Dynamically Enabled Robustness of Geometric Phases and Entanglement in the Nonlinear Jaynes-Cummings Model

TL;DR

This paper reveals a geometric criterion for protecting geometric phases and entanglement in nonlinear light-matter systems by aligning coherent and dissipative trajectories, enhancing robustness against environmental effects.

Contribution

It introduces a dynamic mechanism linking stability of quantum features to trajectory alignment in Hilbert space within the nonlinear Jaynes-Cummings model.

Findings

Environmental action can reshape state-space geometry rather than just cause decoherence.

Protection of quantum features occurs when dissipation preserves the structure of unitary dynamics.

Alignment of coherent and dissipative trajectories enables robustness of geometric phases and entanglement.

Abstract

Robustness in dissipative light-matter systems has recently been associated with resonance conditions or geodesic evolution. We show that, in the nonlinear Jaynes-Cummings model, these conditions are necessary but not sufficient. Using a Kerr-type extension together with a Lindblad description of cavity losses and atomic decoherence, we identify a dynamically enabled mechanism in which the stability of geometric phases and entanglement is governed by the alignment between coherent and dissipative trajectories in Hilbert space. Our results reveal that environmental action does not merely suppress quantum features, but reshapes the geometry of state-space evolution: protection emerges only when dissipation preserves the structure of the underlying unitary dynamics. This establishes a general geometric criterion for decoherence resilience in nonlinear light-matter systems and provides guiding principles for engineering protected evolution in open quantum platforms.