Theory of preparation and relaxation of a p-orbital atomic Mott insulator

We develop a theoretical framework to understand the preparation and relaxation of a metastable Mott insulator state within the first excited band of a 1D optical lattice. The state is loaded by "lifting" atoms from the ground to the first excited band by means of a stimulated Raman transition. We determine the effect of pulse duration on the accuracy of the state preparation for the case of a Gaussian pulse shape. Relaxation of the prepared state occurs in two major stages: double-occupied sites occurring due to quantum fluctuations initially lead to interband transitions followed by a spreading of particles in the trap and thermalization. We find the characteristic relaxation times at the earliest stage and at asymptotically long times approaching equilibrium. Our theory is applicable to recent experiments performed with 1D optical lattices [T. M\"uller, S. F\"olling, A. Widera, and I. Bloch, Phys. Rev. Lett. \textbf{99}, 200405 (2007)].