The role of position-momentum correlations in coherence freezing and purity behavior of macromolecular gaussian states

We explore the effects of Markovian bath coupling and initial position-momentum correlations on the coherence and purity of Gaussian quantum states of macromolecules. Our analysis focuses on the roles these factors play in the dynamics of quantum coherence, coherence lengths, and state purity. Our results reveal that initial position-momentum correlations have a remarkable impact on the quantum properties of the mixed state. These correlations lead to opposing behaviors in coherence and purity: as quantum coherence increases in response to stronger correlations, purity diminishes, and vice versa. This inverse relationship illustrates the phenomenon where, governed by these initial correlations, a state with greater mixing can display enhanced quantum coherence compared to a less mixed state. We also observe an unanticipated coherence freezing phenomenon for fullerene matter waves, quantified by the relative entropy of coherence. Notably, the freezing is driven by initial position-momentum correlations, but the final frozen value remains independent of these correlations. Experimental verification of this phenomenon in macromolecules could elucidate fundamental questions and enable new applications.