Entangled states of the light: interference as a symmetry problem

Abstract

Recently, the interference pattern, first observed by Thomas Young in 1804, has been obtained and understood within the framework of quantum optics through light–matter interactions, in which both light and matter are quantized. To this end, multiple fields interact simultaneously with the same material system, such that the superposition of these interactions gives rise to nontrivial detection outcomes. From this perspective, interference is a collective phenomenon. Based on this premise, this thesis develops a unified formalism that shows how symmetry relations are connected to interference effects. As a motivating and technologically relevant case, we analyze reset dynamics in a generic quantum computing and show that collective effects and symmetry relations can dominate the evolution due to shared couplings. Employing tunable features of the device, time-dependent symmetry relations are engineered to dynamically alter the brightness of collective states, enabling the reset of any initial state. In quantum optics, interference effects can be understood as a symmetry problem between the detectable and undetectable components of the field. For coherent and single-photon multimode fields, we derive phase conditions that distinguish bright and dark states, revealing the predominance of the latter. In diffraction gratings, this accounts for the extent of dark regions, where local phases give rise to dark states (zero intensity), while also explaining the high intensity observed in bright fringes. The same reasoning reinterprets cavity pulses as temporal interference between stationary modes, rather than as energy flow, suggesting new insights into the relationship between field intensity and its energy. By extending the analysis to collective thermal states, it is verified that a significant fraction of the energy can remain in dark modes even after interaction with the other systems. Furthermore, a thought experiment was simulated in order to verify how the breaking of symmetry in the interactions can provide access to the energy stored in dark states. Finally, a more fundamental condition for the emergence of collective effects was discussed. Based on shared interactions, Changes in the dynamics of waves of distinct natures, namely mechanical and electromagnetic, were observed when interactions with a common system were considered, as well as in the dynamics of two non-overlapping electromagnetic waves. Nevertheless, the results obtained were consistent with those of the cases previously studied under more restrictive conditions.