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Physical Review A

Reply to “Comment on ‘Dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium: A numerical approach’ ”

Shih-Chuan Gou, Shih-Wei Su, Ite A. Yu

Published Oct 2, 2017• 2 citations
Publisher

Abstract

A damping term in the theoretical model of our paper [Phys. Rev. A 83, 013827 (2011)] was questioned by the author of the Comment. The author argued this damping term cannot exactly describe the spontaneous decay or quantum jump process and, thus, concluded that our results are prone to be incorrect. However, the physics of electromagnetically induced transparency (EIT) is mainly determined by the ground-state coherence and the optical coherence of the probe transition. We show here that the damping term in our paper described the relaxation process of optical coherence in the EIT system, but not the spontaneous decay process of the population. The case of spontaneous decay used in the argument of the Comment is not an issue in typical EIT studies, in which the probe field is weak and treated as the perturbation. Furthermore, the experimental data in the paper were taken under the condition of a weak probe field. Our theoretical model in the weak-probe condition actually deals with the two coherences of EIT physics, and is suitable for analysis of the data. We believe the results of the study, focusing on the dynamics of slow light and light storage in Doppler-broadened EIT media, are correct.

DOI
10.1103/physreva.96.047801

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A damping term in the theoretical model of our paper [Phys. Rev. A 83, 013827 (2011)] was questioned by the author of the Comment. The author argued this damping term cannot exactly describe the spontaneous decay or quantum jump process and, thus, concluded that our results are prone to be incorrect. However, the physics of electromagnetically induced transparency (EIT) is mainly determined by the ground-state coherence and the optical coherence of the probe transition. We show here that the damping term in our paper described the relaxation process of optical coherence in the EIT system, but not the spontaneous decay process of the population. The case of spontaneous decay used in the argument of the Comment is not an issue in typical EIT studies, in which the probe field is weak and treated as the perturbation. Furthermore, the experimental data in the paper were taken under the condition of a weak probe field. Our theoretical model in the weak-probe condition actually deals with the two coherences of EIT physics, and is suitable for analysis of the data. We believe the results of the study, focusing on the dynamics of slow light and light storage in Doppler-broadened EIT media, are correct.
We present a numerical scheme to study the dynamics of slow light and light storage in an electromagnetically-induced-transparency (EIT) medium at finite temperatures. Allowing for the motional coupling, we derive a set of coupled Schr\"odinger equations describing a boosted closed three-level EIT system according to the principle of Galilean relativity. The dynamics of a uniformly moving EIT medium can thus be determined by numerically integrating the coupled Schr\"odinger equations for atoms plus one ancillary Maxwell-Schr\"odinger equation for the probe pulse. The central idea of this work rests on the assumption that the loss of ground-state coherence at finite temperatures can be ascribed to the incoherent superposition of density matrices representing the EIT systems with various velocities. Close agreements are demonstrated in comparing the numerical results with the experimental data for both slow light and light storage. In particular, the distinct characters featuring the decay of ground-state coherence can be well verified for slow light and light storage. This warrants that the current scheme can be applied to determine the decaying profile of the ground-state coherence as well as the temperature of the EIT medium.
We present a systematic theoretical study to deal with linear and nonlinear light propagations in a Doppler-broadened three-level $\ensuremath{\Lambda}$ system via electromagnetically induced transparency (EIT), with incoherent population exchange between two lower energy levels taken into account. Through a careful analysis of base state and linear excitation, we show that the EIT condition of the system is given by $|{\ensuremath{\Omega}}_{c}|{}^{2}{\ensuremath{\gamma}}_{31}\ensuremath{\gg}2{\ensuremath{\gamma}}_{21}\ensuremath{\Delta}{\ensuremath{\omega}}_{D}^{2}$, where ${\ensuremath{\Omega}}_{c}$ is half the Rabi frequency of the control field, $\ensuremath{\Delta}{\ensuremath{\omega}}_{D}$ is the Doppler width, and ${\ensuremath{\gamma}}_{\mathit{jl}}$ is the decay rate of the coherence between states $|j\ensuremath{\rangle}$ and $|l\ensuremath{\rangle}$. Under this condition, the effect of incoherent population exchange is insignificant, while dephasing dominates the decoherence of the system. This condition also ensures the validity of the weak nonlinear perturbation theory used in this work for solving the Maxwell-Bloch equations with inhomogeneous broadening. We then investigate the nonlinear propagation of the probe field and show that it is possible to form temporal optical solitons in the Doppler-broadened medium. Such solitons have ultraslow propagating velocity and can be generated in very low light power. The possibility of realizing (1+11+11+1)-dimensional and (2+12+12+1)-dimensional spatial optical solitons in the adiabatic regime of the system is also discussed.
The transient dynamics of electromagnetically induced transparency (EIT) are fundamental to understanding coherent light–atom interactions and the advancement of quantum technologies such as optical switching and quantum memory. However, in room-temperature atomic vapors, Doppler broadening significantly alters these dynamics, yet a comprehensive understanding of its impact on the transient EIT response remains lacking. In this study, we combine analytical and numerical methods to investigate the absorption dynamics of a weak probe field in a three-level Λ-type system driven by a strong coupling field, based on the optical Bloch equations and Laplace transform techniques. Our results show that the transient response is highly sensitive to both the atomic spontaneous emission rate and the Rabi frequency of the coupling field. Increasing the coupling field intensity not only accelerates the approach to steady state but also induces oscillatory dynamics and negative absorption. Under Doppler broadening, the time required to reach steady state increases by approximately three orders of magnitude compared to the Doppler-free case—an effect that is surprisingly insensitive to temperature variations across the 100–400 K range. Moreover, restoring a short steady-state time under broadened conditions necessitates increasing the coupling laser intensity by two orders of magnitude. These findings provide key insights into the influence of Doppler broadening on coherent transient processes and offer practical guidelines for the design of room-temperature atomic devices, including quantum memories and optical modulators.
We analyze the energy storage process of light propagating with slow group velocity in a sample where electromagnetically induced transparency (EIT) is created by a strong coupling field. We compare the formation of slow light in EIT and in self-induced transparency (SIT). For SIT, soliton-like propagation of light with essentially reduced group velocity takes place because of the temporary storage of an appreciable part of the pulse energy in the atoms. For EIT, no energy of the probe is stored in the atoms. This energy is transformed to the coupling field and leaves the sample with phase velocity c without absorption. Slow light is formed by a low frequency coherence induced at the input by the probe and coupling fields in a two-quantum excitation process. This coherence propagates as a “spin wave” with small group velocity, and at a large distance from the input, the coherence rules the process of the energy transformation from the coupling field to the probe, reproducing exactly the temporal profile of the probe at the input.