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Physical Review A

Three fully polarized fermions close to a p -wave Feshbach resonance

M. Jona-Lasinio, Ludovic Pricoupenko, Yvan Castin

Published Apr 9, 2008• 102 citations
Publisher

Abstract

We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the $\mathit{p}$-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.

DOI
10.1103/physreva.77.043611

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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\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 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 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 study three-body recombination of fully spin-polarized 6Li^{6}\mathrm{Li}6Li atoms that are interacting resonantly in relative ppp 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 ppp-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.
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.
We investigate the three-body properties of two identical ↑ fermions and one distinguishable ↓ atom interacting in a strongly confined two-dimensional geometry.We compute exactly the atom-dimer scattering properties and the three-body recombination rate as a function of collision energy and mass ratio m ↑ /m ↓ .We find that the recombination rate for fermions is strongly energy dependent, with significant contributions from higher partial waves at low energies.For m ↑ m ↓ , the s-wave atom-dimer scattering below threshold is completely described by the scattering length.Furthermore, we examine the ↑↑↓ bound states (trimers) appearing at large m ↑ /m ↓ and find that the energy spectrum for the deepest bound trimers resembles that of a hydrogen atom confined to two dimensions.
Hybrid atom-ion experiments have recently entered the few-partial wave regime in which magnetically tunable Feshbach resonances dominate the three-body loss dynamics. This necessitates a treatment of three-body recombination that can incorporate the role of the resonant dimer channel. Here, we develop a two-step Lindemann-type model for resonant atom-atom-ion three-body recombination that combines multichannel quantum-defect theory for the long-range polarization potential with a universal quantum-capture treatment of the inelastic atom-dimer step. We show that within our model, rate competition can lead to a peak in the three-body-recombination cross section of higher partial-wave channels at energies well below their corresponding centrifugal barrier. Investigating the resulting loss rates under numerically obtained non-thermal collision-energy distributions, we find that these effects survive the energy averaging and can be observed in state-of-the-art hybrid experimental setups. Our findings pave the way for a detailed characterization of atom-ion Feshbach resonances via the analysis of inelastic three-body-recombination processes.