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arXiv:cond-mat/0507219 · Physical Review Letters

Interaction-Driven Dynamics of K 40 − Rb 87 Fermion-Boson Gas Mixtures in the Large-Particle-Number Limit

C. Ospelkaus, Silke Ospelkaus, K. Sengstock, Kai Bongs

Published Jan 18, 2006• 153 citations
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Abstract

We have studied effects of interspecies attraction in a Fermi-Bose mixture over a large regime of particle numbers in the $^{40}\mathrm{K}\mathrm{\text{\ensuremath{-}}}^{87}\mathrm{Rb}$ system. We report on the observation of a mean-field driven collapse at critical particle numbers of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $^{87}\mathrm{Rb}$ atoms in the condensate and $7.5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ $^{40}\mathrm{K}$ atoms consistent with mean-field theory for a scattering length of ${a}_{\mathrm{FB}}=\ensuremath{-}284{a}_{0}$. For large overcritical particle numbers, we see evidence for revivals of the collapse. Part of our detailed study of the decay dynamics and mechanisms is a measurement of the ($^{87}\mathrm{Rb}\mathrm{\text{\ensuremath{-}}}^{87}\mathrm{Rb}\mathrm{\text{\ensuremath{-}}}^{40}\mathrm{K}$) three-body loss coefficient ${K}_{3}=(2.8\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}28}\text{ }\text{ }{\mathrm{cm}}^{6}/\mathrm{s}$, which is an important parameter for dynamical studies of the system.

DOI
10.1103/physrevlett.96.020401

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We present experimental investigations on the mutual influence of fermionic 40K and bosonic 87Rb atoms during the various trapping and cooling stages needed to reach quantum degeneracy of the sample. In particular we present particle number optimization strategies, which have led to large 40K–87Rb mixtures in the quantum degenerate regime. In fact the achievable particle numbers are only limited by a collapse due to an attractive overall mean-field interaction for the mixture. We discuss the influence of dynamical effects on the collapse parameters and find our critical particle numbers consistent with predictions based on recent Feshbach resonance measurements. We also investigate loss mechanisms of the mixture where we have identified three-body K–Rb–Rb losses as the dominant loss process and have measured the loss coefficient to be .
Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present experimental data on the collapse of high-density 85{}^{85}85Rb condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the 85{}^{85}85Rb three-body loss coefficient K3{K}_{3}K3​ at small positive and negative scattering lengths.
This work is inspired by recent experimental observations in ultracold atomic Bose-Fermi mixtures [DeSalvo et al., Nature 568 (2019)]. These experiments reveal the emergence of an attractive fermion-mediated interaction between bosons, as well as a stability-instability transition. We give the first mathematical demonstration of this transition by studying the low-energy spectrum of a many-body interspecies Hamiltonian. More precisely, we show the convergence of its eigenvalues towards those of an effective Bose Hamiltonian, which includes fermion-mediated effects. Applying this result to a model with short-range potentials, we derive a stability-instability transition in the bosonic subsystem, driven by the Bose-Fermi coupling strength ggg. For small ∣g∣|g|∣g∣, the bosons form a stable Bose-Einstein condensate with the energy per particle uniformly bounded from below. For large ∣g∣|g|∣g∣, the energy per particle is no longer uniformly bounded from below, signaling the collapse of the condensate.
A quantum degenerate, dilute gas mixture of bosonic and fermionic atoms was produced using 87Rb^{87}\mathrm{Rb}87Rb and 40K^{40}\mathrm{K}40K. The onset of degeneracy was confirmed by observing the spatial distribution of the gases after time-of-flight expansion. Furthermore, the magnitude of the interspecies scattering length between the doubly spin-polarized states of 87Rb^{87}\mathrm{Rb}87Rb and 40K^{40}\mathrm{K}40K, $\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}$, was determined from cross-dimensional thermal relaxation. The uncertainty in this collision measurement was greatly reduced by taking the ratio of interspecies and intraspecies relaxation rates, yielding $\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}=250\ifmmode\pm\else\textpm\fi{}30\phantom{\rule{0.3em}{0ex}}{a}_{0}$, which is a lower value than what was reported in [M. Modugno et al., Phys. Rev. A 68, 043626 (2003)]. Using the value for $\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}$ reported here, current T=0T=0T=0 theory would predict a threshold for mechanical instability that is inconsistent with the experimentally observed onset for sudden loss of fermions in [G. Modugno et al., Science 297, 2240 (2002)].