Energy absorption of a Bose gas in a periodically modulated optical lattice

We compute the energy absorbed by a one-dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for three-dimensional systems as well. Our calculations, based on bosonization techniques and strong-coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low-dimensional systems and Luttinger liquid physics. We compare our results with experiments and find good agreement.

Figure 1

Energy absorption rate (EAR) for 1D interacting bosons in a weak optical lattice, for the MI phase (with small Mott gap) with different values of the parameter $K$ (in brackets are the corresponding values of $\gamma$ [17]).

Figure 2

Spectral weight of the first resonance peak in the MI phase in one dimension. In the inset we show the predicted 1D shape of the peak for $U∕J=36$, and the comparison with (normalized in the vertical axis) experimental results from Ref. 2.

Figure 3

Width at the base of the first resonance peak in the MI phase. In the 1D, 1D-3D crossover, and 3D cases we take $V_{\perp }=30E_R$, $V_{\perp }=20E_R$, and $V_{\perp }=V_{x0}$, respectively, and $n_0=1$. The 3D Expt. case is the same as 3D but with $n_0=2$, which is closer to the experimental values. The inset compares the predicted half widths with the experimental data from Ref. 2 for one dimension.