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Physical Review A

Collision of solitons in electromagnetically induced transparency

Vaduganathan Ramesh Kumar, R. Radha, Miki Wadati

Published Oct 24, 2008• 9 citations
Publisher

Abstract

We investigate the Maxwell-Bloch equations representing the propagation of electric fields through a three-level atomic system. We then generate soliton solutions for the field variables and study the interaction of solitons. We show how the signatures of electromagnetically induced transparency are manifested in the collision of solitons which can then be used for quantum-information processing.

DOI
10.1103/physreva.78.041803

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We investigate the Maxwell-Bloch equations representing the propagation of electric fields through a three-level atomic system. We then generate soliton solutions for the field variables and study the interaction of solitons. We show how the signatures of electromagnetically induced transparency are manifested in the collision of solitons which can then be used for quantum-information processing.
Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell–Bloch (MB) equations for a three-level Λ-type atomic configuration. By employing a generalized gauge transformation, we systematically construct explicit N-soliton solutions from the corresponding Lax pair. Explicit forms of one-, two-, three-, and four-soliton solutions are derived and analyzed. The resulting pulse structures reveal various nonlinear phenomena, such as temporal asymmetry, energy trapping, and soliton interactions. They also highlight coherent propagation, elastic collisions, and partial storage of pulses, which have potential implications for the design of quantum memory, slow light, and photonic data transport in EIT media. In addition, the conservation of fundamental physical quantities, such as the excitation norm and Hamiltonian, is used to provide direct evidence of the integrability and stability of the constructed soliton solutions.
One-dimensional pulse propagations in the electromagnetically induced media are studied. The Maxwell–Bloch equations for a three-level medium are simplified with the approximations of slowly varying amplitudes, negligible irreversible relaxations and exact resonances. An analysis is made for the case where the integrable condition is satisfied; the oscillation strengths for the two transitions are equall. Through the Bäcklund transformation, one-soliton solutions including the so-called simulton are derived.
We examine the dynamics of counterpropagating self-induced transparency solitons in three-level media. In a multilevel system, self-induced transparency gives rise to soliton solutions if the propagation is unidirectional, but the collision of counterpropagating pulses destroys the integrability of the underlying equations. We consider the collision of a rightward and a leftward moving self-induced transparency solitary wave by solving the full Maxwell-Bloch equations numerically using a finite-difference time-domain approach. Depending on pulse duration, amplitude and relative polarizations of the initial solitary waves we observe different regimes of interaction. For high group velocities and orthogonal polarizations, secondary solitary waves are born during the interaction, whereas the collision of solitary waves with the same polarization never produces secondary solitary waves but leaves behind a population grating in the interaction region. Because the crucial parameters can be controlled, an experimental confirmation of the predicted interaction regimes should be feasible.