Spin Relaxation and Band Excitation of a Dipolar Bose-Einstein Condensate in 2D Optical Lattices

We observe interband transitions mediated by dipole-dipole interactions for an array of 1D quantum gases of chromium atoms, trapped in a 2D optical lattice. Interband transitions occur when dipolar relaxation releases an energy larger than the lattice band gap. For symmetric lattice sites, and a magnetic field parallel to the lattice axis, we compare the measured dipolar relaxation rate with a Fermi golden rule calculation. Below a magnetic field threshold, we obtain an almost complete suppression of dipolar relaxation, leading to metastable 1D gases in the highest Zeeman state.

Figure 1

Band mapping results above threshold. The false colored picture is an average of 4 absorption images of the BEC released from the lattice. (a) Integrated population profile along $z$: the first excited band (second Brillouin zone, BZ) in the $y$ direction is populated, contrary to below threshold (which gives the sharper peak). (b) Integrated profile along $y$ showing a non-Gaussian velocity distribution; lines are results of a double Gaussian fit, yielding an effective temperature. (c) Sketch of the 2D lattice arrangement: the 1D traps are along $z$, the imaging beam is sent along $x$.

Figure 2

Evidence for a threshold in dipolar relaxation: (a) $v=1$ population as a function of Larmor frequency after 25 ms of dipolar relaxation for 25 $E_r$; (b) Effective temperature along the tubes as a function of Larmor frequency after 75 ms, for two different lattice depths (circles: 12 $E_r$; squares: 25 $E_r$). The shaded areas represent the respective widths of the second energy band. Lines are guides for the eye.

Figure 3

Dynamics of dipolar relaxation when the magnetic field is increased above threshold. Threshold is reached at $t=25\mathrm{ms}$. (a) shows the effective temperature (see text), and (b) the measured proportion of atoms in the first excited band. Lines are guides for the eye.

Figure 4

Heating in the lattice below threshold after 40 ms, as a function (a) of the angle $\theta$ between the magnetic field and the tube axis, (b) of the transverse ellipticity $({\omega }_x-{\omega }_y{)}^2/({\omega }_x+{\omega }_y{)}^2$ of the lattice sites (where ${\omega }_{x,y}$ are the oscillation frequency of the lattice site along the two main axes $x$ and $y$). Lines are guides for the eye.