We propose a smooth pseudopotential for the contact interaction acting between ultracold atoms confined to two dimensions. The pseudopotential reproduces the scattering properties of the repulsive contact interaction up to 200 times more accurately than a hard disk potential, and in the attractive branch gives a 10-fold improvement in accuracy over the square well potential. Furthermore, the new potential enables diffusion Monte Carlo simulations of the ultracold gas to be run 15 times quicker than was previously possible.
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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