Thorsten Köhler

Production of Cold Molecules via Magnetically Tunable Feshbach Resonances

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose and two-spin-component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled-channels theory provides a rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, and the classification in terms of entrance- and closed-channel-dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic-field sweeps in cold Bose and Fermi gases and pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean-field, as well as beyond mean-field approaches are reviewed in detail, including the associated ranges of validity.

Three-Body Problem in a Dilute Bose-Einstein Condensate

We derive the explicit three-body contact potential for a dilute condensed Bose gas from microscopic theory. The three-body coupling constant exhibits the general form predicted by Wu [Phys. Rev. 115, 1390 (1959)]] and is determined in terms of the amplitudes of two- and three-body collisions in vacuum. In the present form, the coupling constant becomes accessible to quantitative studies which should provide the crucial link between few-body collisions and the stability of condensates with attractive two-body forces.

Microscopic quantum dynamics approach to the dilute condensed Bose gas

We derive quantum evolution equations for the dynamics of dilute condensed Bose gases. The approach contains, at different orders of approximation, for cases close to equilibrium, the Gross-Pitaevskii equation and the first-order Hartree-Fock-Bogoliubov theory. The proposed approach is also suited for the description of the dynamics of condensed gases that are far away from equilibrium. As an example the scattering of two Bose condensates is discussed.

Microscopic theory of atom-molecule oscillations in a Bose-Einstein condensate

In a recent experiment at JILA [E. A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of {sup 85}Rb 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.

Adiabatic association of ultracold molecules via magnetic-field tunable interactions

We consider in detail the situation of applying a time-dependent external magnetic field to a 87Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Kohler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.

Conventional character of the BCS-BEC crossover in ultracold gases of {sup 40}K

We use the standard fermionic and boson-fermion Hamiltonians to study the BCS-BEC crossover near the 202 G resonance in a two-component mixture of fermionic {sup 40}K atoms employed in the experiment of Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)]. Our mean-field analysis of many-body equilibrium quantities shows virtually no differences between the predictions of the two approaches, provided they are both implemented in a manner that properly includes the effect of the highest excited bound state of the background scattering potential, rather than just the magnetic-field dependence of the scattering length. Consequently, we rule out the macroscopic occupation of the molecular field as a mechanism behind the fermionic pair condensation and show that the BCS-BEC crossover in ultracold {sup 40}K gases can be analyzed and understood on the same basis as in the conventional systems of solid state physics.

Association of molecules using a resonantly modulated magnetic field

We study the process of associating molecules from atomic gases using a magnetic field modulation that is resonant with the molecular binding energy. We show that maximal conversion is obtained by optimizing the amplitude and frequency of the modulation for the particular temperature and density of the gas. For small modulation amplitudes, resonant coupling of an unbound atom pair to a molecule occurs at a modulation frequency corresponding to the sum of the molecular binding energy and the relative kinetic energy of the atom pair. An atom pair with an off-resonant energy has a probability of association which oscillates with a frequency and time-varying amplitude which are primarily dependent on its detuning. Increasing the amplitude of the modulation tends to result in less energetic atom pairs being resonantly coupled to the molecular state and also alters the dynamics of the transfer from continuum states with off-resonant energies. This leads to maxima and minima in the total conversion from the gas as a function of the modulation amplitude. Increasing the temperature of the gas leads to an increase in the modulation frequency providing the best fit to the thermal distribution, and weakens the resonant frequency dependence of the conversion. Mean-field effects can alter the optimal modulation frequency and lead to the excitation of higher modes. Our simulations predict that resonant association can be effective for binding energies of order

Long-range nature of Feshbach molecules in Bose-Einstein condensates

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Molecular Production in Two Component Atomic Fermi Gases

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Making cold molecules by time-dependent feshbach resonances

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.