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arXiv:cond-mat/0212572 · Physical Review Letters

Atom-Molecule Laser Fed by Stimulated Three-Body Recombination

Bogdan Borca, Josh W. Dunn, Viatcheslav Kokoouline, Chris H. Greene

Published Aug 15, 2003• 23 citations
arXivHTMLPDF

Abstract

Using three-body recombination as the underlying process, we propose a method of coherently driving an atomic Bose-Einstein condensate (BEC) into a molecular BEC. Superradiantlike stimulation favors atom-to-molecule transitions when two atomic BECs collide at a resonant kinetic energy, the result being two molecular BEC clouds moving with well-defined velocities. Potential applications include the construction of a molecule laser.

DOI
10.1103/physrevlett.91.070404

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Using three-body recombination as the underlying process, we propose a method of coherently driving an atomic Bose-Einstein condensate (BEC) into a molecular BEC. Superradiantlike stimulation favors atom-to-molecule transitions when two atomic BECs collide at a resonant kinetic energy, the result being two molecular BEC clouds moving with well-defined velocities. Potential applications include the construction of a molecule laser.
Summary form only given. Parametric solitons or simultaneous solitary waves (simultons), involving the optical /spl chi//sup (2)/ nonlinearity, have been the topic of much recent theoretical and experimental interest in nonlinear optics. We propose a novel mechanism by which a similar phenomenon may occur in nonlinear atomic optics, in which coherent molecule formation in a Bose-Einstein condensate takes the place of second harmonic generation. This requires a coupling that converts two atoms into one molecule, thus generating coupled atomic and molecular Bose-Einstein condensates. Our model includes a coherent molecular formation process (i.e., without dissipation) in an atomic BEC vapor, either through a Feshbach resonance or Raman photo-association. The coherently coupled atom-molecular condensate could provide a route to the observation of a localized three-dimensional BEC soliton, even in the absence of a trap potential. A possible application is in the free propagation of a non-diverging atom laser pulse, thus greatly increasing the intensity in an atom laser beam.
Summary form only given. Coherent conversion of an atomic to a molecular Bose-Einstein condensate (BEC) is a first step towards 'superchemistry', which is the atom optics analog of frequency conversion in nonlinear optics. A number of studies of this have shown that direct conversion via Raman photo-association appears feasible, based on stimulated free-bound and bound-bound transitions in the presence of two laser fields E/sup (1)/=E/sub 0//sup (1)/ cos(/spl omega//sup (1)/t) and E/sup (2)/=E/sub 0//sup (2)/ cos(/spl omega//sup (2)/t). Here pairs of atoms from the two-atom continuum are transferred-via an excited bound molecular state-to a bound molecular state of lower energy. Raman photo-association allows coupling to a single molecular state, which can be selected by the Raman laser frequencies /spl omega//sup (1)/ and /spl omega//sup (2)/. However, practical calculations using available lasers and transitions indicate that coherent transfer is often limited by spontaneous emission from the intermediate molecular excited electronic state. A possible route towards minimizing losses and decoherence from spontaneous emission is to use the stimulated Raman adiabatic passage (STIRAP) method (Drummond et al, Phys. Rev. Lett. vol. 81, p. 3055, 1998) in which a counter-intuitive pulse sequence is used where the first input pulse couples the molecular levels, even when there are no molecules present.
Abstract Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose–Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a 87Rb BEC has been used to produce 87Rb2 molecules in a single rotational-vibrational state1, and ultracold molecules have also been formed2 through photoassociation of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work3, 4, 5, 6, 7. Here we make use of a time-varying magnetic field near a Feshbach resonance8, 9, 10, 11, 12 to produce coherent coupling between atoms and molecules in a 85Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules—two chemically different species.
Robust stimulated Raman exact passages are requisite for controlling nonlinear quantum systems, with wide applications, ranging from ultracold molecules to nonlinear optics to superchemistry. Inspired by shortcuts to adiabaticity, we propose the fast-forward scaling of stimulated Raman adiabatic processes with nonlinearity involved, describing the transfer from an atomic Bose-Einstein condensate to a molecular one by controllable external fields. The fidelity and robustness of atom-molecule conversion are shown to surpass those of conventional adiabatic passages, assisted by the fast-forward driving field. Finally, our results are extended to fractional stimulated Raman adiabatic processes for the coherent superposition of atomic and molecular states.
We study the theory of several aspects of the dynamics of coherent atom-molecule conversion in spin-one Bose-Einstein condensates. Specifically, we discuss how, for a suitable dark-state condition, the interplay of spin-exchange collisions and photo association leads to the stable creation of an atom-molecule pair from three initial spin-zero atoms. This process involves two two-body interactions and can be intuitively viewed as an effective three-body recombination. We investigate the relative roles of photo association and of the initial magnetization in the ``resonant'' case, where the dark-state condition is perfectly satisfied. We also consider the ``nonresonant'' case, where that condition is satisfied either only approximately---the so-called adiabatic case---or not at all. In the adiabatic case, we derive an effective nonrigid pendulum model that allows one to conveniently discuss the onset of an antiferromagnetic instability in an ``atom-molecule pendulum,'' as well as large-amplitude pair oscillations and atom-molecule entanglement.