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arXiv:cond-mat/0412105 · Physical Review A

Fluctuations in the formation time of ultracold dimers from fermionic atoms

Hermann Uys, T. Miyakawa, D. Meiser, Pierre Meystre

Published Nov 16, 2005• 11 citations
arXivHTMLPDF

Abstract

We investigate the temporal fluctuations characteristic of the formation of molecular dimers from ultracold fermionic atoms via Raman photoassociation. The quantum fluctuations inherent to the initial atomic state result in large fluctuations in the passage time from atoms to molecules. Assuming degeneracy of kinetic energies of atoms in the strong coupling limit, we find that a heuristic classical stochastic model yields qualitative agreement with the full quantum treatment in the initial stages of the dynamics. We also show that in contrast to the association of atoms into dimers, the reverse process of dissociation from a condensate of bosonic dimers exhibits little passage time fluctuations. Finally, we explore effects due to the nondegeneracy of atomic kinetic energies.

DOI
10.1103/physreva.72.053616

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We investigate the temporal fluctuations characteristic of the formation of molecular dimers from ultracold fermionic atoms via Raman photoassociation. The quantum fluctuations inherent to the initial atomic state result in large fluctuations in the passage time from atoms to molecules. Assuming degeneracy of kinetic energies of atoms in the strong coupling limit, we find that a heuristic classical stochastic model yields qualitative agreement with the full quantum treatment in the initial stages of the dynamics. We also show that in contrast to the association of atoms into dimers, the reverse process of dissociation from a condensate of bosonic dimers exhibits little passage time fluctuations. Finally, we explore effects due to the nondegeneracy of atomic kinetic energies.
This review describes recent experimental and theoretical advances in forming molecules in ultracold gases of trapped alkali metal atoms, both by magnetic tuning through Feshbach resonances and by photoassociation. Molecular Bose-Einstein condensation of long-range states of both boson dimers and fermion dimers was achieved in 2002-3. Condensates of boson dimers were found to be short-lived, but long-lived condensates of fermion dimers have been produced. Signatures of triatomic and tetraatomic molecules have recently been observed. Both homonuclear and heteronuclear molecules have been formed by photoassociation, mostly in very high vibrational levels. Recent attempts to produce ultracold molecules in short-range states (low vibrational levels) are described. Experimental and theoretical work on collisions of ultracold molecules is discussed.
This review describes recent experimental and theoretical advances in forming molecules in ultracold gases of trapped alkali metal atoms, both by magnetic tuning through Feshbach resonances and by photoassociation. Molecular Bose–Einstein condensation of long-range states of both boson dimers and fermion dimers was achieved in 2002–2003. Condensates of boson dimers were found to be short-lived, but long-lived condensates of fermion dimers have been produced. Signatures of triatomic and tetraatomic molecules have recently been observed. Both homonuclear and heteronuclear molecules have been formed by photoassociation, mostly in very high vibrational levels. Recent attempts to produce ultracold molecules in short-range states (low vibrational levels) are described. Experimental and theoretical work on collisions of ultracold molecules is discussed. Molecule formation in ultracold atomic gasesAll authorsJeremy M. Hutson & Pavel Soldánhttps://doi.org/10.1080/01442350600921772Published online:11 October 2010Table Download CSVDisplay Table
We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.
We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-PPP representation method. This allows us to provide an exact treatment of the molecular field depletion and sss-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process---which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion---is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.
We calculate the momentum distribution and the second-order correlation function in momentum space, ${g}^{(2)}(\mathbf{p},{\mathbf{p}}^{\ensuremath{'}},t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultracold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.
We report on the spectra of the long-range attractive molecular states of the Cs/sub 2/ dimer below the dissociation limits 6s+6p/sub 1/2/ and 6s+6p/sub 3/2/ which are accessible by molecular photoassociation of cold Cs atoms. For the states O/sub u//sup +/ and O/sub g//sup -/(6s+6p/sub 3/2/), we have performed trap-loss measurements, which are in good agreement with the theoretical calculations, performed in a perturbative approach. For the O/sub g//sup -/ and 1/sub u/(6s+6p/sub 3/2/) states, we observe, after spontaneous decay of the electronically excited molecules, the formation of translationally cold molecules. A rate of formation of cold molecules of the order of /spl sim/10/sup 6/ molecules per second is obtained in the case of the state O/sub g//sup $/.