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Effective multibody interactions of harmonically confined ultracold neutral bosons



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


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.
New Journal of Physics


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


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], (Accessed April 24, 2024)
Created March 20, 2012, Updated October 12, 2021