Effective-range dependence of resonantly interacting fermions

Forbes, Michael McNeil; Gandolfi, Stefano; Gezerlis, Alexandros

doi:10.1103/physreva.86.053603

Cited by 63 publications

(84 citation statements)

References 47 publications

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“…The Pöschl-Teller interaction gives the exact phase shift with scattering length a and effective range R eff in the lowest angular momentum channel [24], and has been used in several studies [11,14,30,31]. At unitarity, a −1 = 0, the potential can be written in terms of its effective range R eff as…”

Section: Pöschl-tellermentioning

confidence: 99%

Effective-range dependence of resonant Fermi gases

Schonenberg

Conduit

2017

Phys. Rev. A

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A Fermi gas of cold atoms allows precise control over the dimensionless effective range, kFR eff , of the Feshbach resonance. Our pseudopotential formalism allows us to create smooth potentials with effective range, −2 ≤ kFR eff ≤ 2, which we use for a variational and diffusion Monte Carlo study of the ground state of a unitary Fermi gas. We report values for the universal constants of ξ = 0.388(1) and ζ = 0.087(1), and compute the condensate fraction, momentum distribution, and pair correlations functions. Finally, we show that a gas with kFR eff 1.9 is thermodynamically unstable.

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Section: Pöschl-tellermentioning

confidence: 99%

Effective-range dependence of resonant Fermi gases

Schonenberg

Conduit

2017

Phys. Rev. A

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“…To ensure that the effective range term is small, Bertaina and Giorgini [21] used k F r c = 2.5 × 10 −3 . The discontinuity of the potential well at r c can be avoided by using a smooth form V (r) = a/ cosh 2 (br) with a < 0 [23,44], but this does not change the essence of the problem as the potential remains uniformly attractive and must be deep and narrow to ensure small R 2 eff . With a small effective radius both potentials are difficult to handle numerically so we propose the UTP as an alternative that allows R 2 eff to be varied independently of r 2 c .…”

Section: A Potential Wellmentioning

confidence: 99%

Effective-range dependence of two-dimensional Fermi gases

2017

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The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges −1.5 ≤ k 2 F R 2 eff ≤ 0, where R eff is the effective range and kF is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit k 2 F R 2 eff → −∞ is a gas of bosons with zero binding energy, whereas ln(kFa) → −∞ corresponds to noninteracting bosons with infinite binding energy.

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“…In this context, it is worth mentioning that both the potentials V + (r) and V − (r) reduce to the same analytical form which is of Potsch-Teller potential in the limits Λ → −1 (or κ → 0) and a s → ±∞ [32], signifying zero-energy resonance. It is worth mentioning that the same from of Pöschl-Teller potential has been used earlier for quantum Monte Carlo simulation of many-body physics of an ultracold Fermi gas of atoms [33][34][35][36][37].…”

Section: Resonant Interactionsmentioning

confidence: 99%

Modeling atom–atom interactions at low energy by Jost–Kohn potentials

Mal¹,

Adhikary²,

Sardar³

et al. 2019

J. Phys. B: At. Mol. Opt. Phys.

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More than 65 years ago, Jost and Kohn [R. Jost and W. Kohn, Phys. Rev. 87, 977 (1952)] derived an explicit expression for a class of short-range model potentials from a given effective range expansion with the s-wave scattering length as being negative. For as > 0, they calculated another class of short-range model potentials [R. Jost and W. Kohn, Dan. Mat. Fys. Medd 27, 1 (1953)] using a method based on an adaptation from Gelfand-Levitan theory [I. M. Gel'fand and B. M. Levitan, Dokl. Akad. Nauk. USSR 77, 557-560 (1951)] of inverse scattering. We here revisit the methods of Jost and Kohn in order to explore the possibility of modeling resonant finite-range interactions at low energy. We show that the Jost-Kohn potentials can account for zero-energy resonances. The s-wave phase shift for positive scattering length is expressed in an analytical form as a function of the binding energy of a bound state. We show that, for small binding energy, both the scattering length and the effective range are strongly influenced by the binding energy; and below a critical binding energy the effective range becomes negative provided the scattering length is large. As a consistency check, we carry out some simple calculations to show that Jost-Kohn potentials can reproduce the standard results of contact interaction in the limit of the effective range going to zero.

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Effective-range dependence of resonantly interacting fermions

Cited by 63 publications

References 47 publications

Effective-range dependence of resonant Fermi gases

Effective-range dependence of resonant Fermi gases

Effective-range dependence of two-dimensional Fermi gases

Modeling atom–atom interactions at low energy by Jost–Kohn potentials

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