We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in nonisotropic traps.We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in nonisotropic traps.

arXiv:cond-mat/0605315Physical Review ASep 19, 200692 citations

Scattering Length Instability in Dipolar Bose-Einstein Condensates

Daniele C. E. Bortolotti, Shai Ronen, John L. Bohn +1 more

We predict a new kind of instability in a Bose-Einstein condensate composed of dipolar particles. Namely, a comparatively weak dipole moment can produce a large, negative two-body scattering length that can collapse the Bose-Einstein condensate. To verify this effect, we validate mean-field solutions to this problem using exact, diffusion Monte Carlo methods. We show that the diffusion Monte Carlo energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly.We predict a new kind of instability in a Bose-Einstein condensate composed of dipolar particles. Namely, a comparatively weak dipole moment can produce a large, negative two-body scattering length that can collapse the Bose-Einstein condensate. To verify this effect, we validate mean-field solutions to this problem using exact, diffusion Monte Carlo methods. We show that the diffusion Monte Carlo energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly.

arXiv:cond-mat/0604432Physical Review LettersOct 18, 200683 citations

Bose Condensates with Small s-wave Scattering Lengths: Effect of Dipolar Interaction

Yong Chen, D. Dries, J. M. Hitchcock +1 more

Bulletin of the American Physical SocietyMay 30, 20080 citations

Quantum corrections to the ground-state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

D. Blume, Chris H. Greene

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, ${n(0)a}^{3}<~2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ $[n(0),$ peak density; a, s-wave scattering length], our calculations confirm that the exact ground-state energy for a sum of two-body interactions depends to a good approximation on only the atomic-physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for $N=2--50$ particles in the trap with positive s-wave scattering length $a=100--10000\mathrm{a}.\mathrm{u}.$ Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see, e.g., E. Braaten and A. Nieto, Phys. Rev. B 56, 14 745 (1997)], leads to a greatly improved description of trapped Bose gases.The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, ${n(0)a}^{3}<~2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ $[n(0),$ peak density; a, s-wave scattering length], our calculations confirm that the exact ground-state energy for a sum of two-body interactions depends to a good approximation on only the atomic-physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for $N=2--50$ particles in the trap with positive s-wave scattering length $a=100--10000\mathrm{a}.\mathrm{u}.$ Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see, e.g., E. Braaten and A. Nieto, Phys. Rev. B 56, 14 745 (1997)], leads to a greatly improved description of trapped Bose gases.

arXiv:cond-mat/0009220Physical Review AMay 4, 200173 citations

Validity of the scattering length approximation in Bose-Einstein condensates

L. A. Frank, W. R. Paterson, K. L. Ackerson +1 more

APSMay 1, 19980 citations

[n(0),

peak density; a, s-wave scattering length], our calculations confirm that the exact ground-state energy for a sum of two-body interactions depends to a good approximation on only the atomic-physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for

N=2--50

particles in the trap with positive s-wave scattering length

a=100--10000\mathrm{a}.\mathrm{u}.

Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see, e.g., E. Braaten and A. Nieto, Phys. Rev. B 56, 14 745 (1997)], leads to a greatly improved description of trapped Bose gases.