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Storage of light: A useful concept?

M. G. Payne, L. Deng

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We show both analytically and numerically that photons from a probe pulse are not stored in several recent experiments. Rather, they are absorbed to produce a two-photon excitation. More importantly, when an identical coupling pulse is re-injected into the medium, we show that the regenerated optical field has a pulse width that is very different from the original probe field. It is therefore, not a faithful copy of the original probe pulse. Recent experiments [1,2] on the extremely slow propagation of a pair of optical pulses in a resonant medium and the subsequent coherent regeneration of the “probe ” pulse have generated much excitement in the fields of optical computing and quantum optics. The physical explanation offered to these extraordinary phenomena rests on the adiabatic theory developed a decade ago by Eberly and coworkers[3]. To a large degree, the “dark-state polariton” theory [4] and all other recent works formulated around it are basically a field theoretical reformulation of the adiabatic approximation of pulse pair propagation in resonant media originally studied reasonably complete in the early 90’s. These new treatments have provided some further understanding of the process, especially from the view point of atomic spin wave excitation and atomic coherence. Two main results of the these works, however, do not, in our view, accurately describe the physical picture of such a highly nonlinear excitation process. In this letter, we show, based on the adiabatic theory, that the claim of the “revival of the probe pulse ” in recent experiments [1,2,5] is not accurate.

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We show both analytically and numerically that photons from a probe pulse are not stored in several recent experiments. Rather, they are absorbed to produce a two-photon excitation. More importantly, when an identical coupling pulse is re-injected into the medium, we show that the regenerated optical field has a pulse width that is very different from the original probe field. It is therefore, not a faithful copy of the original probe pulse. Recent experiments [1,2] on the extremely slow propagation of a pair of optical pulses in a resonant medium and the subsequent coherent regeneration of the “probe ” pulse have generated much excitement in the fields of optical computing and quantum optics. The physical explanation offered to these extraordinary phenomena rests on the adiabatic theory developed a decade ago by Eberly and coworkers[3]. To a large degree, the “dark-state polariton” theory [4] and all other recent works formulated around it are basically a field theoretical reformulation of the adiabatic approximation of pulse pair propagation in resonant media originally studied reasonably complete in the early 90’s. These new treatments have provided some further understanding of the process, especially from the view point of atomic spin wave excitation and atomic coherence. Two main results of the these works, however, do not, in our view, accurately describe the physical picture of such a highly nonlinear excitation process. In this letter, we show, based on the adiabatic theory, that the claim of the “revival of the probe pulse ” in recent experiments [1,2,5] is not accurate.
We present a detailed semiclassical study of the propagation of a pair of optical fields in resonant media with and without the adiabatic approximation. In the case of near- and on-resonance excitation, we show detailed calculations, both analytical and numerical, of the extremely slowly propagating probe pulse and the subsequent regeneration of a pulse via a coupling laser. Further discussions of the adiabatic approximation provide much subtle understanding of the process, including the effect on the bandwidth of the regenerated optical field. We show that the adiabatic condition does not generally predict that the regenerated field will have the same bandwidth as that of the original probe pulse. Indeed, we show analytically that for a set of coupling pulses well satisfying the adiabatic conditions, the regenerated field usually has a different bandwidth from the original probe pulse. For very-far-off resonance excitations, we show that the analytical solution is nearly detuning independent, providing a simple condition is satisfied. This surprising result is vigorously tested and compared to numerical calculations with very good agreement.
Coherent interactions of laser light with atomic ensembles allow one to modify dispersive properties of a medium and lead to new optical phenomena. Studies of the controlled light propagation and storing in such media have recently become a dynamically developing field of research motivated both by the fundamental character of the processes and by potential applications. This article briefly reviews basic theoretical approach to the dynamics of the propagation of laser pulses in optically modified media. The method and the physical processes are discussed that allow one to slow down the group velocity of laser pulse to zero (stopping of light), to transfer the state of a light pulse to atomic coherences and to restore the pulse. The interpretation of these phenomena in the formalism of dark-state polaritons is presented. Examples of possible coherent manipulations on a stored light are also discussed.
Polariton formalism is applied for studying the propagation of a probe field of light in a cloud of cold atoms influenced by two control laser beams of larger intensity. The laser beams couple resonantly three hyperfine atomic ground states to a common excited state, thus forming a tripod configuration of the atomic energy levels involved. The first control beam can have an optical vortex, with the intensity of the beam going to zero at the vortex core. The second control beam without a vortex ensures the lossless (adiabatic) propagation of the probe beam at a vortex core of the first control laser. We investigate the storage of the probe pulse into atomic coherences by switching off the control beams and its subsequent retrieval by switching the control beams on. The optical vortex is transferred from the control to the probe fields during the storage or retrieval of the probe field. We analyze the conditions needed for the vortex to be transferred efficiently to the regenerated probe beam and discuss the possibilities of experimental implementation of the proposed scheme using atoms such as rubidium or sodium.
We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to 87Rb^{87}\mathrm{Rb}87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.
We consider slow-light propagation in an atomic medium with a tripod level scheme. We show that the coexistence of two types of dark-state polaritons leads to the propagation dynamics, which is qualitatively different from that in a $\mathrm{\ensuremath{\Lambda}}$ medium, and allows therefore for very efficient conversion of signal photons into spin excitations. This efficiency is shown to be very close to 1 even for very long signal light pulses, which could not be entirely compressed into a $\mathrm{\ensuremath{\Lambda}}$ medium at a comparable strength of the control field.
We consider propagation, storing and retrieval of slow light (probe beam) in a resonant atomic medium illuminated by two control laser beams of larger intensity.The probe and two control beams act on atoms in a tripod configuration of light-matter coupling.The first control beam is allowed to have an orbital angular momentum (OAM).Application of the second vortex-free control laser ensures the adiabatic (lossless) propagation of the probe beam at the vortex core where the intensity of the first control laser goes to zero.Storing and release of the probe beam is accomplished by switching off and on the control laser beams leading to the transfer of the optical vortex from the first control beam to the regenerated probe field.A part of the stored probe beam remains frozen in the medium in the form of atomic spin excitations, the number of which increases with increasing intensity of the second control laser.We analyze such losses in the regenerated probe beam and provide conditions for the optical vortex of the control beam to be transferred efficiently to the restored probe beam.