Probing Number Squeezing of Ultracold Atoms across the Superfluid-Mott Insulator Transition

The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.

Figure 1

Illustration of the number statistics measurement. Spin-changing collisions turn atom pairs initially in the Zeeman substate $m=0$ (no arrow) to pairs in $m=\pm 1$ states (up and down arrows). This process happens for sites with $n=2$ (a) or $n=3$ (b) atoms. For one atom per site on average, whether this occurs depends drastically on the many-body correlations. For a Bose-Einstein condensate (c), large on-site fluctuations create a finite number of sites with 2 or 3 atoms, where $\pm 1$ pairs can be created. On the contrary, for a MI state (d), only isolated atoms are found and no $m=\pm 1$ pairs are created.

Figure 2

Time sequence of the experiment.

Figure 3

Resonance curve of the spin-oscillation amplitude in the far-detuned microwave field, measured at a magnetic field $B\approx 1.2\mathrm{G}$ and at a fixed hold time $t_{\mathrm{hold}}=15.5\mathrm{ms}$. Solid (open) circles denote the population in the Zeeman substate $m=0$ ($m=\pm 1$).

Figure 4

Amplitude of the spin oscillation vs atom number and different lattice depths: $V_0=4,8,11,13,20,40E_r$ (a)–(f). The thin dashed lines show the prediction of a theoretical model, where the atom number distribution is deduced from a mean-field approach at $T=0$ (see text). The thin solid lines show only the fraction of atom pairs calculated from the same model. The thick solid lines are guides to the eye. In (f), the vertical lines indicate where Mott plateaus with 2 and 3 atoms per site are expected to form.