Instability of insulating states in optical lattices due to collective phonon excitations

The effect of collective phonon excitations on the properties of cold atoms in optical lattices is investigated. These phonon excitations are collective excitations, whose appearance is caused by intersite atomic interactions correlating the atoms, and they do not arise without such interactions. These collective excitations should not be confused with lattice vibrations produced by an external force. No such force is assumed. But the considered phonons are purely self-organized collective excitations, characterizing atomic oscillations around lattice sites, due to intersite atomic interactions. It is shown that these excitations can essentially influence the possibility of atoms' being localized. The states that would be insulating in the absence of phonon excitations can become delocalized when these excitations are taken into account. This concerns long-range as well as local atomic interactions. To characterize the region of stability, the Lindemann criterion is used.

Figure 1

Integrand of the last equation in Appendix pp2 as a function of temperature $T$ (in units of the hopping energy), describing the increase in phonon fluctuations with rising temperature, for $\sqrt{h_1^2+h_2^2}=0.01$, 0.8, and 1 (from bottom to top), $d=3$, and $\mu =1.2$.