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APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts

Atoms and molecules in a Bose-Einstein condensate with strong interactions

S. J. J. M. F. Kokkelmans

Published May 1, 2003• 0 citations
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Abstract

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.

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arXiv:1109.2977•Sep 14, 2011•3 citations
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.
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.
Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Stable condensates of up to 104 atoms have been created by using a magnetic-field-induced Feshbach resonance to reverse the sign of the zero-field scattering length. These condensates provide unique opportunities for the study of BEC physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a very wide range. This range extended from very strong repulsive self-interactions to large attractive ones. The effect of moving the condensate through the Feshbach resonance has been studied and compared with theory. Long-lived metastable condensates with attractive interactions have been produced near the zero of the Feshbach resonance. The transition from repulsive to attractive interactions can lead to a “collapse” of the condensate in which the cloud shrinks below our resolution limit, loses a significant number of atoms due to inelastic losses, and emits a burst of high-energy atoms.
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.
We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two c-field formalism, one c-field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate a recent experiment [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008] investigating the effects of strong interactions on the Bragg spectrum from a 85Rb BEC. Results from these simulations are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.