Ground state of the Frenkel–Kontorova model with a globally deformable substrate potential

Abstract

The classical ground state of the Frenkel–Kontorova model is investigated for the case of a globally deformable substrate potential, whose amplitude is a function of the position of all particles. This system serves as an idealised description of a one-dimensional crystal of trapped ions in an optical cavity, where the deformable potential originates from the cavity back action due to the dynamical Stark shift. In the limit of a low relative substrate depth, a sine-Gordon field theory is obtained with coefficients that are functionals of the chain configuration. It is shown that the back action modifies the phase diagram, where the order and scaling of the phase-transition can be controlled by the cavity parameters. Due to the back action, the kinks, which constitute topological soliton solutions in the sine-Gordon model, are shown to exhibit two stable profiles with qualitatively different properties. The choice between the stable configurations is made collectively, all kinks taking either one form or the other.