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arXiv:0902.0752 · Physical Review A

Phase modulation induced by cooperative effects in electromagnetically induced transparency

Robert Fleischhaker, Tarak Nath Dey, Jörg Evers

Published Jul 14, 2010• 9 citations
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Abstract

We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency set up for a density at the onset of cooperative effects. To this end, we include mean-field models for the influence of local-field corrections and radiation trapping into our calculation. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local-field-induced phase modulation and demonstrate that it distinctively differs from the nonlinear self-phase-modulation that a strong pulse experiences in a Kerr medium.

DOI
10.1103/physreva.82.013815

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We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency set up for a density at the onset of cooperative effects. To this end, we include mean-field models for the influence of local-field corrections and radiation trapping into our calculation. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local-field-induced phase modulation and demonstrate that it distinctively differs from the nonlinear self-phase-modulation that a strong pulse experiences in a Kerr medium.
The influence of a phase-modulated control field on the phenomenon of electromagnetically induced transparency (EIT) is investigated theoretically. We show that the phase modulation changes the dispersive properties of the medium considerably since it results in temporal oscillations of the transparency window in frequency space. This is in marked contrast to the standard EIT setup, where the transparency window is fixed and determined by the two-photon resonance condition. In particular, we find that the phase modulation enables the propagation of probe pulses with disjoint frequency spectra at different times and allows the shifting of the central frequency of a probe pulse almost without distortion of its shape. We employ the time-dependent susceptibility of the medium to explain and analyze our results and demonstrate that this concept yields qualitative as well as quantitative agreement with the numerical integration of Maxwell-Bloch equations. Our theoretical model can be applied to other media with time-dependent susceptibilities.
The results of a theoretical investigation of the evolution of a probe pulse under electromagnetically induced transparency in the Λ -scheme of degenerated inhomogeneously broadened quantum transitions are presented. It supposed that the interacted light fields are elliptically polarized, and their influence on the medium can be either strictly resonant or quasiresonant. It is demonstrated that the probe pulse in the medium can be presented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarized fields propagating independently of each other. Due to the fact that velocities of normal mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside of the medium, each of which transfers the energy of one of the normal modes. If normal modes are not phase modulated at the input surface, then in the case of quasi-resonance they become phase modulated during propagation in the medium, whereas this does not occur in the case of strict resonance. The total probe field, which is the sum of normal modes, has phase modulation before it splits into the mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.
We study the dynamics of the phase pulses of laser radiation with two resonant frequency components propagating in an atomic three-level Λ type medium under coherent population trapping. Using the density matrix adiabatic approach we show that the effect of a very large slowing down occurs not only for amplitude pulses, but also for phase pulses. The group velocity of phase pulses can be controlled by the amplitudes of resonant fields. The analytical solution describing the mutual influence of the phase modulation of one field component on another is obtained.
Abstract We report the results of an analytical and numerical analysis of the evolution of nanosecond probe pulses in the case of electromagnetically induced transparency in the Λ-scheme of degenerate quantum transitions. It is assumed that the probe and control fields at the active medium input are elliptically polarised, and one of them is phase modulated. It is shown analytically that probe radiation in a medium is the sum of two normal modes propagating independently of each other. Because the group velocities of normal mode pulses are different, a single probe pulse entering the medium decays inside the medium into separate pulses, each of which transfers the energy of one of the normal modes. Numerical simulations have shown that with a sufficiently large phase modulation, normal modes, whose intensity on the input surface is described by a bell-shaped curve, turn into trains of subpulses in the medium. Phase modulation of the input field has practically no effect on the group propagation velocities of normal modes, but it reduces the transparency of the medium for probe radiation.