Three-Body Recombination Rates Near a Feshbach Resonance within a Two-Channel Contact Interaction Model

Abstract

We calculate the three-body recombination rate into a shallow dimer in a gas of cold bosonic atoms near a Feshbach resonance using a two-channel contact interaction model. The two-channel model naturally describes the variation of the scattering length through the Feshbach resonance and has a finite effective range. We confront the theory with the available experimental data and show that the two-channel model is able to quantitatively describe the existing data. The finite effective range leads to a reduction of the scaling factor between the recombination minima from the universal value of 22.7. The reduction is larger for larger effective ranges or, correspondingly, for narrower Feshbach resonances. IntroductionQuantum-mechanical three-body systems of identical bosons exhibit universal features when the two-body scattering length becomes exceedingly large. In this limitcalled the universal regime-the properties of the system depend largely on the scattering length alone and can be described by a universal one-channel zero-range model [1,2].The one-channel zero-range model predicts, in particular, that in the limit of large positive scattering lengthwith a shallow dimer-the low-energy recombination rate of three identical bosons into a shallow dimer exhibits, as function of the scattering length, a geometric scaling: characteristic periodic minima in logarithmic scale with the period equal to 22.7.

Finite-range effects in energies and recombination rates of three identical bosons

“…This model has background scattering lengths in open and closed channels that we denote a open and a closed respectively. The full scattering length and effective range parameters of this model are (all details of this model are described in our previous work [36])…”

Few-Body Physics of Ultracold Atoms and Molecules With Long-Range Interactions

“…A relatively straightforward way to do this is to write the three-body wave function Ψ as a superposition of open-and closed-channel components ψ open and ψ close , and match Ψ separately in the open-and closed-channel zero-range boundary conditions. [148][149][150] A more rigorous way is to build the internal degrees of freedom -such as spins -directly to individual atoms, as the multichannel zerorange model by. 151 Thanks to their simplicity, the multichannel zero-range models have recently been applied to fit three-body recombination losses in ultracold experiments 150 and to study spinor condensates.…”

“…[148][149][150] A more rigorous way is to build the internal degrees of freedom -such as spins -directly to individual atoms, as the multichannel zerorange model by. 151 Thanks to their simplicity, the multichannel zero-range models have recently been applied to fit three-body recombination losses in ultracold experiments 150 and to study spinor condensates. 152 It should be noted, however, that the zero-range boundary condition for the closed-channel wave function implies a weakly-bound two-body Feshbach state in the closed channel, which is rarely the case for realistic systems.…”

Analytic Expression for Three-Body Recombination Rates into Deep Dimers

“…The three-body system with zero-range potentials must be regularized [11] at some short-range scale r. The regularized wave-function at ρ |a 1 | thus takes the form…”