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arXiv:cond-mat/0110566 · Physical Review Letters

Coherent Molecular Solitons in Bose-Einstein Condensates

P. D. Drummond, Karen V. Kheruntsyan, Hao He

Published Oct 12, 1998• 215 citations
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Abstract

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEC, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output.

DOI
10.1103/physrevlett.81.3055

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We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEC, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output.
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.
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom sss-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schr\"odinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.
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We propose a scheme for making a Bose-Einstein condensate (BEC) of molecules from a BEC of atoms in a strongly confining two-dimensional optical lattice and a weak one-dimensional optical lattice in the third dimension. The stable solutions obtained for the order parameters take the form of a different type of gap soliton, with both atomic and molecular BECs, and also standard gap solitons with only a molecular BEC. The strongly confining dimensions of the lattice stabilize the BEC against inelastic energy transfer in atom-molecule collisions. The solitons with atoms and molecules may be obtained by starting with an atomic BEC, and gradually tuning the resonance by changing the external magnetic-field strength until the desired atom-molecule soliton is obtained. A gap soliton of a BEC of only molecules may be obtained nonadiabatically by starting from an atom-only gap soliton, far from a Feshbach resonance and adjusting the magnetic field to near Feshbach resonance. After a period of time in which the dimer field grows, change the magnetic field such that the detuning is large and negative and Feshbach effects wash out, turn off the optical lattice in phase with the atomic BEC, and turn on an optical lattice in phase with the molecules. The atoms disperse, leaving a gap soliton composed of a molecular BEC. Regarding instabilities in the dimension of the weak optical lattice, the solitons which are comprised of both atoms and molecules are sometimes stable and sometimes unstable---we present numerically obtained results. Gap solitons comprised of only molecules have the same stability properties as the standard gap solitons: stable from frequencies slightly below the middle of the band gap to the top, and unstable below that point. Instabilities are only weakly affected by the soliton velocities, and all instabilities are oscillatory.