Bragg spectroscopy of ultracold atoms loaded in an optical lattice

We study Bragg spectroscopy of ultracold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott-insulator phase, in particular the one-particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor and use it to calculate the imparted energy which was shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear-response analysis. Finally we show that when the system is deep in the Mott-insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap.

Figure 1

Energy transfer for a homogeneous system at zero temperature. Solid line, exact solution; crosses, perturbative solution (envelope, dashed line). Other parameters: $M=N=9$, $J\tau ∕\hslash =20$, $U∕J=45$.

Figure 2

Energy transfer for a system at finite temperature. Solid line, $k_{B}T∕U=0.007$; crosses, $k_{B}T∕U=0.21$. The other parameters are the same as those in Fig. 1.