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Science

Collapse of a Degenerate Fermi Gas

Giovanni Carlo Modugno, G. Roati, Francesco Riboli, Francesca Ferlaino, Robert J. Brecha, M. Inguscio

Published Sep 27, 2002• 346 citations
Publisher

Abstract

A degenerate gas of identical fermions is brought to collapse by the interaction with a Bose-Einstein condensate. We used an atomic mixture of fermionic potassium-40 and bosonic rubidium-87, in which the strong interspecies attraction leads to an instability above a critical number of particles. The observed phenomenon suggests a direction for manipulating fermion-fermion interactions on the route to superfluidity.

DOI
10.1126/science.1077386

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A degenerate gas of identical fermions is brought to collapse by the interaction with a Bose-Einstein condensate. We used an atomic mixture of fermionic potassium-40 and bosonic rubidium-87, in which the strong interspecies attraction leads to an instability above a critical number of particles. The observed phenomenon suggests a direction for manipulating fermion-fermion interactions on the route to superfluidity.
Recent experiments performed with fermionic /sup 6/Li and /sup 40/K atoms, which possess both Feshbach resonances at convenient magnetic fields are discussed. When /sup 40/K is mixed with a Bose-Einstein condensate of /sup 87/Rb, for sufficient atom numbers of both species, a collapse of the Fermi gas is observed. This is the result of the strong interspecies attractive interaction which overcomes the Fermi pressure in the quantum degenerate regime. As for the case of phonon-induced interaction between electrons in superconductors, it is predicted that the boson-fermion attractive interaction favors Cooper pairing of fermions when prepared in a mixture of two states.
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.
We report on the formation of a stable quantum degenerate mixture of fermionic ^{6}Li and bosonic ^{133}Cs in an optical trap by sympathetic cooling near an interspecies Feshbach resonance. New regimes of quantum degenerate Bose-Fermi mixtures are identified. With moderate attractive interspecies interactions, we show that a degenerate Fermi gas of Li can be fully confined in a Cs Bose-Einstein condensate without external potentials. For stronger attraction where mean-field collapse is expected, no such instability is observed. Potential mechanisms to explain this phenomenon are discussed.
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 $1.2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ 87Rb^{87}\mathrm{Rb}87Rb atoms in the condensate and $7.5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ 40K^{40}\mathrm{K}40K 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.
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 .