Transfer dynamics of a quasiparticle in a nonlinear dimer coupled to an intersite vibration: Chaos on the Bloch sphere.

Abstract

The quasiparticle transfer in a coupled nonlinear dimer-vibration system is analyzed. The quasiparticle is subjected to both an intrasite cubic polarization nonlinearity and an intersite vibration. The system is a realization of a Hamiltonian flow on the foliated phase space represented by the Bloch sphere (density-matrix dynamics of the quasiparticle) and the plane (state of the oscillator). The analysis is performed starting from the uncoupled case for which the Hamiltonian flow on the Bloch sphere is characterized by a homoclinic structure for polarization strength above a critical value dividing the solutions into two different classes of partially trapped and untrapped transfer behavior. Then the modifications for a finite coupling, in particular, how chaos on the Bloch sphere develops, are investigated in detail, applying the Melnikov method and direct numerical integration for increasing coupling strength. The development of chaos on the Bloch sphere implies a transition from partially trapped to untrapped transfer behavior, destroying quasiparticle self-trapping.