Theory of coherent plasmon in one dimensional insulators*

Recent microwave reflection measurements of Josephson junction ladders have suggested the presence of nearly coherent collective charge oscillations deep in the
insulating phase. Here we develop a qualitative understanding of such coherent charge modes by studying the local dynamical charge susceptibility of the insulating phase of the
Sine-Gordon model. By considering parameters near the non-interacting Fermion
limit where the charge operator dominantly couples to soliton-antisoliton bound states of the Sine-Gordon model, we find that the local charge susceptibility shows an array of sharp peaks
in frequency representing coherent plasma oscillations on top of an incoherent background. The strength of the coherent peaks relative to the incoherent background
increases as a powerlaw in frequency whose exponents depend on system parameters. The charge susceptibility also clearly shows the insulating gap. We then compare the controlled results in the high frequency limit to phase-slip-induced decay of
plasmons in the Josephson junction ladder.