We discuss the long-range nature of the molecules produced in recent experiments on molecular Bose-Einstein condensation. The properties of these molecules depend on the full two-body Hamiltonian and not just on the states of the system in the absence of interchannel couplings. The very long-range nature of the state is crucial to the efficiency of production in the experiments. Our many-body treatment of the gas accounts for the full binary physics and describes properly how these molecular condensates can be directly probed.
We discuss the long-range nature of the molecules produced in recent experiments on molecular Bose-Einstein condensation. The properties of these molecules depend on the full two-body Hamiltonian and not just on the states of the system in the absence of interchannel couplings. The very long-range nature of the state is crucial to the efficiency of production in the experiments. Our many-body treatment of the gas accounts for the full binary physics and describes properly how these molecular condensates can be directly probed.
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.
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.
Recent advances in molecular cooling have enabled the realization of strongly dipolar Bose--Einstein condensates (BECs) of molecules, and BECs of many different molecular species may become experimentally accessible in the near future. Here, we explore the unique properties of such BECs and the new insights they may offer into dipolar quantum fluids and many-body physics. We explore which parameter regimes can realistically be achieved using currently available experimental techniques, discuss how to implement these techniques, and outline which molecular species are particularly well suited to explore exotic new states of matter. We further determine how state-of-the-art beyond mean-field theories, originally developed for weakly dipolar magnetic gases, can be pushed to their limits and beyond, and what other long-standing questions in the field of dipolar physics may realistically come within reach using molecular systems.
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 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.
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.
In a recent experiment at JILA [E. A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of 85Rb atoms was exposed to a specially designed time-dependent magnetic-field pulse in the vicinity of a Feshbach resonance. The production of additional components of the gas as well as their oscillatory behavior have been reported. We apply a microscopic theory of the gas to identify these components and determine their physical properties. Our time-dependent studies allow us to explain the observed dynamic evolution of all fractions, and to identify the physical relevance of the pulse shape. Based on ab initio predictions, our theory strongly supports the view that the experiments have produced a molecular condensate.