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Laser Physics

Interaction of a laser double beam with the Bose-Einstein condensate of rarefied atomic gases

N. I. Shamrov

Published Jun 1, 2007• 1 citation
Publisher

Abstract

A quasi-resonant interaction of two oppositely directed light waves with the Bose-Einstein condensate of sodium vapor is studied using a semiclassical model at higher (dressing) and lower (probe) frequencies. It is demonstrated that, under the experimental conditions, a single state with nonzero momentum that corresponds to the absorption of a dressing photon and the emission of a probe photon is populated. A variation in the experimental conditions, in particular, an increase in the dressing-wave intensity or a decrease in the detuning of its resonance from the electronic transition under study can lead to the excitation of other atomic states whose momenta are codirectional and represent multiples of the given one. The shape of the probe pulse is found for various conditions of its interaction with the dressed condensate.

DOI
10.1134/s1054660x07060126

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Laser Physics•Aug 30, 2006•7 citations
A quasi-resonant interaction of two oppositely directed light waves with the Bose-Einstein condensate of sodium vapor is studied using a semiclassical model at higher (dressing) and lower (probe) frequencies. It is demonstrated that, under the experimental conditions, a single state with nonzero momentum that corresponds to the absorption of a dressing photon and the emission of a probe photon is populated. A variation in the experimental conditions, in particular, an increase in the dressing-wave intensity or a decrease in the detuning of its resonance from the electronic transition under study can lead to the excitation of other atomic states whose momenta are codirectional and represent multiples of the given one. The shape of the probe pulse is found for various conditions of its interaction with the dressed condensate.
Semiclassical equations describing the interaction of a probe pulse with a 'dressed' Bose—Einstein condensate of a rarefied atomic gas are proposed. The analytic solution of these equations is obtained for low-intensity pulses. The conditions of the appearance of a diffraction grating from recoil atoms are found. The existence of induced superradiance at the probe-beam frequency is predicted. The pulse propagation velocity in the condensate is determined as a function of its energy. The limits of the applicability of the two-level model of a 'dressed' atom are estimated.
When an atomic vapor interacts with an intense nearly resonant laser field, the ac Stark effect causes a profound modification of the weak-field absorption spectrum. Two of the induced spectral features can lead to amplification of a weak probe wave. We have previously measured in atomic sodium vapor high probe-wave gain (G = 38) due to the three-photon effect and a somewhat lower gain (G = 4) when the probe wave is detuned from the pump laser frequency by the inverse of the atomic response time.1 We present the results of an experimental and theoretical study of the energy coupling between two intense laser fields of comparable intensity through their interaction with an atomic vapor. In our experiments, a tunable alexandrite laser provides microsecond laser pulses of the required intensity that are nearly resonant with the 4s → 4p transition in potassium. We observed large energy transfer (50%) between the two waves at the nearly degenerate resonance and measured the intensity dependence of the coupling efficiency. Theoretical modeling of the interaction is based on a continued-fraction solution of the density-matrix equations of motion.
We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k 0. We assume that the detuning Δ~\tilde \Delta Δ~ from resonance between the energy ħω ex (k 0)+L 0 of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at Δ~=0\tilde \Delta = 0Δ~=0 the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when Δ~<0\tilde \Delta < 0Δ~<0 , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k 0−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at Δ~≈0\tilde \Delta \approx 0Δ~≈0 and depend on the orientation of the vectors q and k 0.
We present a theoretical treatment of dynamics of an atomic Bose–Einstein condensation interacting with a single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initially in a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed that atoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions, in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with two different sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs. It should be emphasized that when without the laser field, both the population difference and the atomic tunnelling current are only a single oscillation. But they will respectively become a superposition of two oscillations with different oscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one always has an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. These conclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of the atomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. By properly selecting the laser field, the expected atomic tunnelling current can be obtained too.
The superradiant Rayleigh scattering of high-intensity light pulses by the Bose-Einstein condensate of rubidium vapor is studied using the model proposed earlier. It is demonstrated that four states with a certain momentum are occupied under the experimental conditions (two states correspond to the forward recoil and two others correspond to the backward recoil). Condensate pulsations between the zero-momentum state and the above states are detected and studied. The corresponding shape of the coherent Rayleigh pulse is found.