Extracting the Mott gap from energy measurements in trapped atomic gases

We show that the measure of the so-called release energy, which is an experimentally accessible quantity, makes it possible to assess the value of the Mott gap in the presence of the unavoidable confinement potential in the actual experimental setup. Indeed, the curve of the release energy as a function of the total number of particles shows kinks that are directly related to the existence of excitation gaps. Calculations are presented within the Gutzwiller approach, but the final results go beyond this simple approximation and represent a genuine feature of the real system. In the case of harmonic confinement, the Mott gaps may be renormalized with respect to the uniform case. On the other hand, in the case of the recently proposed off-diagonal confinement, our results show good agreement with the homogeneous case.

Figure 1

Energy per site vs density in the case of the 1D homogeneous model for different values of $U/t$.

Figure 2

Upper panel: release energy. Middle panel: local density $n_i$ across the lattice sites. Lower panel: local density fluctuations ${\Delta }_i$ across the lattice sites. A value of $V_0/t=0.01$ is considered. All quantities are shown as a function of the total number of bosons $N$, and the interaction is set to $U/t=4$. Calculations are shown for the 1D model.

Figure 3

The same as in Fig. 2 for $U/t=15$.

Figure 4

Upper panels: the first Mott gap obtained from the release energy as function of $U/t$ for $V_0/t=0.01$; for comparison, the homogeneous case is also reported (left) with release-energy curves for different $U/t$ and $V_0/t=0.01$ (right). Lower panel: the first Mott gap as a function of $V_0/t$ for $U/t=15$. Calculations are shown for the 1D model.

Figure 5

Upper panels: 2D results on local density fluctuations ${\Delta }_i$ across the lattice before (left) and after (right) the kink in the release energy for $U/t=20$. Lower panel: release energy for different values of $U/t$ and fixed $V_0/t=0.01$.

Figure 6

Results of total energy of the confined system in the 2D model as a function of the number of particles for different values of $U/t$.

Figure 7

The same as in Fig. 3 but for an off-diagonal confinement. The number of sites is $L=200$, and $n=N/L$ is the density.