Stability of a dipolar Bose-Einstein condensate in a one-dimensional lattice

We show that in contrast with contact interacting gases, an optical lattice changes drastically the stability properties of a dipolar condensate, inducing a crossover from dipolar destabilization to dipolar stabilization for increasing lattice depths. Performing stability measurements on a ${}^{52}$Cr Bose-Einstein condensate in an interaction-dominated regime, repulsive dipolar interaction balances negative scattering lengths down to $-17$ Bohr radii. Our findings are in excellent agreement with mean-field calculations, revealing the important destabilizing role played by intersite dipolar interactions in deep lattices.

Figure 1

Experimental setup. The measurements are performed in a 1D optical lattice (blue) with underlying crossed optical dipole trap (red). The magnetic field used to reach the Feshbach resonance is produced by two Helmholtz coils (black) and polarizes the dipoles along the lattice direction $z$. For deep lattices we obtain a stack of oblate dipolar BECs as depicted on the lower right.

Figure 2

Atom number vs scattering length for different lattice depths. For a moderate lattice depth of $U=(6.2\pm 0.6)E_{\text{R}}$ (open blue dots), the condensate becomes unstable at $a_{\mathrm{crit}}=(6.5\pm 1.9)a_0$, while in a deep lattice at $U=(37\pm 4)E_{\text{R}}$ (filled red dots), we observe a stable BEC until $a=(-13.2\pm 2.5)a_0$. The solid lines are fits to the data using the arbitrarily chosen form $N_{\mathrm{BEC}}=max\{0,N_0{(a-a_{\mathrm{crit}})}^{\beta }\}$, from which we extract the critical scattering length $a_{\mathrm{crit}}$ ($\beta \simeq 0.2$).

Figure 3

Stability diagram of the dipolar condensate in the 1D optical lattice. The critical scattering length $a_{\mathrm{crit}}$ is plotted vs the lattice depth $U$ [23]. The lines are results of the numerical simulations for different atom numbers. We explore the full crossover from a dipolar destabilized ($a_{\mathrm{crit}}>0$) to a dipolar stabilized ($a_{\mathrm{crit}}<0$) regime. At $U=50E_{\text{R}}$ we observe a stable condensate down to $a_{\mathrm{crit}}=(-17\pm 3)a_0$. For comparison, the dashed-dotted line (green) shows the simulated critical scattering length disregarding the dipolar interaction. We find $|a_{\mathrm{crit}}|<0.4a_0$ on the whole range, approaching $a_{\mathrm{crit}}=0$ (gray dotted line) for increasing lattice depth.

Figure 4

Intersite coupling mediated by dipolar interactions: zoom on Fig. 3 in the deep lattice regime. Intersite hopping is negligible on experimental time scales. Solid line: numerical simulation using the full dipolar potential $V_{\mathrm{dd}}\left(\mathbf{r}\right)$. Dashed-dotted line: simulation with the truncated dipolar potential $V_{\mathrm{dd}}^{\mathrm{box}}\left(\mathbf{r}\right)$ (see text), for which intersite coupling is not taken into account. The deviation of the simulation with the truncated potential to the experimental data indicates significant mean-field energy contributions from long-range intersite interactions.