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Physical Review A

Feshbach resonances in cold collisions of potassium atoms

Arturo Bambini, S. Geltman

Published Jun 4, 2002• 7 citations
Publisher

Abstract

In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state $F=1, {\ensuremath{\mu}}_{F}=\ensuremath{-}1$ of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole ${C}_{6}$ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species ${}^{39}\mathrm{K}$ or ${}^{41}\mathrm{K}.$ Our results demonstrate that there is a range of ${C}_{6}$ values for which the collision of two ${}^{39}\mathrm{K}$ atoms displays a single resonance, while for other values of ${C}_{6}$ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two ${}^{41}\mathrm{K}$ atoms for almost all values of the dispersion coefficient ${C}_{6}$ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two ${}^{41}\mathrm{K}$ atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.

DOI
10.1103/physreva.65.062704

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Physical Review Letters•Dec 7, 1998•499 citations
In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state F=1,\ensuremathμF=\ensuremath−1F=1, {\ensuremath{\mu}}_{F}=\ensuremath{-}1F=1,\ensuremathμF​=\ensuremath−1 of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole C6{C}_{6}C6​ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species 39K{}^{39}\mathrm{K}39K or 41K.{}^{41}\mathrm{K}.41K. Our results demonstrate that there is a range of C6{C}_{6}C6​ values for which the collision of two 39K{}^{39}\mathrm{K}39K atoms displays a single resonance, while for other values of C6{C}_{6}C6​ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two 41K{}^{41}\mathrm{K}41K atoms for almost all values of the dispersion coefficient C6{C}_{6}C6​ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two 41K{}^{41}\mathrm{K}41K atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.
We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes 39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K. The sss-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the K2{\mathrm{K}}_{2}K2​ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.
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.
We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of 40K87Rb+87Rb^{40}\mathrm{K}^{87}\mathrm{Rb}+^{87}\mathrm{Rb}40K87Rb+87Rb. We show multiple types of resonance due to long-range states with rotational and/or hyperfine excitation, and consider the likelihood of them existing at low to moderate magnetic fields.
We explore the anisotropic nature of Feshbach resonances in the collision between ultracold highly magnetic submerged-shell dysprosium atoms in their energetically lowest magnetic sublevel, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where broadest (strongest) Feshbach resonances are hyperfine induced and due to rotationless bound states. Our first-principle coupled-channel calculation of the collisions between these spin-polarized bosonic dysprosium atoms reveals a strong interplay between the anisotropies in the dispersion and magnetic dipole-dipole interaction. The former anisotropy is absent in alkali-metal and chromium collisions. We show that both types of anisotropy significantly affect the Feshbach spectrum as a function of an external magnetic field. Effects of the electrostatic quadrupole-quadrupole interaction are small. Over a 20 mT magnetic field range, we predict about 10 Feshbach resonances and show that the resonance locations depend on the dysprosium isotope.
We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of 40^{40}40K87^{87}87Rb+87^{87}87Rb. We show multiple types of resonance due to long-range states with rotational and/or hyperfine excitation, and consider the likelihood of them existing at low to moderate magnetic fields.
A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2$ state of 85Rb{}^{85}\mathrm{Rb}85Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 104{0}^{4}04, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient C6{C}_{6}C6​, the singlet scattering length aS{a}_{S}aS​, and the triplet scattering length aT{a}_{T}aT​.