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arXiv:cond-mat/9911132 · Physical Review A

Cooper pairing in ultracold 40K using Feshbach resonances

John L. Bohn

Published Apr 17, 2000• 78 citations
arXivHTMLPDF

Abstract

We point out that the fermionic isotope ${}^{40}\mathrm{K}$ is a likely candidate for the formation of Cooper pairs in an ultracold atomic gas. Specifically, in an optical trap that simultaneously traps the spin states $|9/2,\ensuremath{-}9/2〉$ and $|9/2,\ensuremath{-}7/2〉,$ there exists a broad magnetic-field Feshbach resonance at ${B=196}_{\ensuremath{-}21}^{+9}$ G that can provide the required strong attractive interaction between atoms. An additional resonance, at ${B=191}_{10}^{+5}$ G, could generate p-wave pairing between identical $|9/2,\ensuremath{-}7/2〉$ atoms. A Cooper-paired degenerate Fermi gas could thus be constructed with existing ultracold-atom technology.

DOI
10.1103/physreva.61.053409

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We point out that the fermionic isotope 40K{}^{40}\mathrm{K}40K is a likely candidate for the formation of Cooper pairs in an ultracold atomic gas. Specifically, in an optical trap that simultaneously traps the spin states ∣9/2,\ensuremath−9/2〉|9/2,\ensuremath{-}9/2〉∣9/2,\ensuremath−9/2〉 and ∣9/2,\ensuremath−7/2〉,|9/2,\ensuremath{-}7/2〉,∣9/2,\ensuremath−7/2〉, there exists a broad magnetic-field Feshbach resonance at B=196\ensuremath−21+9{B=196}_{\ensuremath{-}21}^{+9}B=196\ensuremath−21+9​ G that can provide the required strong attractive interaction between atoms. An additional resonance, at B=19110+5{B=191}_{10}^{+5}B=19110+5​ G, could generate p-wave pairing between identical ∣9/2,\ensuremath−7/2〉|9/2,\ensuremath{-}7/2〉∣9/2,\ensuremath−7/2〉 atoms. A Cooper-paired degenerate Fermi gas could thus be constructed with existing ultracold-atom technology.
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.
The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the 39K{}^{39}\mathrm{K}39K triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the 41K{}^{41}\mathrm{K}41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope 40K{}^{40}\mathrm{K}40K is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.
After the experimental realization of Bose-Einstein condensation in dilute gases of alkali atoms, experimentalists started to trap the fermionic isotopes. The degenerate state for fermions was reported in 1999. The main objective of these experiments is to obtain superfluidity of fermionic gases. When there are attractive interactions between the fermions, the Fermi sea becomes unstable with respect to the formation of atomic Cooper pairs and the system becomes a superfluid. It turns out that the existing experimental cooling techniques allow minimum temperatures for fermions of the order of the Fermi temperature. Using Feshbach resonances induced by magnetic fields enhances the effective interactions between the atoms leading to superfluid transition temperatures of the order of the Fermi energy. This is a completely new regime of fermionic superfluidity far from the BCS superconductors, He and even high- superconductors. The achievement of superfluidity on gases
The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the N\'eel antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional ppp-wave interactions. In this strong-coupling limit, the 1D trapped Fermi gas exhibits an effective Heisenberg spin XXZXXZXXZ chain in the anisotropic ppp-wave scattering channels. For a particular ppp-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the antiferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of 40K^{40}\mathrm{K}40K atoms with very close sss-wave and ppp-wave Feshbach resonances.
We predict the presence of several magnetic Feshbach resonances in selected Zeeman sublevels of the isotopic pairs $^{40}\mathrm{K}\mathrm{\text{\ensuremath{-}}}^{87}\mathrm{R}\mathrm{b}$ and $^{41}\mathrm{K}\mathrm{\text{\ensuremath{-}}}^{87}\mathrm{R}\mathrm{b}$ at magnetic fields up to 103 G{10}^{3}\text{ }\mathrm{G}103 G. Positions and widths are determined combining a new measurement of the $^{40}\mathrm{K}\mathrm{\text{\ensuremath{-}}}^{87}\mathrm{R}\mathrm{b}$ inelastic cross section with recent experimental results on both isotopes. The possibility of driving a K-Rb mixture from the weak to the strong interacting regime tuning the applied field should allow one to achieve the optimal conditions for boson-induced Cooper pairing in a multicomponent $^{40}\mathrm{K}\mathrm{\text{\ensuremath{-}}}^{87}\mathrm{R}\mathrm{b}$ atomic gas and for the production of ultracold polar molecules.
Abstract We discuss the possible signatures of superfluidity induced by the Feshbach resonance in the ultracold gas of fermion atoms. Optically or magnetically trapped atoms such as 6Li or 40K are used in two hyperfine states where part of them is converted into the diatomic molecules. These fermion and boson entities get coupled in a presence of the external magnetic field. Eventually, at critical Tc, they simultaneously undergo transition to the superfluid state. Approaching this transition from above there appear various signatures manifesting a gradually emerging order parameter, but yet the long range coherence is not established due to the strong quantum fluctuations. Fermion atoms are characterized by the gapped excitation spectrum (pseudogap) up to temperature Tp (larger than Tc) while boson molecules exhibit collective features such as first sound showing up above a certain critical momentum q.crit (T) Upon lowering temperature to Tc this critical value shifts to zero and hence there appears the Goldstone mode signaling the symmetry broken superfluid state. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)