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

Mal, Subhanka; Adhikary, Kingshuk; Sardar, Dibyendu; Saha, Abhik Kumar; Deb, Bimalendu

doi:10.1088/1361-6455/ab2378

Cited by 4 publications

(13 citation statements)

References 45 publications

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“…Unlike the case of contact interaction, the use of this exact T-matrix element allows us to calculate accurately the energy dependence of the gap without requiring any renormalisation of the interaction. The effective range effects described in this paper may be experimentally realisable with a relatively dense cloud of ultracold fermionic atoms near a Feshbach resonance for which the effective range is finite, positive and likely to be tunable with an external field [30,41]. In fact, the effective range near a narrow Feshbach resonance may become large and even negative [41][42][43].…”

Section: Discussionmentioning

confidence: 80%

“…The purpose of this paper is to explore the effects of the effective range of interaction on the superfluidity of a unitary Fermi gas. Towards this end, we resort to the finite-range Jost-Kohn (JK) model potential [30] which has been recently shown to account for the unitary regime. The use of this model interaction potential allows us to study the finite range effects and energy dependence of superfluid gap and density over a wide range of a s including the resonance limit.…”

Section: Introductionmentioning

confidence: 99%

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A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

Mal¹,

Deb²

2022

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

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We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution of the potential, we derive two-body ${\mathbf T}$-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the \textcolor{red}{unitary} regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated \textcolor{red}{in mean-field theory with contact potential}. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be $0.42 E_F$ which is quite close to the recent result of the quantum Monte Carlo simulation [2018 {\rm Phys. Rev.A} {\bf 97}, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.

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Section: Discussionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

Mal¹,

Deb²

2022

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Unlike the case of contact interaction, the use of this exact T-matrix element allows us to calculate accurately the energy dependence of the gap without requiring any renormalisation of the interaction. The effective range effects described in this paper may be experimentally realisable with a relatively dense cloud of ultracold fermionic atoms near a Feshbach resonance for which the effective range is finite, positive and likely to be tunable with an external field [28,38]. In fact, the effective range near a narrow Feshbach resonance may become large and even negative [38][39][40].…”

Section: Discussionmentioning

confidence: 80%

“…The purpose of this paper is to explore the effects of the effective range of interaction on the superfluidity of a unitary Fermi gas. Towards this end, we resort to the finite-range Jost-Kohn model potential [28] which has been recently shown to account for the unitary regime. The use of this model interaction potential allows us to study the finite range effects and energy dependence of superfluid gap and density over a wide range of a s including the resonance limit.…”

Section: Introductionmentioning

confidence: 99%

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

Mal,

Deb

2021

Preprint

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We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 J. Phys. B: At. Mol. Opt. Phys. 52, 165004]. Using exact scattering solution of the potential, we derive two-body Tmatrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy-and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitarity regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitarity limits is found to be 0.42E F which is quite close to the recent result of the quantum Monte Carlo simulation [2018 Phys. Rev.A 97, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.

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“…We consider fermions as having two spin components and the bosons as spinless or spin-polarized or two-component spin. We assume that, unlike commonly used contact-type pseudo-potential, the atoms interact via finite-range model interaction potentials of Jost and Kohn [24][25][26]. We use exact numerical single-particle solutions of the trap in calculating the Hubbard parameters under tightbinding two-mode approximation.…”

Section: Introductionmentioning

confidence: 99%

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

Mal¹,

Adhikary²,

Deb³

2019

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

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In a recent work, Murmann et. al. [Phys. Rev. Lett. 114, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first discuss building up the Hubbard models using the model finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms. We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single-and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

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

Cited by 4 publications

References 45 publications

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

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