Pairing Without Superfluidity: The Ground State of an Imbalanced Fermi Mixture

Schunck, Christian H.; Shin, Yeong Gil; Schirotzek, André; Zwierlein, Martin; Ketterle, Wolfgang

doi:10.1126/science.1140749

Cited by 180 publications

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“…R p = 53.6 µm is slightly smaller than the measured radius R, which we attribute to finite temperature effects. Previous studies of rf spectroscopy of Fermi gases [10,11] demonstrated that the spectral peak shifts to higher energy at lower temperature, which is interpreted as the increase of the pairing gap energy. In the outer region of lower density, the local T /T F becomes higher, consequently reducing h∆ν p /ε F .…”

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confidence: 92%

“…Radio-frequency (rf) spectroscopy measures an excitation spectrum by inducing transitions to different hyperfine spin states. This method has been employed in strongly interacting Fermi gases, leading to the observation of unitarity limited interactions [7,8], molecule formation on the BEC side of the Feshbach resonance [9] as well as pairing in the crossover regime [10,11]. Rf spectroscopy provides valuable information on the nature of the pairs.…”

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confidence: 99%

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Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

et al. 2007

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We present spatially resolved radio-frequency spectroscopy of a trapped Fermi gas with resonant interactions and observe a spectral gap at low temperatures. The spatial distribution of the spectral response of the trapped gas is obtained using in situ phase-contrast imaging and 3D image reconstruction. At the lowest temperature, the homogeneous rf spectrum shows an asymmetric excitation line shape with a peak at 0.48(4)εF with respect to the free atomic line, where εF is the local Fermi energy. Radio-frequency (rf) spectroscopy measures an excitation spectrum by inducing transitions to different hyperfine spin states. This method has been employed in strongly interacting Fermi gases, leading to the observation of unitarity limited interactions [7,8], molecule formation on the BEC side of the Feshbach resonance [9] as well as pairing in the crossover regime [10,11]. Rf spectroscopy provides valuable information on the nature of the pairs. Since an rf photon can dissociate bound molecules or fermion pairs into the free atom continuum, the binding energy of the pairs or the excitation gap is determined. Furthermore the excitation line shape is related to the wave function of the pairs, e.g. larger pairs have narrower lines. However, currently all experimental measurements on the excitation spectrum in strongly interacting Fermi gases [10,12] have been performed with samples confined in a harmonic trapping potential so that the spectral line shape is broadened due to the inhomogeneous density distribution of the trapped samples, preventing a more stringent comparison with theoretical predictions [13,14,15,16].In this Letter, we demonstrate spatially resolved rf spectroscopy of a trapped, population-balanced Fermi gas at unitarity at very low temperature. The spatial distribution of the rf-induced excited region in the trapped gas was recorded with in situ phase-contrast imaging [17] and the local rf spectra were compiled after 3D image reconstruction. In contrast to the inhomogeneous rf spectrum, the homogeneous local rf spectrum shows a clear spectral gap with an asymmetric line shape. We observe that the spectral peak shifts by 0.48(4)ε F to higher energy and that the spectral gap is 0.30(8)ε F with respect to the free atomic reference line, where ε F is the local Fermi energy. This new spectroscopic method overcomes the line broadening problem for inhomogeneous samples and provides homogeneous rf spectra of a resonantly interacting Fermi gas revealing the microscopic physics of fermion pairs.We prepared a degenerate Fermi gas of spin-polarized 6 Li atoms in an optical trap, using laser cooling and sympathetic cooling with 23 Na atoms, as described in Ref. [18]. An equal mixture of the two lowest hyperfine states |1 and |2 (corresponding to the |F = 1/2, m F = 1/2 and |F = 1/2, m F = −1/2 states at low magnetic field) was created at a magnetic field B = 885 G. A broad Feshbach resonance located at B 0 = 834 G strongly enhanced the interactions between the two states. The final evaporative cooling by lowering the t...

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Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

et al. 2007

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“…2. One may hope that when long-lived molecular condensates are produced, nontrivial behavior of E (1) gap (ν) and the full excitation spectra may be observed in Ramsey fringes 4 , and in Bragg and RF spectroscopy experiments 52,53,54,55 .…”

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confidence: 99%

Superfluidity and phase transitions in a resonant Bose gas

2008

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The atomic Bose gas is studied across a Feshbach resonance, mapping out its phase diagram, and computing its thermodynamics and excitation spectra. It is shown that such a degenerate gas admits two distinct atomic and molecular superfluid phases, with the latter distinguished by the absence of atomic off-diagonal long-range order, gapped atomic excitations, and deconfined atomic π-vortices. The properties of the molecular superfluid are explored, and it is shown that across a Feshbach resonance it undergoes a quantum Ising transition to the atomic superfluid, where both atoms and molecules are condensed. In addition to its distinct thermodynamic signatures and deconfined half-vortices, in a trap a molecular superfluid should be identifiable by the absence of an atomic condensate peak and the presence of a molecular one.

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“…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.…”

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Determination of the fermion pair size in a resonantly interacting superfluid

Schunck

Shin

Schirotzek

et al. 2008

Nature

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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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Pairing Without Superfluidity: The Ground State of an Imbalanced Fermi Mixture

Cited by 180 publications

References 33 publications

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Superfluidity and phase transitions in a resonant Bose gas

Determination of the fermion pair size in a resonantly interacting superfluid

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