Quantum-to-classical transition of non-Gaussian bosonic systems in non-markovian dynamics

Abstract

Non-Gaussian bosonic states offer resources that are inaccessible to Gaussian states and essential for quantum applications such as quantum computing and error correction. However, their fragility raises the question of whether their key features can survive realistic environments. Reservoirs with memory are promising candidates for state protection, since they can induce revivals of those features. This thesis investigates that mechanism within quantum Brownian motion (QBM), the minimal archetype of a structured bosonic environment and the standard description of a broad range of experimental platforms. QBM has the further advantage of remaining exactly tractable despite describing dynamics that are simultaneously non-Gaussian and non-Markovian. Our main methodological result is a set of closed expressions for the purity, the coherence, the non-Gaussianity and the Wigner function of the cat state and its two squeezed generalisations, valid for any environment of this class. Applying them to a bath with a band gap shows that the structure of the environment, rather than the strength of its coupling, decides what survives: part of the dynamics is trapped in an undamped bound mode–a mechanism already observed experimentally–which generates revivals that keep recurring at arbitrarily long times. However, the protection is only partial, since the gap shields the system from dissipation but not from thermal noise, which still degrades the superposition. Finally, we show that squeezing redistributes robustness among these features, so that no single squeezing is optimal for all of them at once.