Figure 1

(a) Solid lines show the $s$-wave scattering length $a$ as a function of the dipole strength $D_{*}$, both in units of $b$, for the two-body potential $V$, Eq. (2). Vertical dotted lines denote those $D_{*}/b$ values at which $a$ diverges and a new bound state appears in the two-body potential. (b) Dashed lines show $E/N$ for two dipoles under external spherical confinement calculated for $b=0.0137a_{\mathrm{ho}}$ as a function of $D_{*}/a_{\mathrm{ho}}$ obtained by solving the linear Schrödinger equation for the Hamiltonian given by Eq. (1). Solid lines show the corresponding GP energy obtained by solving Eq. (4) for the pseudopotential $V_{\mathrm{eff}}$, Eq. (3), using the dipole-dependent scattering length. The GP energies are plotted for each branch of the two-body spectrum. Note that the $D_{*}$ values shown in (a) and (b) extend over the same range.Reuse & Permissions

Figure 2

Symbols show the energy per particle $E/N$ calculated by the DMC method for $b=0.0137a_{\mathrm{ho}}$ as a function of $D_{*}/a_{\mathrm{ho}}$ for $N=4$, 10, 20, and 50. Vertical error bars indicate statistical uncertainties. For completeness, a dashed line shows $E/N$, calculated using $B$ splines, for $N=2$. Solid lines show $E/N$ calculated by solving the nonlinear GP equation, Eq. (4), with the dipole-dependent scattering length. For comparison, a dotted line shows $E/N$ for $N=10$ calculated by solving the nonlinear GP equation, Eq. (4), with the bare scattering length, i.e., the cutoff radius $b$.Reuse & Permissions

Figure 3

Partial stability diagram for a dipolar condensate. The white regions depict parameters for which the gas is predicted to be mechanically unstable. Shaded areas are regions of stability, and dark shaded areas denote parameters that are expected to produce stable condensates even in free space. The top axis translates the dipole length $D_{*}$ into a dipole moment, assuming a trap of frequency $\nu =1\mathrm{kHz}$ and a molecular mass 20 amu.Reuse & Permissions