Theory of rf-Spectroscopy of Strongly Interacting Fermions

Punk, Matthias; Zwerger, W.

doi:10.1103/physrevlett.99.170404

Cited by 123 publications

(135 citation statements)

References 21 publications

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“…We will show that such a Fermi liquid is perfectly consistent with the experiment of Ref. 19, and that the observed shift in the RF spectrum of the minority atoms is the result of large self-energy effects due to the Feshbach resonant scattering, as also emphasized in parallel recent studies [32,33,34]. Based on this we suggest that a far better test of the nature of the ground state is a measurement of the momentum distribution n 2 (k) of the minority atoms; in the following the label σ = 1, 2 denotes the majority and minority species, respectively.…”

Section: Introductionsupporting

confidence: 88%

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Radio-frequency spectroscopy of a strongly imbalanced Feshbach-resonant Fermi gas

et al. 2008

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A sufficiently large species imbalance (polarization) in a two-component Feshbach resonant Fermi gas is known to drive the system into its normal state. We show that the resulting stronglyinteracting state is a conventional Fermi liquid, that is, however, strongly renormalized by pairing fluctuations. Using a controlled 1/N expansion, we calculate the properties of this state with a particular emphasis on the atomic spectral function, the momentum distribution functions displaying the Migdal discontinuity, and the radio frequency (RF) spectrum. We discuss the latter in the light of the recent experiments of Schunck et al. (Science 316, 867 (2007)) on such a resonant Fermi gas, and show that the observations are consistent with a conventional, but strongly renormalized Fermi-liquid picture.

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Section: Introductionsupporting

confidence: 88%

“…The recent RF spectroscopy experiments on a strongly polarized Fermi gas [19,27], have rekindled theoretical studies of such a system with a focus on the unitarity regime [28,29,30] and its strong interactions in the normal state [31,32,33,34,35,36].…”

Section: Introductionmentioning

confidence: 99%

Radio-frequency spectroscopy of a strongly imbalanced Feshbach-resonant Fermi gas

et al. 2008

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“…Here a is the s-wave scattering length and we use a i (a f ) for the initial (a,b) (final (a,c)) interactions. As discussed in detail below, final state interactions severely affect the rf dissociation spectra when |k F a f | > 1 [13,14,15]. To overcome this problem, one has to change the interactions in the final state without changing those in the initial one.…”

Section: Figmentioning

confidence: 99%

Determination of the fermion pair size in a resonantly interacting superfluid

Schunck

Shin

Schirotzek

et al. 2008

Nature

124

158

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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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“…In most recent experiments on 6 Li the states involved are the three lowest energy hyperfine states |↑ = |1 , |↓ = |2 and |x = |3 , (E 1 < E 2 < E 3 ) though other combinations are possible [22]. The spectrum I(ν) measures, for a fixed probe intensity, the rate of population transfer from ↓ to x as a function of the detuning ν from the free-space resonance.In principle, moments of this spectrum can be calculated from the sum rule [11,12,13],, where v ij (r) is the interaction potential between atoms in states i and j, and ψ σ is an annihilation operator. As pointed out by Pethick and Stoof [23], extracting useful information from this result is problematic because this expectation value (which is closely related to the expectation value of the interaction energy) is not a low energy observable: different potentials which give rise to the same low energy scattering properties will give completely different values forν; hard spheres haveν = 0, while point interaction yield ν = ∞.…”

mentioning

confidence: 99%

“…We quantify our arguments by presenting a simplified calculation of the spectrum of a trapped two-component Fermi gas in the limit n ↓ /n ↑ → 0. Although we include final-state interactions [11,12,13,14,15,16,17,18,19] in our quantitative calculations, we emphasize that the bimodality is not a final-state effect. In the highly polarized limit, final state effects set the frequency scale for the spectral line but do not significantly change its shape or temperature dependence.…”

mentioning

confidence: 99%

Generic features of the spectrum of trapped polarized fermions

Mueller

2008

Phys. Rev. A

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We show that bimodal radio frequency spectra universally arise at intermediate temperatures in models of strongly interacting trapped Fermi gases. The bimodality is independent of superfluidity or pseudogap physics, depending only on the functional form of the equation of state -which is constrained by dimensional analysis at low temperatures and the virial expansion at high temperatures. In addition to these model independent results, we present a simple calculation of the radio frequency line-shape of a highly polarized Fermi gas which uses energetic considerations to include final state interactions. While this model only qualitatively captures the line-shapes observed in the experiments, it provides a conceptually clean and powerful technique for estimating the energy scales and how they vary with experimental parameters. Can spectroscopy be used to detect pairing in a gas of fermionic atoms? The paradigm for thinking about this question was set in 2003, when Greiner, Regal and Jin [1] presented an experimental study of the microwave spectrum of a two component gas of 40 K on the BEC side of resonance (where two potassium atoms are capable of forming weakly bound molecules). Their sample consisted of a noncondensed gas of diatomic molecules in chemical equilibrium with a gas of atoms. They found an easily interpreted bimodal spectrum: a sharp line came from the excitations of free atoms, and a broad peak from the dissociation of molecules. Later experiments on colder samples in different parameter ranges showed similar bimodality and were interpreted in similar ways [2,3]. In particular, when such a bimodal peak was seen by Chin, Bartensein, Altmeyer, Riedl, Jochim, Denschlag, and Grimm [2] on the BCS side of resonance, it was taken as a sign of Cooper pairing. This interpretation was further reinforced by mean field calculations which showed that the finite temperature trapped paired gas does indeed produce bimodal spectra [4,5,6,7]. This paradigm has been shattered by the realization that there exist models which produce bimodal spectra in the absence of pairing [8]. Here we give a simple argument for why trapped strongly interacting Fermi gases generically show a bimodal spectrum, irrespective of the presence of pairing.Our argument relies on two ingredients: a harmonic trap plus qualitative features of the equation of state. We establish that the equation of state of the unitary Fermi gas has these features through a dimensional analysis argument supplemented by the first terms of the virial expansion. Consistent with previous results [4,5,6,7,8], we conclude that one of the spectral peaks comes from atoms at the edge of the cloud, and the other from atoms at the center. This is similar to the mechanism by which multiple spectral peaks appear in the spectra of clouds of Bosons in an optical lattice [9,10]. We quantify our arguments by presenting a simplified calculation of the spectrum of a trapped two-component Fermi gas in the limit n ↓ /n ↑ → 0. Although we include final-state interactions [11,12,13,1...

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Theory of rf-Spectroscopy of Strongly Interacting Fermions

Cited by 123 publications

References 21 publications

Radio-frequency spectroscopy of a strongly imbalanced Feshbach-resonant Fermi gas

Radio-frequency spectroscopy of a strongly imbalanced Feshbach-resonant Fermi gas

Determination of the fermion pair size in a resonantly interacting superfluid

Generic features of the spectrum of trapped polarized fermions

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