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Journal of Chemical Biological and Physical Sciences

An evaluation of magnetic field and density dependence of the Josephson frequency in atom-Molecule Coherence in Bose gases and study of emergence of molecular Bose-Einstein condensate from a Fermi gas

Published Jan 30, 2018• 1 citation

Abstract

Using the theoretical formalism of R A Duine and H T C Stoof (arXiv: cond-mat/0303230v) 22 March 2003), we have theoretically evaluated magnetic field and density dependence of the Josephson frequency in coherence atom-molecule oscillation in Bose-Einstein condensed gas.Our theoretically obtained results show that Josephson frequency increases with both magnetic field for constant condensate density and also with condensate density for fixed magnetic field.Our theoretically evaluated results are in good agreement with the experimental data and also with other theoretical workers.Using the theoretical formalism of Markes Greiner etal (Nature, 26 Nov (2005)) , we have studied the emergence of molecular Bose-Einstein condensate from a Fermi gas of 6 Li atoms.The study has been performed with the help of Feshbach resonance.We have evaluated molecular condensate fraction N0/N as a function of (T/TC) and as a function of (T/TF).We have also evaluated scattering length 'a' in unit of a0, of mixture of two lowest hyperfine states of 6 Li atom, temperature (µK) all as a function of magnetic field (mT) near the crossing of the An evaluation …

DOI: 10.24214/jcbps.c.8.1.06476

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Using the theoretical formalism of R A Duine and H T C Stoof (arXiv: cond-mat/0303230v) 22 March 2003), we have theoretically evaluated magnetic field and density dependence of the Josephson frequency in coherence atom-molecule oscillation in Bose-Einstein condensed gas.Our theoretically obtained results show that Josephson frequency increases with both magnetic field for constant condensate density and also with condensate density for fixed magnetic field.Our theoretically evaluated results are in good agreement with the experimental data and also with other theoretical workers.Using the theoretical formalism of Markes Greiner etal (Nature, 26 Nov (2005)) , we have studied the emergence of molecular Bose-Einstein condensate from a Fermi gas of 6 Li atoms.The study has been performed with the help of Feshbach resonance.We have evaluated molecular condensate fraction N0/N as a function of (T/TC) and as a function of (T/TF).We have also evaluated scattering length 'a' in unit of a0, of mixture of two lowest hyperfine states of 6 Li atom, temperature (µK) all as a function of magnetic field (mT) near the crossing of the An evaluation …

Motivated by recent experiments (Claussen et al 2003 Preprint cond-mat/0302195) we investigate the magnetic-field dependence of the Josephson frequency of coherent atom–molecule oscillations near a Feshbach resonance. Far off resonance this frequency is determined by two-atom physics. However, the Josephson frequency is relatively large in this case and a description purely in terms of scattering lengths turns out to be inadequate. In particular, we have to include the effective range parameter of the interatomic interaction in our calculations. Close to resonance, the frequency deviates from the two-body results due to various many-body shifts. Considering also the many-body effects, we find perfect agreement with the experimental results over the entire range of magnetic field.

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.

Atom–molecule coherence in a Bose-Einstein condensate (BEC) has been demonstrated. Sudden changes were made to the magnetic field near a Feshbach resonance such that oscillations between atomic and molecular states were excited. The frequency of these oscillations was measured over a large range of magnetic fields and was found to be in excellent quantitative agreement with the predicted energy difference between two colliding atoms and the bound molecular state. This agreement indicates that we have created a quantum superposition of atoms and diatomic molecules, which are chemically different species. 1

We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6Li gas at magnetic fields above a Feshbach resonance, where no stable 6Li2 molecules would exist in vacuum. We accurately determined the position of the resonance to be 822+/-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of C. A. Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)]] who has recently observed this crossover temperature.

We create atom-molecule superpositions in a Bose-Fermi mixture of

^{87}\text{R}\text{b}

and

^{40}\text{K}

atoms. The superpositions are generated by ramping an applied magnetic field near an interspecies Fano-Feshbach resonance to coherently couple atom and molecule states. Rabi- and Ramsey-type experiments show oscillations in the molecule population that persist as long as $150\text{ }\ensuremath{\mu}\text{s}$ and have up to 50% contrast. The frequencies of these oscillations are magnetic-field dependent and consistent with the predicted molecule binding energy. This quantum superposition involves a molecule and a pair of free particles with different statistics (i.e., bosons and fermions) and furthers exploration of atom-molecule coherence in systems without a Bose-Einstein condensate.