Using system-reservoir methods to derive effective field theories for broadband nonlinear quantum optics: a case study on cascaded quadratic nonlinearities

• URL: http://arxiv.org/abs/2311.03597v1
• Date: Mon, 6 Nov 2023 23:00:47 GMT
• Title: Using system-reservoir methods to derive effective field theories for broadband nonlinear quantum optics: a case study on cascaded quadratic nonlinearities
• Authors: Chris Gustin, Ryotatsu Yanagimoto, Edwin Ng, Tatsuhiro Onodera, Hideo Mabuchi
• Abstract summary: nonlinear interactions among a large number of frequency components induce complex dynamics that may defy analysis. We introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical $\chi^{(2)}$ (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics.

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