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Journal of Modern Optics

The energy storage in the formation of slow light

R. N. Shakhmuratov

Published Mar 29, 2010• 7 citations
Publisher

Abstract

Slow light formation in media with (i) an electromagnetically induced transparency, (ii) a doublet structure, and (iii) a single absorption line, detuned from resonance, is considered with the help of a simple model. The model is based on the description of particles in these media by a pseudospin 1/2, which is subject to two ‘orthogonal fields’. We mainly focus on the analysis of the reversible process of the particle excitation–de-excitation resulting in the temporal storage of the light-pulse energy without the pulse corruption. The influence of irreversible relaxation processes on the slow light formation is studied.

DOI
10.1080/09500341003654450

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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.

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A number of experiments have been performed on light slowing and stopping in the electromagnetically induced transparency (EIT) media of hot atomic gases where the Doppler-shift may add detunings to the field frequencies in an inhomogeneous fashion. We provide here a theoretical analysis as to the effect of such a Doppler-broadened environment on the dynamics of the system in comparison to a cold atomic medium. We will show that one of the most critical factors in the formation of a stationary light pulse is the enhancement of the excited-state decay rate caused by the collisions between the atoms of the medium and the molecules of the buffer gas.

Journal of the Korean Physical Society•Nov 1, 2018•1 citation
Slow light formation in media with (i) an electromagnetically induced transparency, (ii) a doublet structure, and (iii) a single absorption line, detuned from resonance, is considered with the help of a simple model. The model is based on the description of particles in these media by a pseudospin 1/2, which is subject to two ‘orthogonal fields’. We mainly focus on the analysis of the reversible process of the particle excitation–de-excitation resulting in the temporal storage of the light-pulse energy without the pulse corruption. The influence of irreversible relaxation processes on the slow light formation is studied.
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.
Slow light, produced in a medium with two widely spaced absorption resonances, is analytically studied. We show that a pulse with frequency tuned in the middle of such a doublet structure slows down due to its energy storage in the excited atomic states. If the lifetime of the atomic excitation is much longer than the pulse duration, the pulse shape is nicely reproduced at the output of a thick sample for pulses with smooth envelopes. Pulses with sharp edges are fairly reproduced at the output. Each abrupt change of the pulse amplitude is followed by transients, which are delayed together with the pulse. A possibility to slow down a single photon is also considered.
Storage of light pulses in Rb vapour with bright Zeeman coherences and the associated enhanced absorption and steep negative dispersion is reported. Our experimental observations are qualitatively similar to the well-known proof-of-principle demonstration of light storage (D F Phillips et al 2001 Phys. Rev. Lett. 86 783), but obtained under conditions where electromagnetically induced transparency (EIT) does not exist and the slow-light dark-state polariton model does not apply. Under the present experimental conditions the retrieved pulses obtained in atomic media with dark or bright Zeeman coherences have very similar exponentially decaying slopes which are independent of the shape of the incoming signal pulse. Numerical modelling based on the optical Bloch equations reproduces the essential features of the experimental observations.
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.
A number of experiments have been performed on light slowing and stopping in the electromagnetically induced transparency (EIT) media of hot atomic gases where the Doppler-shift may add detunings to the field frequencies in an inhomogeneous fashion. We provide here a theoretical analysis as to the effect of such a Doppler-broadened environment on the dynamics of the system in comparison to a cold atomic medium. We will show that one of the most critical factors in the formation of a stationary light pulse is the enhancement of the excited-state decay rate caused by the collisions between the atoms of the medium and the molecules of the buffer gas.