Decoherence Properties of Qubits and Oscillators Coupled to Minimal Environments

Decoherence refers to the loss of quantum coherence through contact with the environment. We are interested in characterizing this decoherence in models of simple quantum systems interacting with a minimal environment, following the work of Vidiella-Baranco [Physica A 402, 209 (2014) & Physica 459,78 (2016)]. We work out the full exact dynamics or approximations to the exact dynamics for coupled systems of qubits, oscillators, and mixed systems of qubits with oscillators. We then trace over the environment degrees of freedom and extract the decoherence of the reduced system as characterized by its linear entropy and visualize the results with Bloch spheres and Husimi functions. We relate decoherence rates to coupling strength. We also observe similarities and differences between solutions for couplings corresponding to the rotating and counter-rotating wave approximations. We notice in particular the disappearance of periodicity above a critical coupling strength in the counter rotating coupling in the oscillator case.