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arXiv:cond-mat/0405419 · Physical Review A

Measurement of the interaction strength in a Bose-Fermi mixture with Rb 87 and K 40

J. Goldwin, S. Inouye, M. L. Olsen, Bonna K. Newman, Brett D DePaola, D. S. Jin

Published Aug 11, 2004• 110 citations
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Abstract

A quantum degenerate, dilute gas mixture of bosonic and fermionic atoms was produced using $^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}$. 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 $^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}$, $\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}$, 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 $T=0$ 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)].

DOI
10.1103/physreva.70.021601

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Quantum Degeneracy and Interactions in the 87Rb -40K Bose-Fermi Mixture

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The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Goldwin, Jonathan Michael (Ph.D., Physics) Quantum Degeneracy and Interactions in the 87Rb-40K Bose-Fermi Mixture Thesis directed by Associate Professor Deborah S. Jin An apparatus for producing dilute-gas quantum degenerate Bose-Fermi mix-tures is presented. The experiment uses forced evaporative cooling to obtain a nearly pure 87Rb Bose-Einstein condensate immersed in a gas of sympathetically cooled 40K atoms at 0.2 times the Fermi temperature. The design, construction, and operation of the apparatus are described in detail. The onset of quantum degeneracy is characterized and contrasted between species, revealing the effects of quantum statistics on the bulk properties of the gases. The apparatus is then used to study the interactions between species in ultracold non-degenerate mixtures. Measurements of rethermalization rates are used to determine the elastic scattering cross-section between species. From these measurements the magnitude of the inter-species s-wave scattering length is de-termined. The scattering length is central to characterizing a variety of static and dynamic properties of the mixture. The apparatus is additionally used to study for the first time Feshbach resonances in the collisions between 87Rb and 40K atoms. These resonances present a means for experimentally tuning the scattering length between species to any desired value. Prospects for future experiments exploiting this real-time control over the interactions are discussed. iv

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Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.

arXiv:1910.01341•Physical Review Letters•Apr 22, 2020•58 citations
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∣aRbK\ensuremath∣\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}\ensuremath∣aRbK​\ensuremath∣, 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∣aRbK\ensuremath∣=250\ifmmode±\else\textpm\fi30a0\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}=250\ifmmode\pm\else\textpm\fi{}30\phantom{\rule{0.3em}{0ex}}{a}_{0}\ensuremath∣aRbK​\ensuremath∣=250\ifmmode±\else\textpm\fi30a0​, 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∣aRbK\ensuremath∣\ensuremath{\mid}{a}_{\mathrm{RbK}}\ensuremath{\mid}\ensuremath∣aRbK​\ensuremath∣ 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)].
The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Goldwin, Jonathan Michael (Ph.D., Physics) Quantum Degeneracy and Interactions in the 87Rb-40K Bose-Fermi Mixture Thesis directed by Associate Professor Deborah S. Jin An apparatus for producing dilute-gas quantum degenerate Bose-Fermi mix-tures is presented. The experiment uses forced evaporative cooling to obtain a nearly pure 87Rb Bose-Einstein condensate immersed in a gas of sympathetically cooled 40K atoms at 0.2 times the Fermi temperature. The design, construction, and operation of the apparatus are described in detail. The onset of quantum degeneracy is characterized and contrasted between species, revealing the effects of quantum statistics on the bulk properties of the gases. The apparatus is then used to study the interactions between species in ultracold non-degenerate mixtures. Measurements of rethermalization rates are used to determine the elastic scattering cross-section between species. From these measurements the magnitude of the inter-species s-wave scattering length is de-termined. The scattering length is central to characterizing a variety of static and dynamic properties of the mixture. The apparatus is additionally used to study for the first time Feshbach resonances in the collisions between 87Rb and 40K atoms. These resonances present a means for experimentally tuning the scattering length between species to any desired value. Prospects for future experiments exploiting this real-time control over the interactions are discussed. iv
We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length aF{a}_{F}aF​. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As 1∕aF1∕{a}_{F}1∕aF​ is increased from a negative value to the Feshbach resonance (1∕aF=0)(1∕{a}_{F}=0)(1∕aF​=0), the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance (1∕aF>0)(1∕{a}_{F}>0)(1∕aF​>0), pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when 1∕aF1∕{a}_{F}1∕aF​ exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.
We determine the interspecies sss-wave triplet scattering length a3{a}_{3}a3​ for all K-Rb isotopic mixtures by measuring the elastic cross section for collisions between 41K^{\mathrm{41}}\mathrm{K}41K and 87Rb^{87}\mathrm{R}\mathrm{b}87Rb in different temperature regimes. The positive value ${a}_{3}=+{163}_{\ensuremath{-}12}^{+57}{a}_{0}$ ensures the stability against collapse of binary $^{41}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates. For the fermion-boson mixture $^{40}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$, we obtain a large and negative scattering length which implies an efficient sympathetic cooling of the fermionic species down to the degenerate regime.
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.
Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.