We study Magnus expansion (ME) approximation scheme for the interaction between an atom and a single quantized cavity mode (Jaynes-Cumming model) in a closed quantum system in resonance or near resonance for a time-dependent coupling coefficient g(t) in both the interaction and rotating picture by implementing a novel numerical method called MG4 and compare out results to the Runge-Kutta 4th (RK4) order solution to demonstrate the conservation of unitary evolution of the ME. A cursory study of open quantum system is given to encourage the study of ME for dissipative systems. Furthermore, we assume that our time-dependent coupling coefficient g(t) can take on two forms, Gaussian and sinusoidal, which are introduced as pulses to study the behavior and response of the cavity. Our results show that ME is a sufficient approximation scheme in our study of closed quantum systems which may have applications in quantum control.
","abstract_html":"<p>We study Magnus expansion (ME) approximation scheme for the interaction between an atom and a single quantized cavity mode (Jaynes-Cumming model) in a closed quantum system in resonance or near resonance for a time-dependent coupling coefficient g(t) in both the interaction and rotating picture by implementing a novel numerical method called MG4 and compare out results to the Runge-Kutta 4th (RK4) order solution to demonstrate the conservation of unitary evolution of the ME. A cursory study of open quantum system is given to encourage the study of ME for dissipative systems. Furthermore, we assume that our time-dependent coupling coefficient g(t) can take on two forms, Gaussian and sinusoidal, which are introduced as pulses to study the behavior and response of the cavity. Our results show that ME is a sufficient approximation scheme in our study of closed quantum systems which may have applications in quantum control.</p>","abstract_has_math":false,"creators":["Jalandoni, Javier"],"institution":null,"degree_name":"Master of Science in Engineering Physics","degree_level":"Thesis - Open Access","degree_discipline":"Physical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-05-01T07:00:00Z","date_published":"2016-05-01T07:00:00Z","updated_at":"2026-07-27T19:26:02Z","subjects":["atoms","photons","quantum control","Quantum Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/217","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Jalandoni, Javier"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Physical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Engineering Physics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["atoms","photons","quantum control","Quantum Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/217"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study Magnus expansion (ME) approximation scheme for the interaction between an atom and a single quantized cavity mode (Jaynes-Cumming model) in a closed quantum system in resonance or near resonance for a time-dependent coupling coefficient g(t) in both the interaction and rotating picture by implementing a novel numerical method called MG4 and compare out results to the Runge-Kutta 4th (RK4) order solution to demonstrate the conservation of unitary evolution of the ME. A cursory study of open quantum system is given to encourage the study of ME for dissipative systems. Furthermore, we assume that our time-dependent coupling coefficient g(t) can take on two forms, Gaussian and sinusoidal, which are introduced as pulses to study the behavior and response of the cavity. Our results show that ME is a sufficient approximation scheme in our study of closed quantum systems which may have applications in quantum control.
"]},{"key":"dc:title","label":"Title","values":["Numerical Case Study of an Atom-Photon Interaction in a Cavity Exploring Quantum Control"]}]}],"canonical_facts":{"dc:creator":["Jalandoni, Javier"],"dc:description.abstract":["We study Magnus expansion (ME) approximation scheme for the interaction between an atom and a single quantized cavity mode (Jaynes-Cumming model) in a closed quantum system in resonance or near resonance for a time-dependent coupling coefficient g(t) in both the interaction and rotating picture by implementing a novel numerical method called MG4 and compare out results to the Runge-Kutta 4th (RK4) order solution to demonstrate the conservation of unitary evolution of the ME. A cursory study of open quantum system is given to encourage the study of ME for dissipative systems. Furthermore, we assume that our time-dependent coupling coefficient g(t) can take on two forms, Gaussian and sinusoidal, which are introduced as pulses to study the behavior and response of the cavity. Our results show that ME is a sufficient approximation scheme in our study of closed quantum systems which may have applications in quantum control.
"],"dc:identifier":["https://commons.erau.edu/edt/217"],"dc:subject":["atoms","photons","quantum control","Quantum Physics"],"dc:title":["Numerical Case Study of an Atom-Photon Interaction in a Cavity Exploring Quantum Control"],"thesis:degree_discipline":["Physical Sciences"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Engineering Physics"]},"updated_at":"2026-07-27T19:26:02Z"}