Phase Coherence of an Atomic Mott Insulator

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.

Figure 1

Absorption images of an ultracold Bose gas released from an optical lattice, for various lattice depths: (a) $8E_{\mathrm{R}}$, (b) $14E_{\mathrm{R}}$, (c) $18E_{\mathrm{R}}$, and (d) $30E_{\mathrm{R}}$.

Figure 2

(a) Visibility of the interference pattern produced by an ultracold cloud released from an optical lattice. The two sets of data shown correspond to $3.6\times {10}^5\mathrm{\text{atoms}}$ (gray circles) and $5.9\times {10}^5\mathrm{\text{atoms}}$ (black circles). The latter curve has been offset vertically for clarity. Arrows mark positions where kinks are visible. (b) Numerical derivative of the above curves.

Figure 3

Visibility of the interference pattern versus $U/zt$, the characteristic ratio of interaction to kinetic energy. The data are identical to those shown in Fig. 2 ($5.9\times {10}^5$, black circles, and $3.6\times {10}^5\mathrm{\text{atoms}}$, gray circles). The former curve has been offset vertically for clarity. The lines are fits to the data in the range $(14–25)E_{\mathrm{R}}$, assuming a power law behavior (see text).

Figure 4

Exponent $\alpha$ (a) and prefactor $A$ (b) extracted from a power law fit $A(U/zt{)}^{\alpha }$ to the visibility data in Fig. 3, plotted versus total atom number. The solid line indicates the expected exponent $\alpha =-1$. In (b), we also indicate the prefactor expected for uniform MI with filling factor $n_0=1$ (dashed line) and $n_0=2$ (dotted line), as well as an extrapolation for the average filling calculated at a lattice depth of $30E_{\mathrm{R}}$ (solid line).