Determination of the fermion pair size in a resonantly interacting superfluid

Abstract

Fermionic superfluidity requires the formation of pairs. The actual size of these fermion pairs varies by orders of magnitude from the femtometer scale in neutron stars and nuclei to the micrometer range in conventional superconductors. Many properties of the superfluid depend on the pair size relative to the interparticle spacing. This is expressed in BCS-BEC crossover theories [1,2,3], describing the crossover from a Bardeen-Cooper-Schrieffer (BCS) type superfluid of loosely bound and large Cooper pairs to Bose-Einstein condensation (BEC) of tightly bound molecules. Such a crossover superfluid has been realized in ultracold atomic gases where high temperature superfluidity has been observed [4,5]. The microscopic properties of the fermion pairs can be probed with radiofrequency (rf) spectroscopy. Previous work [6,7,8] was difficult to interpret due to strong and not well understood final state interactions. Here we realize a new superfluid spin mixture where such interactions have negligible influence and present fermion-pair dissociation spectra that reveal the underlying pairing correlations. This allows us to determine the spectroscopic pair size in the resonantly interacting gas to be 2.6(2)/kF (kF is the Fermi wave number). The fermions pairs are therefore smaller than the interparticle spacing and the smallest pairs observed in fermionic superfluids. This finding highlights the importance of small fermion pairs for superfluidity at high critical temperatures [9]. We have also identified transitions from fermion pairs into bound molecular states and into many-body bound states in the case of strong final state interactions.The properties of pairs are revealed in a dissociation spectrum, where pair dissociation is monitored as a function of the applied energy E. The spectrum has a sharp onset at the pair's binding energy E b , where the fragments have zero kinetic energy, and then spreads out to higher energy. Since a rf photon has negligible momentum, the allowed momenta for the fragments reflect the Fourier transform Φ(k) of the pair wavefunction φ(r), which has a width on the order of 1/ξ where ξ is the pair size. Thus the pair size can be estimated from the spectral line width E w as ξ 2 ∼ 2 /mE w (m is the mass of the particles and is Planck's constant h divided by 2π).The conceptually simplest pairs in the BCS-BEC crossover are the weakly bound molecules in the BEC limit, which are described by a spatial wavefunction φ m (r) ∝ e −r/b /r with a binding energy E b = 2 /mb 2 . When the molecules are dissociated into noninteracting free particles, the spectral response is I m ∝ √ E − E b /E 2 , showing a highly asymmetric line shape with a steep rise at the molecular binding energy E b and a long "tail" to higher energies (Fig. 1a) [5,10]. This general behavior of the dissociation spectrum holds also in the BCS limit where pairing is a many-body effect [5,11]. The rf dissociation process discussed below, in the limit of negligible final state interactions, can be considered as breaking a Cooper pair into...

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