We investigate the shape-preserving propagation of N optical pulses in an ( N +1)-level medium. We solve Maxwell-Schrödinger equations exactly and provide several types of explicit coupled soliton solutions, which are temporally amplitude- and group-velocity-matched multi-mode slow-optical pulses of the system.
The physics of slow-light propagation in atomic Lambda systems is described by the theory of integrable systems, which allows the existence of solitons. Slow-light solitons are stable polarization structures that propagate through the atomic medium at a controllable speed. They represent generalizations of the experimentally demonstrated slow-light pulses in atomic media where one light polarization dominates the other, the probe, and controls its group velocity. In the general case, the overall intensity controls the speed of the entire polarization structure. For zero detuning between light and atoms, even more general shape-preserving pulses exist. Quantum fluctuations of slow-light pulses can be stored in atomic media. In the case of solitons, these are fluctuations of the soliton parameters.
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.
The B\"acklund transformation for the three-level coupled Schr\"odinger-Maxwell equation is presented in the matrix potential formalism. By applying the B\"acklund transformation to a constant-electric-field background, we obtain a general solution for matched pulses (a pair of solitary waves) that can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady-state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe [Phys. Rev. Lett. 73, 2559 (1994)]. A nonlinear superposition rule is derived from the B\"acklund transformation and used for the explicit construction of two solitons as well as non-Abelian breathers. Various features of these solutions are addressed. In particular, we analyze in detail the scattering of ``binary solitons,'' a specific pair of different wavelength solitons, one of which moves with the velocity of light. Unlike the usual case of soliton scattering, the broader soliton changes its sign after the scattering, thus exhibiting a binary behavior. Surprisingly, the light velocity soliton receives a time advance through the scattering, thereby moving faster than light, which, however, does not violate causality.