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arXiv:cond-mat/9804015

Feshbach Resonance and Hybrid Atomic/Molecular BEC-Systems

Paolo Tommasini, Eddy Timmermans, Mahir Saleh Hussein, Arthur K. Kerman

Published Apr 2, 1998• 2 citations
arXivHTMLPDF

Abstract

The interactions responsible for Feshbach resonances in binary atom collisions produce a condensate of molecules in the atomic BEC-system. We discuss the `ground state' of the condensate system and illustrate that its properties differ quantitatively and qualitatively from the properties of a single condensate with atom-atom interactions described by the effective scattering length that characterizes the binary atomic collisions. We show, for example, that the tunneling of atom pairs between the atomic and molecular condensates lowers the energy and can bind the condensate system, giving it the liquid-like property of a self-determined density.

DOI
10.48550/arxiv.cond-mat/9804015

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The interactions responsible for Feshbach resonances in binary atom collisions produce a condensate of molecules in the atomic BEC-system. We discuss the `ground state' of the condensate system and illustrate that its properties differ quantitatively and qualitatively from the properties of a single condensate with atom-atom interactions described by the effective scattering length that characterizes the binary atomic collisions. We show, for example, that the tunneling of atom pairs between the atomic and molecular condensates lowers the energy and can bind the condensate system, giving it the liquid-like property of a self-determined density.
In the atomic Bose-Einstein condensate, the interactions that bring a binary atom system to an intermediate state molecule in the Feshbach resonance create a second condensate component of molecules. The atomic and molecular condensates coherently exchange pairs of atoms. We discuss a signature of the coherent intercondensate exchange: Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the energy detuning. The dependence of the many-body ground state energy on volume suggests that the on-resonant ground state is a dilute condensate with the liquidlike property of a self-determined density.
With help of a Feshbach scattering resonance it is possible to change the effective two-body interaction of ultra-cold atoms from repulsive to attractive, from weak to strong. Regular field theory for the description of Bose-Einstein condensates is based on a single interaction parameter only, the scattering length. Such a description, however, is not valid anymore for the resonance regime. We formulated a field-theory that incorporated the microscopic energy-dependent two-body interactions, that also takes pair correlations into account. This theory allowed us to explain an experiment at JILA where Ramsey fringes were observed in a ^85Rb Bose-Einstein condensate by making use of a Feshbach resonance. The theory and experiment show that coherent molecules are created, a first step in the direction of molecular BEC. For non-resonant interactions, the self-energy corresponding to the atom-atom interactions is proportional to the scattering length. Close to resonance, however, this relationship no longer applies, and the energy will level off to a finite value on resonance. We investigate this resonance self-energy, and compare it with experimental results from strongly interacting Fermi systems.
Recently, effects of Feshbach resonances in atom-atom interactions were observed by varying the external magnetic field of an atomic Bose-Einstein condensate (BEC). We point out that the quasi-bound molecules created in the intermediate state of the resonance can form a second, molecular condensate. The many-body state of the system is then a hybrid atomic/molecular condensate with inter-condensate tunneling of atom pairs. A sudden variation of the magnetic field results in oscillations of the number of atoms and molecules in their respective condensates, providing a signature of this novel type of quantum tunneling.
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length as{a}_{s}as​ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.
A new facet was added to the study of dilute gases by the production and subsequent Bose–Einstein condensation of diatomic molecules from a gas of fermionic atoms. Feshbach resonances which, as we have seen in Sec. 5.4, make it possible to tune the atom–atom interaction, play a crucial role in the experiments. At the magnetic field strength for which the binding energy of the molecule vanishes, the inverse of the scattering length, which determines the low-energy effective interaction between atoms, passes through zero. In the experiments to produce molecules, one starts with a mixture of two species of fermion, most commonly different hyperfine states of the same isotope, in a magnetic field of such a strength that the molecular state has an energy higher than that of two zero-momentum atoms in the open channel. The magnetic field is then altered to a value at which the molecular state is bound with respect to two atoms in the open channel, and in this process, many of the atoms combine to form molecules. These molecules have binding energies in the 10 −9 eV range, and are thus extremely weakly bound by the standards of conventional molecular physics. In addition, they are very extended, with atomic separations as large as one micron. These molecules, being bosons, can undergo Bose–Einstein condensation, just as bosonic atoms do.
To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].