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Physical Review A

Double switching from normal to anomalous dispersion via trichromatic phase manipulation of electromagnetically induced transparency

Xiangming Hu, Guangling Cheng, Jin-hua Zou, Xing Li, Dan Du

Published Aug 4, 2005• 32 citations
Publisher

Abstract

We present a theoretical analysis of trichromatic phase manipulation of electromagnetically induced transparency and show that it is possible to obtain double switching, in which switching from normal to anomalous dispersion occurs in two separate frequency regimes. In particular, a four-level system in the N configuration is considered, in which electromagnetically induced transparency is established in the $\ensuremath{\Lambda}$ subsystem and the additional transition is connected to the probe transition and is coupled by a trichromatic field. It is shown that the sum of the relative phases of the sideband components compared to that of the central component plays a crucial role in the absorption and dispersion spectra. Normal dispersion with negligible absorption or anomalous dispersion with small gain can be achieved in multiple-frequency regimes by varying the sum of the relative phases. When the sum phase is changed from 0 to $\ensuremath{\pi}$, switching from normal to anomalous dispersion occurs in the two different frequency regimes. On the other hand, so long as we fix the sum of two relative phases, the absorption and dispersion spectra keep their own features unchanged no matter how we vary the respective relative phases.

DOI
10.1103/physreva.72.023803

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We present a theoretical analysis of trichromatic phase manipulation of electromagnetically induced transparency and show that it is possible to obtain double switching, in which switching from normal to anomalous dispersion occurs in two separate frequency regimes. In particular, a four-level system in the N configuration is considered, in which electromagnetically induced transparency is established in the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ subsystem and the additional transition is connected to the probe transition and is coupled by a trichromatic field. It is shown that the sum of the relative phases of the sideband components compared to that of the central component plays a crucial role in the absorption and dispersion spectra. Normal dispersion with negligible absorption or anomalous dispersion with small gain can be achieved in multiple-frequency regimes by varying the sum of the relative phases. When the sum phase is changed from 0 to \ensuremathπ\ensuremath{\pi}\ensuremathπ, switching from normal to anomalous dispersion occurs in the two different frequency regimes. On the other hand, so long as we fix the sum of two relative phases, the absorption and dispersion spectra keep their own features unchanged no matter how we vary the respective relative phases.
We study the dependence of absorption and dispersion spectra on amplitudes and phases of the driving fields in multiple electromagnetically induced transparency. For this purpose we consider trichromatic excitation in a three-level Λ atomic system, in which a trichromatic control laser and a monochromatic probe laser are applied to two different transitions, respectively. We numerically calculate the absorption and dispersion spectra. Two characteristic features are found. Firstly, the central transparency can be made to appear or to disappear by utilizing the amplitudes and phases of the driving components. Secondly, so long as we fix the sum of two relative phases of two sideband excitation components to the central component, the absorption and dispersion spectra keep their own lineshapes unchanged no matter how we vary the respective relative phases.
The phase dependence and independence of the response of a trichromatically driven two-level medium to an arbitrarily intense probe field have been studied. The sum of the relative phases of the sideband components of the trichromatic field compared to the central component plays a crucial role in the response of the medium. For a weak probe field, as the sum of the relative phases changes from 0 to π, multiple switching can be achieved, in which switching from normal to anomalous dispersion occurs in multiple separate frequency regimes. The remarkable dependence on the sum phase is also shown for a strong probe field. On the other hand, when the sum of the two relative phases is fixed, the changes in the respective phases have no influence on the response of the medium.
We suggest that a three-level cascade medium be used to achieve the switching from normal dispersion to anomalous dispersion. In the cascade medium, two dipole-allowed transitions are coupled by two different coherent fields, respectively. A probe field is applied either to the upper transition or to the lower transition. The equations for density matrix elements are transformed into a set of equations with time-independent coefficients in the steady state via harmonic expansion, which are solved by matrix inversion. By the solutions we obtain the absorption and dispersion spectra. It is shown that for each case, the medium exhibits either normal or anomalous dispersion at the same frequency regime. The switching from normal dispersion to anomalous dispersion is obtained by varying the intensity from couple to probe transition. The two differences lie between the proposed cascade system and the Λ and V systems. Firstly, near degenerate levels are required for the Λ and V systems when the probe field is simultaneously coupled to the two transitions to achieve dispersion switching. The present scheme is based on an equivalent realization of near degeneracy in the dressed picture, and the interval is controlled by the corresponding field. Secondly, dispersion switching does not occur in the Λ and V systems when the probe field is only coupled to either of two transitions and the decoupled state plays a dominant role. In contrast, the present scheme does not involve the decoupled state.
In this paper,we discussed the electromagnetically induced transparency(EIT) in three-level system driven by a trichromatic field.Firstly,we studied the transitions in three-level system driven by a trichromatic field and probed by a monochromatic field.Based on that,we wrote out the density matrix equation.Then we solved the equations by the method of numerical calculation and drawing the absorption and dispersion spectra.Two characteristic features are found.One is that the central transparency can be made by controlling the phases of excitation components and the other is that we can get different lineshapes of absorption and dispersion spectra by changing the relative phases of two sideband excitation components to the central component.
We show that the trichromatic manipulation of the absorption spectrum leads to sub-half-wavelength atom localization. In particular, a three-level atom in the Λ configuration is considered, in which one transition is coupled by a trichromatic field with one sideband component being a standing-wave field while the other transition is probed by a weak monochromatic field. By varying the sum of relative phases of the sideband components of the trichromatic field to the central component, the atom is localized in either of the two half-wavelength regions with 50% detecting probability when the absorption spectrum is measured.
A new scheme is suggested to manipulate the probe transitions (and hence the optical properties of atomic vapors) via double-control destructive and constructive quantum interferences. The influence of phase coherence between the two control transitions on the probe transition is also studied. The most remarkable feature of the present scheme is that the optical properties (absorption, transparency and dispersion) of an atomic system can be manipulated using this double-control multi-pathway interferences (multiple routes to excitation). It is also shown that a four-level system will exhibit a two-level resonant absorption because the two control levels (driven by the two control fields) form a dark state (and hence a destructive quantum interference occurs between the two control transitions). However, the present four-level system will exhibit electromagnetically induced transparency to the probe field when the three lower levels (including the probe level and the two control levels) form a three-level dark state. The present scenario has potential applications in new devices (e.g. logic gates and sensitive optical switches) and new techniques (e.g. quantum coherent information storage).