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.
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.
We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of the (cavity) electromagnetic field, in a perfect or dissipative cavity, respectively. In the dissipative model, the nonunitary effects arise from the outflow of photons through the cavity walls and the incoherent pumping of the two-level system. Our approach allows to compare the geometric phases acquired in these models, leading to an exhaustive characterization of the corrections introduced by the presence of the environment. We also provide geometric interpretations for the observed behaviors. When the resonance condition is satisfied, we show the geometric phase is robust, exhibiting a vanishing correction under a nonunitary evolution. This fact is supported with a geometrical explanation as well.
The analytical description of the dynamics of a nonlinear atom-field system described by a diagonal f -deformed Jaynes-Cummings model for a chosen initial state is obtained. The purity loss of the global system, and the atomic and field subsystems are discussed. Information on entanglement between the field and matter is studied by comparing the results for mutual entropy, which is a measure of the total correlation, and the negativity as a measure of the amount of entanglement. It is found that the nonlinearity of the dissipation tends to accelerate the decoherence of the global, field, and atomic states. In addition, we find that the so-called entanglement sudden death can occur when both of the nonlinearity couplings between the cavity field and the dissipation are combined. Subject Index: 061
We investigate the dynamics of Einstein-Podolsky-Rosen (EPR) steering in a double Jaynes-Cummings model, where two initially entangled spatially separated two-level atoms in two cavities interact with independent cavity modes. We study how the intrinsic noise in an initial Werner-type state affects the steering dynamics in this type of quantum optical system. We also analyze the evolution of steering under experimentally relevant conditions, including atom-cavity detuning and dipole-dipole interactions. We find that both detuning and dipole-dipole coupling help reduce steering sudden death in the system. We further identify a direct correlation between steering and state fidelity, revealing a threshold below which steering disappears. This suggests that fidelity may serve as a practical indicator of steerability in cavity QED systems. Our results provide insight into the controllability and robustness of non-classical correlations in realistic light-matter platforms.
Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.
The full quantum theory is applied to the investigation of the entanglement between atom and field and the losses of coherence of the total system and its subsystems in the Jaynes-Cummings model with a Kerr medium.Linear entropies of the system,the atom and the field are calculated under the assumptions of dispersive atom-field interaction and initial coherent field states.The results show that the coherence loss of the atom is independent of the Kerr effect,the coherence loss of the system and that of the field are enhanced by the presence of the Kerr medium,and the entanglement between atom and field is suppressed by the medium.The time evolution of field entropy is affected by the cavity dissipation qualitatively as well as quantitatively.Only through cavity dissipation can the influence of Kerr effect on field entropy exhibit.
The ability to prepare and manipulate non-classical states, such as entangled qubits, is fundamental to the development of quantum information processing, communication, and computation. In this work, we investigate the dynamics of a double Jaynes-Cummings model, a well-established theoretical framework for studying light-matter interactions that captures essential features of a wide range of quantum systems, including circuit QED, optomechanics, and atomic cavity systems. We examine the model under the influence of Markovian noise and static (glassy) cavity disorder. The study aims to elucidate the impact of these imperfections on entanglement dynamics. The system is initialized with the cavity fields in vacuum and the two atoms in a specific entangled superposition state. Through numerical simulations, we observe that the presence of noise and nonlinear pumping gives rise to nontrivial features in the entanglement evolution, including the emergence of entanglement sudden death (ESD) and subsequent revivals in scenarios where such phenomena are absent in the idealized model. Markovian noise leads to a monotonic decay of entanglement, while disorder tends to wash out the entanglement features. Nonlinear interactions, on the other hand, accelerate the dynamical evolution. The combined and competing effects of noise, disorder, and nonlinearity are systematically analyzed, revealing rich and intricate behavior in the entanglement dynamics. These results contribute to a deeper understanding of the robustness and control of entanglement in open quantum systems with imperfections, which is essential for realistic implementations of quantum technologies.