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Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons | P.R. Johnson
; D. Blume
; X. Y. Yin
; W.F. Flynn
; E. Tiesinga
; | Date: |
13 Jan 2012 | Abstract: | We calculate the renormalized effective two-, three-, and four-body
interactions for N neutral ultracold bosons in the ground state of an isotropic
harmonic trap, assuming two-body interactions modeled with the combination of a
zero-range and energy-dependent pseudopotential, and working to third-order in
the free-space scattering length a, defined at zero collision energy. The
results take into account the influence of quantum fluctuations to excited
orbitals and finite-range effects for realistic two-body interactions. The
leading-order, effective four-body interaction energy is U4 =
+(2.43317...)(a/l)^3 + O[(a/l)^4]; l and w are the harmonic oscillator length
and frequency, and energies are in units of (hbar)(w). After renormalization,
the effective dimensionless three-body interaction energy is U3 =
-(0.85576...)(a/l)^2 + 2.7921(1)(a/l)^3 + O[(a/l)^4]. The one-standard
deviation error 0.0001 for the third-order coefficient in U3 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 the energy-dependent pseudopotential
accurately captures the finite-range physics, through third order, and in
combination with multi-body effective interactions gives excellent agreement
with the numerical simulations, validating our theoretical analysis and
predictions. | Source: | arXiv, 1201.2962 | Services: | Forum | Review | PDF | Favorites |
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