Effective multibody interactions of harmonically confined ultracold neutral bosons

Published

March 21, 2012

Author(s)

Philip Johnson, W F. Flynn, D Blume, X Y. Yin, Eite Tiesinga

Abstract

We use renormalized perturbation theory to calculate effective two-, three-, and four-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming only two-body interactions modeled with a zero-range pseudopotential, and working to third-order in the free-space scattering length a_t(0) defined at zero collision energy. The leading-order four-body interaction energy is U_4(w)=+(2.43317...)[a_t(0)/l(w)]^3+O (a_t^4), where w and l(w) are the harmonic oscillator frequency and length, respectively. After renormalization the three-body interaction energy is U_3}(w) =-(0.85576...)[a_t(0)/l(w)]^2+2.7921(1)[a_t (0)/l(w)]^3+O(a_t^4). The one-standard deviation error +/-0.0001 for the third-order coefficient in U_3(w) is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. We then perform numerical simulations for a finite-range boson--boson potential and comparison to the zero-range predictions reveals that finite-range effects must be taken into account. In particular, we show that an energy-dependent pseudopotential accurately captures the finite-range physics, through third order, and in combination with multibody interactions gives excellent agreement to the numerical simulations, validating our theoretical analysis.

Citation

New Journal of Physics

Pub Type

Journals

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Keywords

ultracold atoms, optical lattices, few-body physics, renormalization theory

Citation

Johnson, P. , Flynn, W. , Blume, D. , Yin, X. and Tiesinga, E. (2012), Effective multibody interactions of harmonically confined ultracold neutral bosons, New Journal of Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910360 (Accessed March 13, 2025)