The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type structures, which arise after the release of a localized state inside a quantum cavity, constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Such a released localized state may represent a radiation mode inserted into a multimode interference device or a cold-atom system released in an optical trap, for instance. Here, without losing any generality, for simplicity, the case of a particle with a mass $m$ is considered and described by a localized state corresponding to the ground state of a square box of width $w$, which is released inside a wider cavity (with a width $L>w$). The effects of decoherence are then numerically investigated by means of a simple dynamical model that captures the essential features of the phenomenon under Markovian conditions, leaving aside extra complications associated with a more detailed dynamical description of the system-environment interaction. As it is shown, this model takes into account and reproduces the fact that decoherence effects are stronger as energy levels become more separated (in energy), which translates into a progressive collapse of the energy density matrix to its main diagonal. However, because energy dissipation is not considered, an analogous behavior is not observed in the position representation, where a proper spatial localization of the probability density does not take place, but rather a delocalized distribution. This result emphasizes the fact that classicality is reached only if both decoherence and dissipation coexist; otherwise, nonclassical traits might still persist. Actually, as it is also shown, in the position representation some off-diagonal correlations indeed survive unless an additional spatial-type factor is included in the model. This makes evident the rather complex nature of the decoherence phenomenon and hence the importance to have a familiarity with how it manifests in different representations, particularly with the purpose to determine and design reliable control mechanisms.

• Received 19 March 2021
• Accepted 27 May 2021

DOI:https://doi.org/10.1103/PhysRevA.103.062210