Determination of thes-Wave Scattering Length of Chromium

Abstract

We have measured the deca-triplet s-wave scattering length of the bosonic chromium isotopes 52 Cr and 50 Cr. From the time constants for cross-dimensional thermalization in atomic samples we have determined the magnitudes |a( 52 Cr)| = (170 ± 39) a0 and |a( 50 Cr)| = (40 ± 15) a0, where a0 = 0.053 nm. By measuring the rethermalization rate of 52 Cr over a wide temperature range and comparing the temperature dependence with the effective-range theory and single-channel calculations, we have obtained strong evidence that the sign of a( Cs [5], Feshbach resonances have been used to tune the scattering length into the right range for achieving BEC. Therefore, a careful measurement of the scattering length is a first requirement before a strategy for the condensation of a new atomic species can be devised.However, elastic collisions are not only essential for evaporative cooling of an atomic gas but they also determine the interaction in a quantum degenerate gas. The presence of this interaction is also responsible for many of the fascinating features of BECs like superfluid behavior or the existence of phonon-like excitations [1]. In the case of chromium, the magnitude of the scattering length will also determine how significant the effects of the anisotropic dipole-dipole interaction will be [6].Up to now, only the s-wave scattering lengths for alkali atoms, hydrogen and metastable helium have been measured. The most precise methods are probably photoassociation spectroscopy [7,8] and Raman spectroscopy [9] between vibrational levels of the electronic molecular ground state. Another possibility is Feshbach resonance spectroscopy [10,11,12] where the position and magnetic field dependence of several Feshbach resonances is determined.For chromium, no molecular spectroscopy data are available for the deca-triplet state which -neglecting the spin-spin interaction -corresponds to the collisional channel for elastic collisions in samples prepared in spinstretched (i.e. |m J | = J) states. Due to the complicated electronic structure with six unpaired outer-shell electrons, accurate ab initio calculations of the molecular potentials are also not available. Fortunately nearthreshold collisions are not sensitive to the details of the short-range interaction potential. They are to a large extent determined by the s-wave scattering length a and by the long-range dispersion interaction, characterized by the leading van der Waals coefficient C 6 .In this paper, we report on a measurement of the swave scattering length of bosonic chromium atoms, spin polarized in the weak-field seeking J = m J = 3 state, from cross-dimensional relaxation in a magnetic trap. By recording the relaxation of an anisotropic temperature distribution in an atomic cloud towards equilibrium, we obtain a relaxation time constant which is proportional to the effective scattering cross-section through the atomic density. This method has been first used by Monroe et al. [13] for 133 Cs and has since been employed to determine the ultra-cold scattering prop...

The inhomogeneous extended Bose‐Hubbard model: A mean‐field theory

“…Here D is the dipole moment, a s is the s-wave scattering constant, and m is the mass. The s-wave scattering constant of chromium is |a( 52 Cr)| = (170 ± 39)a 0 and |a( 50 Cr)| = (40 ± 15)a 0 , where a 0 = 0.053 nm [27]. We hope that our work will stimulate experiments designed to explore SF, MI, DW, and SS shells in dipolarcondensate systems [16,17].…”

Vortex competition in a rotating two-component dipolar Bose-Einstein condensate

“…Since the strength of a DDI is fixed, the value of dimensionless g measures the relative strength of the contact interactions to the DDIs. Experimentally the s-wave scattering length a s can be tuned between 0 ∼ 100a B [36] via Feshbach resonance [15][16][17][18] with a B the Bohr radius, so g can be estimated to be tuned from 0 to 0.1 √ λ. In addition, to guarantee both the convergence and efficiency of iteration of the GP equations, dτ is chosen to be between 0.01 and 0.1 in numerical calculations.…”

Collisional decoherence of internal-state superpositions in a trapped ultracold gas

“…The scattering lengths α ν for ultracold atoms are usually found from thermalization measurements [38][39][40], which yield results with significant error bars. Decoherence rates can be measured sensitively by observing the damping rate of coherent oscillations [27,28,41].…”