Doublon Relaxation in the Bose-Hubbard Model

The decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires the creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average occupation number is sufficiently small, the corresponding exponent may be evaluated exactly. To this end we develop the quasiclassical approach to calculation of the high-order tree-level decay amplitudes.

Figure 1

An example of a tree-level diagram for the amplitude of the doublon decay in $n=5$ particles. (a) Doublon propagator $⟨d\overline{d}⟩$; (b) particle propagator $⟨c_{\pi }{\overline{c}}_{\pi }⟩$; (c) condensate amplitude $c_0\propto \sqrt{{\rho }_0}$; (d) doublon decay vertex ${\overline{c}}_{\pi }{\overline{c}}_{\pi }d$; (e) particle interaction with the condensate vertex $\overline{d}{c}_0{c}_{\pi }$. Crossed lines denote the mass-shell particles.