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arXiv:cond-mat/0604432 · Physical Review Letters

Scattering Length Instability in Dipolar Bose-Einstein Condensates

Daniele C. E. Bortolotti, Shai Ronen, John L. Bohn, D. Blume

Published Oct 18, 2006• 83 citations
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Abstract

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.

DOI
10.1103/physrevlett.97.160402

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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 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 study the stabilization properties of dipolar Bose-Einstein condensate by temporal modulation of short-range two-body interaction. Through both analytical and numerical methods, we analyze the mean-field Gross-Pitaevskii equation with short-range two-body and long-range, nonlocal, dipolar interaction terms. We derive the equation of motion and effective potential of the dipolar condensate by variational method. We show that there is an enhancement of the condensate stability due to the inclusion of dipolar interaction in addition to the two-body contact interaction. We also show that the stability of the dipolar condensate increases in the presence of time varying two-body contact interaction; the temporal modification of the contact interaction prevents the collapse of dipolar Bose-Einstein condensate. Finally we confirm the semi-analytical prediction through the direct numerical simulations of the governing equation.
We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density E of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda* that determines the low-energy observables in the three-body sector. The second-order correction to E has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative a, we calculate the coefficient of the three-body mean-field term in E in terms of a and Lambda*. It can be very large if there is an Efimov state near threshold.
The ground-state solutions of a dilute Bose condensate with contact and magnetic dipole-dipole interactions are examined. By lowering the value of the scattering length, Goral et al. [Phys. Rev. A 61, 051601 (2000)] numerically predict a region of unstable solutions, accompanied by a neighborhood where the ground-state wave functions have internal structure. On the contrary, we find that the dipolar condensate has an intuitively located stability region, and ground-state solutions near the instability threshold that are without any unusual structure.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
This tutorial presents a detailed discussion of the generation of a Bose–Einstein condensate (BEC) of chromium atoms. This constitutes the first realization of a Bose–Einstein condensate of atoms with strong dipole–dipole interaction. Due to the special electronic and magnetic properties of chromium atoms, standard methods cannot be applied to generate a chromium BEC. The tutorial contains a detailed discussion of the techniques that we use to create the chromium BEC. Compared to all other BECs that have been created so far, chromium atoms have an extraordinarily large magnetic dipole moment and therefore underlie strong magnetic dipole–dipole interaction which is in contrast to the contact interaction that stems from s-wave scattering of the atoms, long-range and anisotropic. A steadily growing number of theoretical publications show that many interesting new phenomena are expected to occur in a 'dipolar' BEC. An experimental investigation of the expansion dynamics of the chromium BEC provides the first experimental proof of a mechanical effect of dipole–dipole interaction in a gas. We describe the condensate by a hydrodynamic model of a superfluid that takes dipole–dipole interaction into account. Our experimental results are in excellent agreement with this theory. We are able to determine the relative strength parameter of the dipole–dipole interaction and deduce the s-wave scattering length of chromium atoms. These two quantities allow us to completely describe the interaction of the atoms in the condensate. The experimental results presented here make the chromium BEC the most promising system for further investigations of dipolar effects in degenerate quantum gases.