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Chinese Physics B

Ultraslow optical solitons via electromagnetically induced transparency: a density-matrix approach

Bin Luo, Hang Chao, Hui‐jun Li, Guoxiang Huang

Published May 1, 2010• 14 citations
Publisher

Abstract

We study the ultraslow optical solitons in a resonant three-level atomic system via electromagnetically induced transparency under a density-matrix (DM) approach. The results of linear and nonlinear optical properties are compared with those obtained by using an amplitude variable (AV) approach. It is found that the results for both approaches are the same in the linear regime if the corresponding relations between the population-coherence decay rates in the DM approach and the energy-level decay rates in the AV approach are appropriately imposed. However, in the nonlinear regime there is a small difference for the self-phase modulation coefficient of the nonlinear Schrödinger equation that governs the time evolution of probe pulse envelope. All analytical predicts are checked by numerical simulations.

DOI
10.1088/1674-1056/19/5/054214

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We study the ultraslow optical solitons in a resonant three-level atomic system via electromagnetically induced transparency under a density-matrix (DM) approach. The results of linear and nonlinear optical properties are compared with those obtained by using an amplitude variable (AV) approach. It is found that the results for both approaches are the same in the linear regime if the corresponding relations between the population-coherence decay rates in the DM approach and the energy-level decay rates in the AV approach are appropriately imposed. However, in the nonlinear regime there is a small difference for the self-phase modulation coefficient of the nonlinear Schrödinger equation that governs the time evolution of probe pulse envelope. All analytical predicts are checked by numerical simulations.
We propose a scheme to obtain stable nonlinear optical pulses and realize their storage and retrieval in an ultracold ladder-type three-level atomic gas via electromagnetically induced transparency. Based on Maxwell-Bloch equations we derive a nonlinear equation governing the evolution of probe field envelope, and show that optical solitons with ultraslow propagating velocity and extremely low generation power can be created in the system. Furthermore, we demonstrate that such ultraslow optical solitons can be stored and retrieved by switching off and on a control field. Due to the balance between dispersion and nonlinearity, the ultraslow optical solitons are robust during propagation, and hence their storage and retrieval are more desirable than that of linear optical pulses. This raises the possibility of realizing the storage and retrieval of light and quantum information by using solitonic pulses.
We propose a scheme to exhibit a Stern–Gerlach effect of n-component (n>2) high-dimensional ultraslow optical solitons in a coherent atomic system with (n+1)-pod level configuration via electromagnetically induced transparency (EIT). Based on Maxwell–Bloch equations, we derive coupled (3+1)-dimensional nonlinear Schrödinger equations governing the spatial-temporal evolution of n probe-field envelopes. We show that under EIT conditions significant deflections of the n components of coupled ultraslow optical solitons can be achieved by using a Stern–Gerlach gradient magnetic field. The stability of the ultraslow optical solitons can be realized by an optical lattice potential contributed from a far-detuned laser field.
The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrödinger-like wave equation that considers only instantaneous Kerr nonlinearity.
This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.
We study nonlinear excitations in a lifetime-broadened Λ-type three-level atomic system with a configuration of electromagnetically induced transparency. Different from previous works, we show that a significant depletion of the control field may occur during the formation and propagation of ultraslow optical solitons for the probe field. We demonstrate that ultraslow optical solitons predicted in previous works correspond to the limits of weak dispersion and weak nonlinearity, adiabatons correspond to the limits of stronger dispersion and stronger nonlinearity, and simultons correspond to the limits of strong dispersion and strong nonlinearity. Between these different limits the system also yields solitonlike nonlinear excitations with different levels of depletion of the control field. The results provided here are useful not only for a deep understanding of the interrelation between ultraslow optical solitons, adiabatons, and simultons, but also for potential applications in optical information processing and transmission.