Waveguide quantum electrodynamics with non-negligible delay between emitters.
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Date
2026
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Publisher
Universidad de Concepción
Abstract
Con justa razón, la aproximación de Markov ha sido clave para el estudio de la física de muchos cuerpos, ya que provee un marco conveniente para describir los sistemas cuánticos abiertos a través de una ecuación maestra de Lindblad que permite elucidar dinámica del sistema dejando de lado la complejidad del ambiente. Esta aproximación puede volver errónea en el contexto guías de onda, donde se considera un sistema de muchos cuerpos acoplados a un ambiente común que permite una interacción entre emisores lejanos. Si estos emisores están lo suficientemente lejanos (con respecto a la longitud de coherencia del campo emitido por uno de estos), entonces la aproximación de Markov falla, al no tomar en cuenta el retraso en la interacción de ambos emisores. Este retraso, que surge de la velocidad finita de propagación en la guía de onda, es justamente el efecto de la memoria en el sistema; el estado del sistema en el futuro depende de su estado en el pasado. En esta tesis exploramos cómo es la dinámica de un conjunto de sistemas atómicos de dos niveles acoplados a una guía de onda, donde el tiempo de propagación de la luz entre un átomo y otro no es despreciable. Homologamos fenómenos tales como la sub y superradiancia, típicamente estudiados bajo ambientes sin memoria, al régimen no-Markoviano. En el proceso encontramos leyes de potencia y comportamientos críticos que invitan a pensar en analogías con sistemas pertenecientes a la física estadística. Hacia el final, exploramos la simulación de un sistema experimental para la implementación de una condición fundamental para el estudio de efectos colectivos: la condición de Bragg.
The Markov approximation has, for good reason, been a cornerstone in the study of many-body physics, since it provides a convenient framework for describing open quantum systems through a Lindblad master equation which elucidates the dynamics of the system overlooking the environment complexity. This approximation might become fallacious in the context of waveguides, where a system of many bodies is considered to be coupled to a common environment which allows long-range interactions. When the separation between emitters becomes sufficiently large compared with the coherence length of the emitted field, the Markov approximation breaks down because it neglects the finite propagation time required for information to travel between them. This propagation delay, arising from the finite speed of light in the waveguide, is precisely the origin of memory effects in the system: its future evolution depends on its past state. In this thesis, we investigate the dynamics of an ensemble of two-level atoms coupled to a waveguide, focusing on the regime in which the propagation time of light between atoms cannot be neglected. We extend collective phenomena such as superradiance and subradiance, traditionally studied in memory-less environments, to the non-Markovian regime. In doing so, we uncover power-law behaviors and critical phenomena that suggest intriguing analogies with systems studied in statistical physics. Finally, we investigate the simulation of an experimental platform capable of realizing one of the fundamental conditions for the observation of collective effects: the Bragg condition.
The Markov approximation has, for good reason, been a cornerstone in the study of many-body physics, since it provides a convenient framework for describing open quantum systems through a Lindblad master equation which elucidates the dynamics of the system overlooking the environment complexity. This approximation might become fallacious in the context of waveguides, where a system of many bodies is considered to be coupled to a common environment which allows long-range interactions. When the separation between emitters becomes sufficiently large compared with the coherence length of the emitted field, the Markov approximation breaks down because it neglects the finite propagation time required for information to travel between them. This propagation delay, arising from the finite speed of light in the waveguide, is precisely the origin of memory effects in the system: its future evolution depends on its past state. In this thesis, we investigate the dynamics of an ensemble of two-level atoms coupled to a waveguide, focusing on the regime in which the propagation time of light between atoms cannot be neglected. We extend collective phenomena such as superradiance and subradiance, traditionally studied in memory-less environments, to the non-Markovian regime. In doing so, we uncover power-law behaviors and critical phenomena that suggest intriguing analogies with systems studied in statistical physics. Finally, we investigate the simulation of an experimental platform capable of realizing one of the fundamental conditions for the observation of collective effects: the Bragg condition.
Description
Tesis presentada para optar al grado de Doctor/a en Ciencias Físicas.
Keywords
Quantum optics, Waveguides, Atomic physics