Multi Quanta Relaxation and Nonclassicality of Nonlinear Oscillators

Doctoral thesis, 2014

The focus of the study is the free quantum evolution of Duffing oscillators which are nonlinearly coupled to bosonic environments. The work evolves from a particular system of an undamped, nonlinear graphene resonator mode to a more generalized framework of oscillator modes interacting with two different configurations of bosonic environments. In a model with no dissipation, the nonlinear Duffing oscillator allows an initial coherent state to evolve into a macroscopic superposition state, a Schrödinger Cat state. By further subjecting a Duffing mode to nonlinear damping, the parity conservation due to the two-quanta system-bath exchange, brings the system to a nonclassical steady state - an equilibrium state very much different from the ground state. The quantum features of this state are analysed for temperatures above zero and in a more realistic scenario where the interplay of linear and nonlinear decay is taken into account. The scope of the study is then extended to bipartite systems of nonlinear interacting oscillators, each nonlinearly coupled to a bosonic environment. The generation of entanglement in initially separable states and entanglement's asymptotic behaviour are investigated. One of the outcomes is the Duffing nonlinearity not affecting the entanglement asymptote. Therefore, finally a bipartite system of harmonic oscillators, with nonlinear system-bath coupling is initiated with entangled, squeezed states, and the asymptotic behaviour is evaluated in the parameter space of temperature, squeezing and dissipation rate. This is done for common and individual reservoir configurations, and either zero or non-zero inter-mode coupling.