Radio-Frequency Spectroscopy of Ultracold Fermions

Gupta, Subhadeep; Hadzibabic, Zoran; Zwierlein, Martin; Stan, C. A.; Dieckmann, Kai; Schunck, Christian H.; Kempen, van Egm Eric; Verhaar, BJ Boudewijn; Ketterle, Wolfgang

doi:10.1126/science.1085335

Cited by 266 publications

(305 citation statements)

References 30 publications

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“…1, the pair size can in principle be obtained from both E th and E w . However, since the whole spectrum may be subject to shifts from Hartree terms [16,18], we focus in the following only on the width of the spectrum.…”

Section: Figmentioning

confidence: 99%

“…We have taken advantage of the fact that any two state mixture (1,2), (1,3), and (2,3) of the three lowest hyperfine states of 6 Li (labeled in the order of increasing hyperfine energy as |1 , |2 and |3 ) exhibits a broad Feshbach resonance [16,17]. So far, all experiments with strongly interacting fermions in 6 Li have been carried out in the vicinity of the (1,2) Feshbach resonance located at about B 12 ∼ 834 G. Surprisingly, inelastic collisions including allowed dipolar relaxation are not enhanced by the (1,3) and (2,3) Feshbach resonances.…”

Section: Figmentioning

confidence: 99%

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Determination of the fermion pair size in a resonantly interacting superfluid

Schunck

Shin

Schirotzek

et al. 2008

Nature

124

161

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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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Section: Figmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Determination of the fermion pair size in a resonantly interacting superfluid

Schunck

Shin

Schirotzek

et al. 2008

Nature

124

161

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“…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%

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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“…Great dividends have been reaped in the study of high T c superconductors where the scanning tunneling microscope (STM), which measures the differential current proportional to the LDOS, provides this function [15]. In ultra-cold Fermi gases, radio-frequency (RF) spectroscopy [16][17][18] could serve as an analogous tool. The RF field induces single-particle excitations by coupling one of the spin species (say | ↑ atoms) out of the pairing state to a third state |3 which is initially unoccupied.…”

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confidence: 99%

Single impurity in ultracold Fermi superfluids

Jiang

Baksmaty

et al. 2011

Phys. Rev. A

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The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we study the effect of a single classical magnetic impurity in trapped ultracold Fermi superfluids. Depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states in a superfluid Fermi gas. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microsope, we propose a modified RF spectroscopic method to measure the local density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.

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Radio-Frequency Spectroscopy of Ultracold Fermions

Cited by 266 publications

References 30 publications

Determination of the fermion pair size in a resonantly interacting superfluid

Determination of the fermion pair size in a resonantly interacting superfluid

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Single impurity in ultracold Fermi superfluids

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