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Quantum Electronics and Laser Science Conference

Coherent atomic-molecular simultons in BEC

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

Published Jan 20, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.1999.807141

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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.
Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time independent atom-molecular coupled equations, the initial atomic and molecular wavefunctions were obtained and the dynamics of the initial atomic and molecular waves in a spherical one-dimensional trap were studied by solving the time-dependent atom-molecular coupled equations. During evolution two types of induced or stimulated decays of the feshbach molecules were switched on. These two types of stimulated decays of the feshbach molecules to the two-atom continuum and to the bound level of the lowest hyperfinee state of the molecule were induced by laser or Radio Frequency fields. Hence the strength of these two induced decays can be controlled by varying the laser or RF field parameters e.g. intensity, detuning etc. It is found that depending on the relative strength of these two types of stimulated or induced decays initial atomic and molecular waves assume solitonic nature as bright solitons during evolution and the stability of these solitonic waves can be achieved by controlling the relative strength of induced decays in two different channels. It is shown that these two induced decays lead to the formation of stable atomic and molecular solitons by suppressing the initial oscillations and instability in the atom-molecular coupled system of 85Rb atoms.
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.
Summary form only given. We have observed a stimulated Raman resonance between free and bound molecular states of atoms in a Bose-condensed gas. In our experiment, we first produce a Bose-condensed cloud containing about 5/spl times/10/sup 5/ /sup 87/Rb 5/sup 2/S/sub 1/2/ (f=1,m/sub f/=-1) atoms in a magnetic TOP trap, with a typical condensate fraction of about 20%. We then illuminate the atoms with a /spl tau/=10 ms duration pulse of light from two laser beams 1 and 2 of frequency /spl nu//sub 1/ and /spl nu//sub 2/, and intensities I/sub 1/=120 W/cm/sup 2/ and I/sub 2/=2.2 W/cm/sup 2/, respectively. We measure the fraction of atoms N(/spl tau/)/N/sub 0/ remaining after the 10 ms pulse with laser-induced fluorescence.
Summary form only given. We consider the quantum theory of two atomic fields interacting coherently to form a molecular field via Raman photoassociation. This can be applied to treat interactions in either atomic Bose condensates or quantum Fermi gases, describing coherent molecule formation together with s-wave scattering This new type of super-chemical reaction (or nonlinear atom optics) has never been observed on Earth-and temperature even in space would be far too hot to observe it naturally. Thus, it would represent a breakthrough into a completely new type of low-temperature physics, only accessible at the temperatures that have been recently obtained experimentally. The theory required is also new, yet surprisingly relatively simple.