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Low Temperature Physics

Feasibility of using Bose-Einstein condensates for filtering optical pulses

Yu. V. Slyusarenko, Andrii Sotnikov

Published Aug 1, 2010• 5 citations
Publisher

Abstract

The feasibility of using the extreme slowing down of light in Bose-Einstein condensates of alkali metal atoms as a means of improving the spectral characteristics of optical signals is studied. The basis of this approach is the resonant character of the slowing down of electromagnetic pulses in these media. In other words, signals with frequency characteristics close to the intervals between levels in the energy spectrum of alkali metal atoms in a Bose-Einstein condensate are slowed down the most. The filtering of electromagnetic signals is described in terms of a microscopic theory for the response of a gas of hydrogenlike atoms to a weak external electromagnetic field. The possibility in principle of signal filtering is demonstrated using the example of an electromagnetic pulse with a normal (gaussian) spectral intensity distribution propagating through a rarefied gas of alkali metal atoms in a Bose-Einstein condensate state. We study in detail the use of the shift in the hyperfine Zeeman levels of sodium atoms in a homogeneous, external, constant magnetic field with an appropriate choice of the Zeeman sublevel populations of the ground states of these atoms. Conditions are determined such that, when an optical signal propagates through a condensate, it is possible to isolate components of that signal with strictly defined frequencies from residual low intensity noise. It is also shown that if the resulting filtered signal is repeatedly passed through a condensate with a different value of the magnetic field, noise can essentially be eliminated entirely from the optical signal.

DOI
10.1063/1.3490659

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The feasibility of using the extreme slowing down of light in Bose-Einstein condensates of alkali metal atoms as a means of improving the spectral characteristics of optical signals is studied. The basis of this approach is the resonant character of the slowing down of electromagnetic pulses in these media. In other words, signals with frequency characteristics close to the intervals between levels in the energy spectrum of alkali metal atoms in a Bose-Einstein condensate are slowed down the most. The filtering of electromagnetic signals is described in terms of a microscopic theory for the response of a gas of hydrogenlike atoms to a weak external electromagnetic field. The possibility in principle of signal filtering is demonstrated using the example of an electromagnetic pulse with a normal (gaussian) spectral intensity distribution propagating through a rarefied gas of alkali metal atoms in a Bose-Einstein condensate state. We study in detail the use of the shift in the hyperfine Zeeman levels of sodium atoms in a homogeneous, external, constant magnetic field with an appropriate choice of the Zeeman sublevel populations of the ground states of these atoms. Conditions are determined such that, when an optical signal propagates through a condensate, it is possible to isolate components of that signal with strictly defined frequencies from residual low intensity noise. It is also shown that if the resulting filtered signal is repeatedly passed through a condensate with a different value of the magnetic field, noise can essentially be eliminated entirely from the optical signal.
This paper studies theoretically the ultraslow light phenomenon in Bose-Einstein condensates of alkali-metal atoms. The description is based on the linear approach that is developed in the framework of the Green function formalism. It is pointed out that the group velocity of light pulses that are tuned up close to resonant lines of the alkali atoms' spectrum may strongly depend on the intensity of the external static magnetic field. The possibility of filtering optical pulses using the ultraslow light phenomenon in Bose condensates is discussed.
We study theoretically the linear response of a gas in the state with Bose-Einstein condensate to the perturbation by an external electromagnetic field (weak laser pulse). The Green’s functions formalism is used to study the dispersion characteristics of a system at finite temperatures. It is shown that the group velocity of the near-resonant pulses in condensate in some cases can strongly depend on the temperature. Basing on the account of the Zeeman splitting of the magnetic states we study also a possibility to filter light pulses by the condensate with several occupied quantum states.
We represent a new microscopic approach that allows studying the propagation properties of microwaves in a Bose-Einstein condensate of alkali atoms. It is assumed that the frequency of signal is tuned up to the transition between hyperfine ground state levels of such atoms. Pulse slowing conditions dependence on the system parameters is found. It is shown that the slowed signal can propagate in mentioned system with rather small energy loss. Such phenomenon is also studied in case of hyperfine levels Zeeman splitting. A possibility of ultra-slow microwaves observing in a condensed gas of cesium atoms is discussed.
We propose a microscopic approach for a description of interaction of the ideal gas of alkali atoms with a weak electromagnetic radiation. The description is constructed in the framework of the Green functions formalism that is based on a new formulation of the second quantization method in case of the bound states (atoms) presence. For a gas in the Bose-condensed (BEC) state we study the dependencies of the propagation velocity and damping rate on the microscopic characteristics of the system. For a condensed dilute gas of sodium atoms we find the conditions of the group velocity reducing for optical pulses tuned up close to the resonant transitions. We also show that the slowing phenomenon can strongly depend on the intensity of the external static magnetic field.
We propose a microscopic approach describing the interaction of an ideal gas of hydrogenlike atoms with a weak electromagnetic field. This approach is based on the Green-function formalism and an approximate formulation of the method of second quantization for quantum many-particle systems in the presence of bound states of particles. The dependencies of the propagation velocity and damping rate of electromagnetic pulses on the microscopic characteristics of the system are studied for a gas of hydrogenlike atoms. For a Bose-Einstein condensate of alkali-metal atoms we find the conditions when the electromagnetic waves of both the optical and microwave regions are slowed. In the framework of the proposed approach, the influence of an external homogeneous and static magnetic field on the slowing phenomenon is studied.
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.