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arXiv:0706.4218 · Physical Review A

Association of heteronuclear molecules in a harmonic oscillator well

Jesper Fevre Bertelsen, Klaus Mølmer

Published Oct 15, 2007• 17 citations
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Abstract

We describe the collisional interaction between two different atoms that are trapped in a harmonic potential. The atoms are exposed to a magnetic field, which is modulated in the vicinity of an $s$-wave Feshbach resonance, and we study the formation of molecular bound states and excited states of the trapped system with nontrivial angular correlations.

DOI
10.1103/physreva.76.043615

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We describe the collisional interaction between two different atoms that are trapped in a harmonic potential. The atoms are exposed to a magnetic field, which is modulated in the vicinity of an sss-wave Feshbach resonance, and we study the formation of molecular bound states and excited states of the trapped system with nontrivial angular correlations.
We have observed 28 heteronuclear Feshbach resonances in ten spin combinations of the hyperfine ground states of a $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture. The measurements were performed by observing the loss rates from an atomic mixture at magnetic fields between 000 and 700G700\phantom{\rule{0.3em}{0ex}}\mathrm{G}700G. These data were used to significantly refine an interatomic potential derived from molecular spectroscopy, yielding a highly consistent model of the $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ interaction. Thus, the measured resonances can be assigned to the corresponding molecular states. In addition, this potential allows for an accurate calculation of the energy differences between highly excited levels and the rovibrational ground level. This information is of particular relevance for the formation of deeply bound heteronuclear molecules. Finally, the model is used to predict Feshbach resonances in mixtures of 87Rb^{87}\mathrm{Rb}87Rb combined with 39K^{39}\mathrm{K}39K or 41K^{41}\mathrm{K}41K.
can be tuned using an external magnetic field. When the energy of the quasi-bound state is magnetically tuned into degeneracy with the energy of the free atomic pair, a resonant scattering process occurs in which the s-wave scattering length diverges and both elastic and inelastic collision cross sections are dramatically enhanced. When the collision involves two distinct atoms, the underlying molecular states can possess an electric dipole moment. In this case, the application of an external electric field can couple the bound molecular states mixing their orbital character and leading to level repulsion which breaks the degeneracy for dierent orbital angular momentum projections. The result is that the electric field shifts the positions of intrinsic magnetic Feshbach resonances, generates copies of resonances previously restricted to a particular partial-wave collision to other partial-wave channels, and splits Feshbach resonances into multiple resonances for states of nonzero angular momenta. This latter phenomenon oers a way to produce and tune an anisotropic interaction in atomic mixtures and to produce p-wave molecules of particular orbital angular momenta projections (1). In this talk, we discuss recent theoretical work and experimental progress on the realization and study of these phenomena associated with electric field dressing of magnetically tunable Feshbach resonances.
We report on the creation and characterization of heteronuclear 40K87Rb^{40}\text{K}^{87}\text{R}\text{b}40K87Rb Feshbach molecules in an optical dipole trap. Starting from an ultracold gas mixture of 40K^{40}\text{K}40K and 87Rb^{87}\text{R}\text{b}87Rb atoms, we create as many as 25 000 molecules at 300 nK by rf association. Optimizing the association process, we achieve a conversion efficiency of 25%. We measure the temperature dependence of the rf association process and find good agreement with a phenomenological model that has previously been applied to Feshbach molecule creation by slow magnetic-field sweeps. We also present a measurement of the binding energy of the heteronuclear molecules in the vicinity of the Feshbach resonance and provide evidence for Feshbach molecules as deeply bound as 26 MHz.
We study properties of two different atoms at a single optical lattice site at a heteronuclear atomic Feshbach resonance. We calculate the energy spectrum, the efficiency of rf association, and the lifetime as a function of magnetic field and compare the results with the experimental data obtained for 40K^{40}\text{K}40K and 87Rb^{87}\text{R}\text{b}87Rb [C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006)]. We treat the interaction in terms of a regularized $\ensuremath{\delta}$ function pseudopotential and consider the general case of particles with different trap frequencies, where the usual approach of separating center-of-mass and relative motion fails. We develop an exact diagonalization approach to the coupling between center-of-mass and relative motion and numerically determine the spectrum of the system. At the same time, our approach allows us to treat the anharmonicity of the lattice potential exactly. Within the pseudopotential model, the center of the Feshbach resonance can be precisely determined from the experimental data.
We present a theoretical model for formation of molecules in an optical lattice well where a resonant coupling of atomic and molecular states is provided by small oscillations of a magnetic field in the vicinity of a Feshbach resonance. As opposed to an adiabatic sweep over the full resonance, this provides a coherent coupling with a frequency that can be tuned to meet resonance conditions in the system. The effective Rabi frequencies for this coupling are calculated and simulations show perfect Rabi oscillations. Robust production of molecules with an adiabatic sweep of the modulation frequency is demonstrated. For very large oscillation amplitudes, the Rabi oscillations are distorted but still effective and fast association is possible.