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arXiv:1010.5900 · Physica Scripta

Magnetic field dependence and the possibility of filtering ultraslow light pulses in atomic gases with Bose–Einstein condensates

Andrii Sotnikov

Published Sep 1, 2010• 1 citation
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Abstract

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.

DOI
10.1088/0031-8949/2010/t140/014061

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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 the temperature dependence of optical properties of dilute gases of alkali-metal atoms in the state with Bose-Einstein condensates. The description is constructed in the framework of the microscopic approach that is based on the Green's-functions formalism. We find the expressions for the scalar Green's functions describing a linear response of a condensed gas to a weak external electromagnetic field (laser). It is shown that these functions depend on the temperature, other physical properties of a system, and on the frequency detuning of a laser. We compare the relative contributions of the condensate and noncondensate particles in the system response. The influence of the temperature effects is studied by the example of two- and three-level systems. We show that in these cases, which are most commonly realized in the present experiments, the group velocity and the absorption rate of pulses practically do not depend on the gas temperature in the region from the absolute zero to the critical temperature. We discuss also the cases when the temperature effects can play a significant role in the phenomenon of slowing of electromagnetic pulses in a gas of alkali-metal atoms with Bose-Einstein condensates.
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.
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.
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.
Light can be slowed down to ultraslow speeds v ia electromagnetically induced transparency in atomic Bose-Einstein condensates. This is thought to be useful for storage of quantum information for weak probe pulses. We investigate the effects of inhomogeneous density profile of the condensate on propagation of such ultraslow pulses. We find that spatial density of an atomic condensate leads to a graded refractive index profile, for an off-resonant probe pulse when condensate parameters are suitably chosen. Within the window of negligible absorption, conditions for degenerate multiple waveguide modes are determined. Both analytical and numerical studies are presented to reveal the effects of experimentally controllable parameters, such as temperature and interatomic interaction strength on the number of modes. Group velocity dispersion and modal dispersion are discussed. The effect of waveguide dispersion, in addition to usual material dispersion, on ultraslow pulses is pointed out.