Unitary gas in an isotropic harmonic trap: Symmetry properties and applications

Werner, Félix; Castin, Yvan

doi:10.1103/physreva.74.053604

Cited by 236 publications

(420 citation statements)

References 58 publications

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“…We note additionally that the spacing between the energy levels associated with breathing modes [18], 2ωb τ = 0.010, is smaller than the inverse temporal extent of our lattice (1/T ≈ 0.017), but larger than our quoted error bars. Furthermore, as an increasing number of particles are added to the system, a near continuum of different angular momentum states may result, also of O(ωb τ ).…”

Section: Possible Additional Sources Of Systematic Errormentioning

confidence: 74%

“…What is known exactly about unitary fermions in the continuum is (i) the spectrum of two unitary fermions in a box of size L [50][51][52][53]; (ii) the spectrum of two and three unitary fermions in a harmonic trap [18]; (iii) the scaling dimension of local composite operators involving unitary fermions 5 . Not known exactly but determined to high numerical accuracy are (iv) the few lowest energy levels for three unitary fermions in a box, extrapolated from a lattice Hamiltonian diagonalization very close to the continuum limit, with lattice size up to L = 50 [29]; and (v) the ground state energies for 4, 5, 6 unitary fermions in a harmonic trap, obtained by solving the Schrödinger equation [57].…”

Section: Parameter Tuningmentioning

confidence: 99%

“…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. A large body of recent theoretical work exists for unitary fermions, both analytical [14][15][16][17][18][19][20] and numerical .…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Possible Additional Sources Of Systematic Errormentioning

confidence: 74%

Section: Parameter Tuningmentioning

confidence: 99%

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Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

et al. 2011

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“…[21][22][23][24][31][32][33][34][35][36][37][38][39][40][41][42]). The ground state of trapped equalmass two-component Fermi gases, e.g., has been investigated numerically by the fixed-node diffusion Monte Carlo approach [21][22][23]39] and the stochastic variational approach [21,22,36,40,42].…”

Section: Introductionmentioning

confidence: 99%

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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We investigate small equal-mass two-component Fermi gases under external spherically symmetric confinement in which atoms with opposite spins interact through a short-range two-body model potential. We employ a non-perturbative microscopic framework, the stochastic variational approach, and determine the system properties as functions of the interspecies s-wave scattering length as, the orbital angular momentum L of the system, and the numbers N1 and N2 of spin-up and spin-down atoms (with N1 − N2 = 0 or 1 and N ≤ 6, where N = N1 + N2). At unitarity, we determine the energies of the five-and six-particle systems for various ranges r0 of the underlying two-body model potential and extrapolate to the zero-range limit. These energies serve as benchmark results that can be used to validate and assess other numerical approaches. We also present structural properties such as the pair distribution function and the radial density. Furthermore, we analyze the one-body and two-body density matrices. A measure for the molecular condensate fraction is proposed and applied. Our calculations show explicitly that the natural orbitals and the momentum distributions of atomic Fermi gases approach those characteristic for a molecular Bose gas if the s-wave scattering length as, as > 0, is sufficiently small.

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“…From The early seminal study of Busch et al (Busch et al 1997) demonstrates that for two trapped fermions in opposite internal states the ground-state energy is 2 ω (see (Zinner 2012) a discussion of this model in both two-and three-dimensional traps and for a review of the relevant theoretical work and experimental support). An important benchmark for the two-component fermionic few-body problem in a harmonic trap is the exact solution for three particles at unitarity where the groundstate energy is 4.27 ω (Werner & Castin 2006a, Werner & Castin 2006b). These results was followed by several numerical studies of three and four trapped fermions (Stetcu et al 2007, Alhassid et al 2008, and for up to 30 fermions (Chang & Bertsch 2007, Blume et al 2007).…”

Section: Fermionic Few-body Systemsmentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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Unitary gas in an isotropic harmonic trap: Symmetry properties and applications

Cited by 236 publications

References 58 publications

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Comparing and contrasting nuclei and cold atomic gases

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