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Physical Review A

Imaging population distribution between two coupled atomic Bose-Einstein condensates by using short laser pulses

Aranya B. Bhattacherjee, Man Mohan

Published Nov 25, 2002• 2 citations
Publisher

Abstract

In this work we investigate scattering of ultrashort light pulses from two coupled neutral atomic Bose-Einstein condensates corresponding to two different ground hyperfine sublevels. Two counterpropagating ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ light waves are employed to excite the atomic condensates. We find that the spectrum of scattered light is determined by the initial preparation of the atomic condensate. The spectrum is found to be a mirror image of the population distribution. The scattered light probes the population distribution between the two condensates. In particular, we find that, when the population is equally distributed between the two ground states, the quantum fluctuations in the spectrum are suppressed due to destructive quantum interference.

DOI
10.1103/physreva.66.053617

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In this work we investigate scattering of ultrashort light pulses from two coupled neutral atomic Bose-Einstein condensates corresponding to two different ground hyperfine sublevels. Two counterpropagating \ensuremathσ+{\ensuremath{\sigma}}_{+}\ensuremathσ+​ and \ensuremathσ\ensuremath−{\ensuremath{\sigma}}_{\ensuremath{-}}\ensuremathσ\ensuremath−​ light waves are employed to excite the atomic condensates. We find that the spectrum of scattered light is determined by the initial preparation of the atomic condensate. The spectrum is found to be a mirror image of the population distribution. The scattered light probes the population distribution between the two condensates. In particular, we find that, when the population is equally distributed between the two ground states, the quantum fluctuations in the spectrum are suppressed due to destructive quantum interference.
Summary form only given.We consider two overlapping and optically thin dilute gas Bose-Einstein condensates occupying two different Zeeman sublevels. We propose an optical method for increasing the number of condensate atoms. Two laser beams drive Raman transitions between the Zeeman states and induce a coherent quantum tunneling between the Bose-Einstein condensates. The scattering of photons is dominantly coherent and in the forward direction due to the Bose enhancement. This corresponds to the scattering of atoms between the two condensates. Some laser-driven Raman transitions also scatter atoms between the condensate and noncondensate atom fractions. For a range of condensate phase differences there is destructive quantum interference of the amplitudes for scattering atoms out of the condensates. Because the total atom scattering rate into the condensates is unaffected the condensates grow. This mechanism is analogous to that responsible for optical lasing without inversion, and it may find application as a pump for an atom laser.
A pulsed atom laser derived from a Bose-Einstein condensate is used to probe a second target condensate. The target condensate scatters the incident atom laser pulse. From the spatial distribution of scattered atoms, one can infer important properties of the target condensate and its interaction with the probe pulse. As an example, we measure the s-wave scattering length that, in low energy collisions, describes the interaction between the |F = 1,m(F) = -1) and |F = 2,m(F) = 0) hyperfine ground states in (87)Rb.
We calculate the spectrum of the scattered light from quantum degenerate atomic gases obeying Bose-Einstein statistics. The atoms are assumed to occupy two ground states, which are optically coupled through a common excited state by two low-intensity off-resonant light beams. In the presence of a Bose condensate in both ground states, the atoms may exhibit light-induced oscillations between the two condensates analogous to the Josephson effect. The spectrum of the scattered light is calculated in the limit of a low oscillation frequency. In the spectrum we are able to observe qualitative features depending on the phase difference between the macroscopic wave functions of the two condensates. Thus, our optical scheme could possibly be used as an experimental realization of the spontaneous breakdown of the U(1) gauge symmetry in the Bose-Einstein condensation.
We propose a light-scattering scheme to measure the relative phase of atomic Bose-Einstein condensates and its diffusion rate. The proposal relies on the existence of two independent condensates coupled to a common excited state. To this end, we consider a two-well ground-state potential together with excited-state trap wave functions that extend over the whole region. When the first trap is driven by a weak monochromatic laser field, the light scattered from the second trap has a nonzero mean-electric field amplitude with a phase shift proportional to the difference of the condensate phases. When both condensates are driven, the phases of the two laser fields can be adjusted to cancel the scattering completely by a quantum interference. The particular value of the laser phase difference that gives zero scattering determines the relative phase of the two condensates.
We investigate atomic population dynamics of two Bose-Einstein condensate (BEC) states that are in different traps or in the same trap and are optically coupled through a common excited state by Raman laser pulses. For large interatomic interactions, almost all of the atoms that are initially in one of the traps (or one of the internal states) are either completely transferred into the other state or stay in the initially occupied state after the laser pulses, and the atoms (populations) are never distributed to both condensate states at the same time. Applications to the atomic logic gate and to output couplers of the atom laser are pointed out.
A scheme is proposed to manipulate the quantum-statistical properties of a neutral atomic Bose-Einstein condensate in an ultracold alkali-atom-trap system with atoms in the ground hyperfine F=1, MF{\mathit{M}}_{\mathit{F}}MF​=\ifmmode\pm\else\textpm\fi{}1,0 states (labeled respectively as \ensuremath{\Vert}${\mathit{g}}_{\ifmmode\pm\else\textpm\fi{},0}$〉). Initially, the atomic condensate is assumed to be prepared in a hyperfine sublevel \ensuremath{\Vert}${\mathit{g}}_{\mathrm{\ensuremath{-}}}$〉. By effective two-photon excitations with two classical (${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$) and quantum (${\mathrm{\ensuremath{\sigma}}}^{+}$) nonresonant copropagating traveling-wave light fields, we show that the atomic system can be settled into a coherent superposition of two atomic Bose-Einstein condensates corresponding to different ground hyperfine sublevels and different quantum statistics. Furthermore, with an appropriate choice of interaction time, atom-field coupling strengths, and quantum features of the quantized laser field, a nonclassical condensate can be prepared in the hyperfine sublevel \ensuremath{\Vert}g+{\mathit{g}}_{+}g+​〉.