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arXiv:cond-mat/9806165 · Physical Review A

Phase conjugation of multicomponent Bose-Einstein condensates

Elena V. Goldstein, Pierre Meystre

Published Feb 1, 1999• 49 citations
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Abstract

We consider a trapped multicomponent atomic Bose-Einstein condensate, concentrating specifically on condensates in the hyperfine ground state $F=1,$ where spin exchange collisions result in a transfer of population between $m=0$ and $m=\ifmmode\pm\else\textpm\fi{}1$ internal states. Drawing an analogy with the optical situation, we show that this system can be regarded as a matter-wave analog of optical multiwave mixing. This opens up the way to realize matter-wave phase conjugation, whereby an incident atomic beam can be ``time reversed.'' In addition, matter-wave phase conjugation also offers novel diagnostic tools to study the coherence properties of condensates, as well as to measure the relative scattering lengths of hyperfine sublevels.

DOI
10.1103/physreva.59.1509

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We consider a trapped multicomponent atomic Bose-Einstein condensate, concentrating specifically on condensates in the hyperfine ground state F=1,F=1,F=1, where spin exchange collisions result in a transfer of population between m=0m=0m=0 and m=\ifmmode±\else\textpm\fi1m=\ifmmode\pm\else\textpm\fi{}1m=\ifmmode±\else\textpm\fi1 internal states. Drawing an analogy with the optical situation, we show that this system can be regarded as a matter-wave analog of optical multiwave mixing. This opens up the way to realize matter-wave phase conjugation, whereby an incident atomic beam can be ``time reversed.'' In addition, matter-wave phase conjugation also offers novel diagnostic tools to study the coherence properties of condensates, as well as to measure the relative scattering lengths of hyperfine sublevels.
We discuss the possibility of observing atomic phase conjugation from Bose condensates, and using it as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that since phase conjugation results from the scattering of a partial matter wave off the spatial grating produced by two other waves, it offers a natural way to directly measure such properties, and as such provides an attractive alternative to the optical methods proposed in the past.
We propose a scheme for parametric amplification and phase conjugation of an atomic Bose-Einstein condensate (BEC) via stimulated dissociation of a BEC of molecular dimers consisting of bosonic atoms. This can potentially be realized via coherent Raman transitions or using a magnetic Feshbach resonance. We show that the interaction of a small incoming atomic BEC with a (stationary) molecular BEC can produce two counterpropagating atomic beams - an amplified atomic BEC and its phase-conjugate or ``time-reversed'' replica. The two beams can possess strong quantum correlation in the relative particle number, with squeezed number-difference fluctuations.
We present an exact quantum-mechanical analysis of collinear four-wave mixing in a multicomponent Bose-Einstein condensate consisting of sodium atoms in the F=1F=1F=1 ground state. Technically, this is achieved by taking advantage of the conservation laws of the system to cast its Hamiltonian in terms of angular momentum operators. We discuss explicitly the build-up of matter-wave side modes from quantum fluctuations, as well as the correlations between these modes. We show the appearance of a strong quantum entanglement between hyperfine states. We also demonstrate that for finite atomic numbers, the system exhibits periodic collapses and revivals in the exchange of atoms between different spin states.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic condensate in the F=1 hyperfine state confined by an optical dipole trap. When the mean-field interaction is attractive (c(0)<0) and the spin-exchange interaction of a spinor condensate is ferromagnetic (c(2)<0), we prove that the system possesses a completely integrable point leading to the existence of multiple bright solitons. By applying results from the inverse scattering method, we analyze a collision law for two-soliton solutions and find that the dynamics can be explained in terms of the spin precession.