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arXiv:cond-mat/0005062 · Physical Review Letters

Formation of Pairing Fields in Resonantly Coupled Atomic and Molecular Bose-Einstein Condensates

Murray Holland, J. Park, R. Walser

Published Mar 5, 2001• 132 citations
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Abstract

We show that pair correlations may play an important role in the dynamical properties of a Bose-Einstein condensed gas composed of an atomic field resonantly coupled with a condensed field of molecular dimers. Specifically, pair correlations in this system can dramatically modify the coherent and incoherent transfers between the atomic and molecular fields.

DOI
10.1103/physrevlett.86.1915

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We show that pair correlations may play an important role in the dynamical properties of a Bose-Einstein condensed gas composed of an atomic field resonantly coupled with a condensed field of molecular dimers. Specifically, pair correlations in this system can dramatically modify the coherent and incoherent transfers between the atomic and molecular fields.
The dynamics of coherent Rabi oscillations in coupled atomic and molecular Bose-Einstein condensates is considered taking into account the atom-atom, atom-molecule, and molecule-molecule elastic interactions. The exact solution for the molecule formation probability is derived in terms of the elliptic functions. The two-dimensional space of the involved parameters intensity and detuning is analyzed and divided into two regions where the Rabi oscillations show different characteristics. A resonance curve is found, on which the molecular formation probability monotonically increases as a function of time. The maximum value of the final transition probability on this curve is 1∕21∕21∕2 (i.e., total transition to the molecular state) and it is achieved at high field intensities starting from a minimal threshold defined by the interspecies interaction scattering lights. The explicit form of the resonance curve is determined, and it is shown that the resonance frequency position reveals a nonlinear dependence on the Rabi frequency of the applied field. A singular point is found on the resonance curve, where a power-law time evolution of the system is observed.
We use numerical integration of coupled differential equations in a truncated Wigner representation to show that the initial quantum state of an atomic Bose-Einstein condensate plays an important role in the process of Raman photoassociation to form a molecular condensate. Comparing the predictions for different initial quantum states, we find that, even when the stochastic prediction for an initial coherent state is close to the Gross-Pitaevskii prediction, other possible states may result in very different dynamics. The mean-field dynamics can be appreciably different, depending on the initial conditions.
We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one-, two-, and three-dimensional geometries and analyze the role of dimensionality on the atom production rate as a function of the dissociation energy. As well as determining the populations and coherences of the atoms, we calculate the correlations that exist between atoms of opposite momenta, including the column density correlations in three-dimensional systems. We compare the results with those of the undepleted molecular field approximation and argue that the latter is most reliable in fermionic systems and in lower dimensions. In the bosonic case we compare the pairing mean-field results with exact calculations using the positive-PPP stochastic method and estimate the range of validity of the pairing mean-field theory. Comparisons with similar first-principle simulations in the fermionic case are currently not available, however, we argue that the range of validity of the present approach should be broader for fermions than for bosons in the regime where Pauli blocking prevents complete depletion of the molecular condensate.
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser molecular samples, however, is frequently hindered by fast inelastic collisions that heat and deplete the population. Here we report the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning g−g-g−wave molecules by inducing pairing interactions in an atomic condensate. The trap geometry and the low temperature of the molecules help reducing inelastic loss to ensure thermal equilibrium. We determine the molecular scattering length to be +220(30)+220(30)+220(30)~Bohr and investigate the unpairing dynamics in the strong coupling regime. Our work confirms the long-sought transition between atomic and molecular condensates, the bosonic analog of the BEC-BCS (Bardeen-Cooper-Schieffer superfluid) crossover in a Fermi gas.