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Physica Scripta

Soliton slow light for closed loop quantum systems

Hamid Reza Hamedi, Mahmoud Jafari, Viačeslav Kudriašov

Published Jan 2, 2019• 7 citations
Publisher

Abstract

Abstract This paper describes the dynamics of solitonic pulse propagation in a closed loop quantum system comprised of five atomic energy levels. In this system four higher energy levels with four control laser fields form a closed ring-shape loop which is coherently coupled to a ground level state by a tunable probe laser field. Although the propagation of an intense probe pulse suffers losses and broadening in linear regime, there exist specific conditions where the probe pulse is found to become robust during its propagation. We attribute this regime to the formation of an optical soliton with a slow group velocity because of the balance between the dispersion and Kerr optical nonlinearity. Results obtained are based on the theoretical model using the coupled Maxwell–Bloch equations for the nonlinear propagation.

DOI
10.1088/1402-4896/aafb93

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Abstract This paper describes the dynamics of solitonic pulse propagation in a closed loop quantum system comprised of five atomic energy levels. In this system four higher energy levels with four control laser fields form a closed ring-shape loop which is coherently coupled to a ground level state by a tunable probe laser field. Although the propagation of an intense probe pulse suffers losses and broadening in linear regime, there exist specific conditions where the probe pulse is found to become robust during its propagation. We attribute this regime to the formation of an optical soliton with a slow group velocity because of the balance between the dispersion and Kerr optical nonlinearity. Results obtained are based on the theoretical model using the coupled Maxwell–Bloch equations for the nonlinear propagation.
Abstract We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N -type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell–Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.
We investigate the weak probe pulse propagation through the atomic medium, in the presence of the strong control laser field, under the regime of the electromagnetically induced transparency (EIT). These fields couple to the medium by forming the 3-level ladder configuration. We focus on two distinct cases: closed system, which is a non-degenerate, and open system, where the middle level is 3-fold degenerate, and the additional levels are coupled to the other levels only via spontaneous emission. The spatio-temporal profile of the probe pulse envelope is obtained by using the formalism of Maxwell-Bloch equations with the help of the Fourier transform method. We study the influence of the control field Rabi frequency, the spectral half-width of the initial pulse and decay rates on the propagation of the probe pulse. Several important pulse parameters are also calculated and discussed. It is shown that the group velocity of light can be controlled in such a manner that one can switch from slow to fast light and vice versa when changing the control Rabi frequency and spectral pulse half-width. Moreover, the possibility of replacing the open with an effective closed system is also discussed.
Coupling a two-level medium, described by the Maxwell-Bloch (MB) equations, to an external cavity mode results in a prescribed boundary value for the electric field that can be tuned to the forbidden band gap of the medium. It is shown that there exists a threshold of energy density flux above which a solitonlike light pulse is generated and propagates in the medium at a fraction of the light velocity. When the driving frequency becomes close to the band gap edge, where the group velocity vanishes, the MB equations tend to the nonlinear Schr\"odinger equation which furnishes the theoretical ground to understand soliton generation by evanescent fields as a manifestation of nonlinear supratransmission, produced by an instability of the evanescent wave. Moreover, the propagation at a fraction of light velocity is shown to result from a continuous periodic exchange between polarization (electromagnetic energy) and population (density of atoms in the excited level). The process is demonstrated to occur at twice the internal frequency of the generated gap soliton. Last, when the medium spatial extension is of the order of the soliton dimension, an optical bistability is shown to occur at the supratransmission threshold allowing for different output intensities corresponding to a given input value.
This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a continuous-wave control laser beam and an assisting incoherent pump field, it is shown how these media can provide an excellent framework to experimentally explore pulse dynamics in the presence of non-conservative terms, either gain or loss. Furthermore, we explore the existence of stable dissipative soliton solutions, testing the analytical results with computational simulations of both the effective (1+1)-dimensional model and the full Maxwell-Bloch system of equations.
We theoretically investigate the simultaneous formation and stable propagation of slow optical soliton pairs in semiconductor quantum dots with a four-level biexciton-exciton cascade configuration. Owing to the destructive interference set up by two continuous wave control fields that couple to a biexciton state, the linear as well as nonlinear dispersion can be dramatically enhanced simultaneously with the absorptions of two weak probe fields being almost suppressed. These results reveal that the detrimental distortions of the two weak-pulsed probe fields due to dispersion effects can be well balanced by the self-phase modulation effect under very low input light intensity, which leads to the slow temporal optical soliton pairs with matched group velocity and amplitude. We also show that the propagation of slow optical solitons can be strongly modified by the biexciton coherence.
Using the Schrödinger Maxwell equations, we theoretically investigate the propagation properties of probe and mixing fields in a lifetime-broadened inverted-Y type cold atomic medium. This system is driven by two strong control (pumping and coupling) fields. The results reveal that the probe (or mixing) field consists of two modes with different group velocity and absorption. Under slowly varying envelope approximation, we discuss the propagation equation of the probe (or mixing) field, which includes the high-order nonlinear term. The solutions show that optical solitons pairs can be generated in the cold atom medium with ultra-slow group velocities.