenta of resonant levels. The conditions are found for the two input weak probe fields linearly polarized in perpendicular planes to exchange their polarizations after the passage through the medium without absorption. The polarization rotation of the probe fields is studied for the atoms being initially in the equilibrium state.
The interaction of a weak probe laser with an inverted Y-type four-level atomic system driven by two additional coherent fields is investigated theoretically. Under the influence of the coherent coupling fields, the steady-state linear susceptibility of the probe laser shows that the system can have single or double electromagnetically induced transparency windows depending on the amplitude and the detuning of the coupling lasers. The corresponding index of refraction associated with the group velocity of the probe laser can be controlled at both transparency windows by the coupling fields. The propagation of the probe field can be switched from superluminal near the resonance to subluminal on resonance within the single transparency window when two coupling lasers are on resonance. We propose an atomic 87Rb system for experimental observation.
Electromagnetically induced transparency (EIT) in an inhomogenously broadened medium consisting of Λ-type three-level atoms has been analyzed. It is shown that the Λ system can induce a transparency of the medium when the probe laser and the coupling laser have the same frequency detunings (including zero). Across the EIT window, the radial variation of the strong coupling laser radiation may lead to electromagnetically induced focusing or defocusing of the weak probe laser at separate probe frequency detuning points.
Using density matrix eqution, the absorption and dispersion properties of a A-type four-level system driven by coherent fields are investigated. The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state, three, double or single electromagnetically induced transparency (EIT) can appear explicitly in this system. And the explanations of these phenomena are given by using the dressed states. In the three EIT, the location of transparent windows can be manipulated by controlling the detuning of the driving field. What's more, it is also found that the medium shows a large refractive index at each transparency window, and the group velocity of the probe laser can be enhanced.
We show that, by simple modifications of the usual three-level Λ-type scheme used for obtaining electromagnetically induced transparency (EIT), phase dependence in the response of the atomic medium to a weak probe field can be introduced. This gives rise to phase dependent susceptibility. By properly controlling phase and amplitudes of the drive fields we obtain variety of interesting effects. On one hand we obtain phase control of the group velocity of a probe field passing through medium to the extent that continuous tuning of the group velocity from subluminal to superluminal and back is possible. While on the other hand, by choosing one of the drive fields to be a standing wave field inside a cavity, we obtain sub-wavelength localization of moving atoms passing through the cavity field.
We study the propagation of coherent light pulses in a medium of three-level atoms with degenerate ground- and excited-state sublevels in an electromagnetically induced transparency (EIT)-type configuration. Both the strong control field and the weak probe pulse have elliptical polarization, which gives rise to concurrent multipath couplings between the ground-state sublevels and the auxiliary stable state. We derive the probe field susceptibility and show that in general, the probe field propagates in two separate polarization modes, one of which is attenuated, the other of which displays EIT. This generic result is valid provided the atomic medium is prepared to be in a pure quantum state over the ground-state sublevels initially. We also investigate the case when the initial state of the medium is described by an incoherent mixture of ground-state sublevels and show how EIT-like pulse propagation degrades. The possibility of controlling the probe susceptibility matrix with control field polarization provides a convenient tool for probing the quantum state of the medium on the degenerate ground-state sublevels.