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arXiv:1911.05749 · Physical Review A

Three-body losses of a polarized Fermi gas near a p -wave Feshbach resonance in effective field theory

Marcel Schmidt, H.‐W. Hammer, Lucas Platter

Published Jun 1, 2020• 24 citations
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Abstract

We study three-body recombination of fully spin-polarized $^{6}\mathrm{Li}$ atoms that are interacting resonantly in relative $p$ waves. Motivated by a recent experiment, we focus on negative scattering volumes where three atoms recombine into a deep dimer and another atom. We calculate the three-body recombination rate using a Faddeev equation derived from effective field theory. In particular, we study the magnetic field and temperature dependences of the loss rate and use the recombination data to determine the effective range of the $p$-wave atom-atom interaction. We also predict the existence of a shallow three-body resonance state that manifests itself as a prominent feature in the energy-dependent three-body recombination rate.

DOI
10.1103/physreva.101.062702

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We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p-wave channel via a Feshbach resonance represented by a two-channel model. The rate of inelastic processes due to recombination to deeply bound dimers is then estimated from the three-body solution using a simple prescription. We obtain numerical and analytical predictions for most of the experimentally relevant quantities that can be extracted from the three-body solution: the existence of weakly bound trimers and their lifetime, the low-energy elastic and inelastic scattering properties of an atom on a weakly bound dimer (including the atom-dimer scattering length and scattering volume), and the recombination rates for three colliding atoms towards weakly bound and deeply bound dimers. The effect of "background" non-resonant interactions in the open channel of the two-channel model is also calculated and allows to determine which three-body quantities are `universal' and which on the contrary depend on the details of the model.
We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p\mathit{p}p-wave channel via a Feshbach resonance represented by a two-channel model. The rate of inelastic processes due to recombination to deeply bound dimers is then estimated from the three-body solution using a simple prescription. We obtain numerical and analytical predictions for most of the experimentally relevant quantities that can be extracted from the three-body solution: the existence of weakly bound trimers and their lifetime, the low-energy elastic and inelastic scattering properties of an atom on a weakly bound dimer (including the atom-dimer scattering length and scattering volume), and the recombination rates for three colliding atoms towards weakly bound and deeply bound dimers. The effect of ``background'' nonresonant interactions in the open channel of the two-channel model is also calculated and allows one to determine which three-body quantities are ``universal'' and which on the contrary depend on the details of the model.
We experimentally measure and theoretically analyze the three-atom recombination rate, L_{3}, around a narrow s-wave magnetic Feshbach resonance of ^{6}Li-^{6}Li at 543.3 G. By examining both the magnetic field dependence and, especially, the temperature dependence of L_{3} over a wide range of temperatures from a few μK to above 200 μK, we show that three-atom recombination through a narrow resonance follows a universal behavior determined by the long-range van der Waals potential and can be described by a set of rate equations in which three-body recombination proceeds via successive pairwise interactions. We expect the underlying physical picture to be applicable not only to narrow s wave resonances, but also to resonances in nonzero partial waves, and not only at ultracold temperatures, but also at much higher temperatures.
We study the three-body recombination of identical fermionic atoms. Using a zero-range model for the ppp-wave interaction, we show that the rate constant of three-body recombination into weakly bound ppp-wave dimers can be written as ${\ensuremath{\alpha}}_{\mathrm{rec}}\ensuremath{\propto}{v}^{5/2}{R}^{1/2}{k}_{T}^{4}(1+C{k}_{T}^{2}{l}_{d}^{2})$ for large and positive scattering volume vvv. Here RRR is the ppp-wave effective range, kT2{k}_{T}^{2}kT2​ gives the average thermal kinetic energy of the colliding atoms, and ld{l}_{d}ld​ is the size of the ppp-wave dimer. The leading term is different from the usually stated v8/3{v}^{8/3}v8/3-scaling law, but is consistent with an earlier two-channel calculation. For the subleading term, we compute the constant CCC by solving the relevant three-body problem perturbatively when the parameter $\ensuremath{\gamma}\ensuremath{\equiv}R/{v}^{1/3}$ is small. The additional CkT2ld2C{k}_{T}^{2}{l}_{d}^{2}CkT2​ld2​ term provides important corrections for the temperature and interaction dependence of ${\ensuremath{\alpha}}_{\mathrm{rec}}$, especially close to resonance when kTld{k}_{T}{l}_{d}kT​ld​ is relatively large.
We predict the resonance-enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate close to 1007G1007\phantom{\rule{0.3em}{0ex}}\mathrm{G}1007G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum, causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.
We describe three-body collisions close to a Feshbach resonance by taking into account two-body scattering processes involving both the open and the closed channels. We extract the atom-dimer scattering length and the three-body recombination rate, predicting the existence at negative scattering length of a sharp minimum in the recombination losses due to the presence of a shallow bound level. We obtain very good agreement with the experimental results in atomic 133Cs^{133}\mathrm{Cs}133Cs of Kraemer et al. [Nature (London) 440, 315 (2006)], and predict the position of Efimov resonances in a gas of 39K^{39}\mathrm{K}39K atoms.