Mechanical stability of a strongly interacting Fermi gas of atoms

Gehm, Michael E.; Hemmer, S. L.; Granade, S. R.; O’Hara, K. M.; Thomas, J. E.

doi:10.1103/physreva.68.011401

Cited by 127 publications

(138 citation statements)

References 19 publications

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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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confidence: 90%

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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confidence: 90%

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

et al. 2007

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“…6 To compute the η * k it is very helpful to recognize that the number of integer three vectors j with equal norm is given by the coefficient of x |j| 2 in the Taylor expansion of [θ 3 (0, x)] 3 , where θ 3 (u, x) is one of the Spatial discretization effects make it impossible to exactly reproduce the continuum η * k on the lattice. For one thing, there are an infinite number of η * k while the lattice transfer matrix has only a finite number of eigenvalues.…”

Section: Parameter Tuningmentioning

confidence: 99%

“…Thus the s-wave phase shift satisfies δ(k) = π/2 for all k and the field theory describing the many-body system is at a conformal fixed point 1 ; in 1998 it was suggested that unitary fermions could serve as the starting point for an effective field theory expansion for nuclear physics [2,3]. Since then the unitary fermion gas has been created and studied experimentally by trapping atoms tuned to a Feshbach resonance by means of an applied magnetic field, exhibiting collective effects interpolating between the well understood phenomena of BCS pairing and Bose-Einstein condensation [4][5][6][7][8][9][10][11][12][13]. The nonperturbative nature of the strongly coupled interaction between unitary fermions poses a nontrivial challenge for theory, and numerical simulation has played an essential role in making progress.…”

Section: Introductionmentioning

confidence: 99%

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

et al. 2011

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We present a new lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For N = 3 unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high precision benchmark calculation to within our 0.3% uncertainty; as additional benchmarks we reproduce precision calculations of N = 3, ..., 6 unitary fermions in a harmonic trap to within our ∼ 1% uncertainty. We then use this action to determine the ground state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64 3 × 72. In contrast to variational calculations we find evidence for persistent deviations from the thermodynamic limit for the range of N considered.

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“…This was explicitly demonstrated for Fermi gases in the crossover region of a Feshbach resonance by Ho and Mueller [11]. The virial expansion in this paper includes contributions from the two-nucleon (deuteron) and four-nucleon (alpha particle) bound states and the relevant low-energy scattering resonances: the dominant ones being the 1 S 0 two-nucleon resonance ( 2 He or 2 n), the P 3/2 Nα resonance and the αα 0 + resonance that is the ground state of 8 Be.…”

Section: Introductionmentioning

confidence: 99%

“…In a separate paper [6], we have calculated the equation of state of low-density neutron matter using the virial expansion, in order to assess quantitatively how close the system is to universal behavior at finite temperature. The equation of state of resonant and dilute Fermi gases has also been studied in laboratory experiments with trapped atoms [7,8,9,10], and Ho et al have used the virial expansion to describe Fermi gases at high temperatures in the vicinity of Feshbach resonances [11,12].…”

Section: Introductionmentioning

confidence: 99%

Cluster formation and the virial equation of state of low-density nuclear matter

2006

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We present the virial equation of state of low-density nuclear matter composed of neutrons, protons and alpha particles. The virial equation of state is model-independent, and therefore sets a benchmark for all nuclear equations of state at low densities. We calculate the second virial coefficients for nucleon-nucleon, nucleon-alpha and alpha-alpha interactions directly from the relevant binding energies and scattering phase shifts. The virial approach systematically takes into account contributions from bound nuclei and the resonant continuum, and consequently provides a framework to include strong-interaction corrections to nuclear statistical equilibrium models. The virial coefficients are used to make model-independent predictions for a variety of properties of nuclear matter over a range of densities, temperatures and compositions. Our results provide constraints on the physics of the neutrinosphere in supernovae. The resulting alpha particle concentration differs from all equations of state currently used in supernova simulations. Finally, the virial equation of state greatly improves our conceptual understanding of low-density nuclear matter.

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Mechanical stability of a strongly interacting Fermi gas of atoms

Cited by 127 publications

References 19 publications

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

Cluster formation and the virial equation of state of low-density nuclear matter

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