Heat Capacity of a Strongly Interacting Fermi Gas

Kinast, J.; Turlapov, Andrey; Thomas, J. E.; Chen, Qijin; Stajic, Jelena; Levin, K.

doi:10.1126/science.1109220

Cited by 383 publications

(564 citation statements)

References 43 publications

(141 reference statements)

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“…1(b) and fitting the non-saturated outer wing profile to a zero-temperature TF distribution, giving ε F 0 = h × 31.5 ± 2.5 kHz. We estimate the universal parameter ξ = (R/R T F ) 4 = 0.50 ± 0.07, which is in good agreement with previous measurements [4,5,24,25,26,27,28] and Quantum Monte Carlo calculations [29,30,31] (ξ ≡ 1+β in some references).…”

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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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“…This makes it possible to study the system as it evolves from a dilute Fermi gas with weak attractive interactions to a bosonic gas of diatomic molecules. This transition from a superfluid BCS state to Bose Einstein condensation (BEC) has been the subject of many experimental [2,3,4,5,6,7,8,9,10,11,12] and theoretical works [13,14,15,16,17,18,19,20,21,22,23].…”

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Density-functional theory for fermions close to the unitary regime

Bhattacharyya

Papenbrock

2006

Phys. Rev. A

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We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density functional and determines the corrections from the analyical results for the harmonically trapped two-body system. The corrections due to the finite scattering length compare well with the result of Monte Carlo simulations. We also apply our results to symmetric neutron matter.PACS numbers: 03.75. Ss,03.75.Hh,05.30.Fk,21.65.+f Ultracold fermionic atom gases have attracted a lot of interest since Fermi degeneracy was achieved by DeMarco and Jin [1]. These systems are in the metastable gas phase, as three-body recombinations are rare. Most interestingly, the effective two-body interaction itself can be controlled via external magnetic fields. This makes it possible to study the system as it evolves from a dilute Fermi gas with weak attractive interactions to a bosonic gas of diatomic molecules. This transition from a superfluid BCS state to Bose Einstein condensation (BEC) has been the subject of many experimental [2,3,4,5,6,7,8,9,10,11,12] and theoretical works [13,14,15,16,17,18,19,20,21,22,23].At the midpoint of this transition, the two-body system has a zero-energy bound state, and the scattering length diverges. If other parameters as the effective range of the interaction can be neglected, the interparticle spacing becomes the only relevant length scale. This defines the unitary limit. In this limit, the energy density is proportional of that of a free Fermi gas, the proportionality constant denoted by ξ. Close to the unitary limit, corrections are due to a finite, large scattering length a and a small effective range r 0 of the potential. Within the local density approximation (LDA), the energy density is given asHere,is the energy density of the free Fermi gas. . We are not aware of any estimate for the constant c 2 in Eq. (1) that concerns the correction due to a small effective range. It is the purpose of this work to fill this gap. This is particularly interesting as experiments also have control over the effective range. Note that the regime of a large effective range has recently been discussed by Schwenk and Pethick [20].In this work, we determine the coefficients c 1 , and c 2 via density functional theory. Recall that the density functional is supposed to be universal, i.e. it can be used to solve the N -fermion system for any particle number N , and for any external potential. Exploiting the universality of the density functional, the parameters c 1 and c 2 can be obtained from a fit to an analytically known solution, i.e. the harmonically trapped two-fermion system [33]. This simple approach has recently been applied [27] to determine the universal constant ξ, and will be followed and extended below.Let us briefly turn to the harmonically trapped twofermion system. The wave function u(r) in the relative coordinate r = r 1 − r 2 of the spin-singlet state is ...

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“…This fact maybe important for the experimental observation of the phenomena discussed here in the In short, the SOC leads to dramatic changes in essentially all the physical quantities such as the quantum phases, excitations spectra and universality classes of quantum and classical phase transitions. All the novel phenomena can be probed by various established experimental techniques [27][28][29][30][31][32][33]. For example, the collective excitations in the PM (Fig1b), SSDW and LSDW+CDW can be detected by the angle-resolved Bragg spectroscopy [31,32], the order parameters φ T /L in Fig.3 may be directly measured by the time of flight experiments, the evolution of the FS topology in Fig.6 can be monitored by spin-injection RF spectroscopy [33], In the appendix A, we contrast the collective modes in the paramagnet with the SOC which breaks the inversion symmetry and those in the conventional FM state without SOC which breaks the Time reversal symmetry.…”

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confidence: 99%

“…Near to the end of the paper, we briefly discuss the effects of the harmonic trap in observing these phenomena. In view of recent ground breaking experimental realizations of a 2d SOC [7][8][9][10], these new phenomena could be probed [27][28][29][30][31][32][33] in near future cold atom experiments and may also be relevant to some materials with SOC [4,18].…”

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confidence: 99%

Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

Zhang

Liu

2016

Phys. Rev. B

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Magnetic phenomena in itinerant electron systems has been at the forefront in material science. Here we show that the Weyl spin-orbit couplings (SOC) in 3 dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations and phase transitions. A putative Ferromagnetic state (FM) is always unstable against a stripe Spiral spin density wave (S-SDW) or a stripe Longitudinal-SDW at small or large SOC strengths respectively. The stripe ordering wavevector is given by the nesting momentum of the two SOC split Fermi surfaces with the same or opposite helicities at small or large SOC strengths respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and FS re-constructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold atom experiments are briefly discussed. In view of recent groundbreaking experimental advances in generating 2d SOC in cold atoms, these phenomena can be observed in current or near future cold atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.

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Heat Capacity of a Strongly Interacting Fermi Gas

Cited by 383 publications

References 43 publications

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Density-functional theory for fermions close to the unitary regime

Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

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