arXiv subjects

Greta Villa

Publications and source records attributed to Greta Villa.

4 recordsLinked to original sources

arXiv2025

Flow topology classification of limit cycles

Recent topological tools offer a powerful way to classify how phases of nonlinear bosonic resonators are organized. Yet, they remain incomplete. In particular, self-sustained oscillations in the form of limit cycles act as robust organizing centers in phase space that are not captured by existing fixed-point-based approaches. In this work, we extend the flow topology framework for nonlinear resonators to include limit cycles as fundamental topological elements. Using a graph-based construction, we show how periodic attractors impact the global connectivity of phase-space flows. We illustrate the approach with a minimal nonlinear Van der Pol resonator model, where limit cycles coexist with stationary points. Our results provide a unified topological description of stationary and time-periodic phases in nonlinear bosonic systems, with direct relevance to photonic, superconducting, and optomechanical platforms, and raise new questions on synchronization and the extension of flow topology to the quantum regime.

cond-mat.mes-hall↗

arXiv2025

Manifestations of flow topology in a quantum driven-dissipative system

In driven-dissipative bosonic systems, the interplay between coherent driving, inter-particle interactions and dissipation leads to a rich variety of non-equilibrium stationary states (NESS). In the semiclassical limit, the flow topology of phase-space dynamics governs the stability and structure of these dynamical phases. Consequently, topological transitions occur when the number of NESS, their chirality, or their connectivity changes, reflecting global reorganization in the system's dynamical phase-space landscape. Here, we study the corresponding topological signatures in a driven-dissipative quantum Kerr oscillator. Employing a Lindblad master equation and quantum trajectory methods, we reveal that quantum dynamics retain key topological features of the underlying classical flows, with clear signatures accessible via quantum state tomography and linear response. In this manner, we predict new phases that are not signaled by Liouvillian gap closing, thereby generalizing the conventional criteria for diagnosing phase transitions. Our findings position phase-space flow topology as a powerful tool to identify and control robust quantum phases, enabling advances in error correction and sensing.

quant-ph↗

arXiv2024

Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions

Characterizing topologically nontrivial photonic lattices by measuring their topological invariants is crucial in topological photonics. In conservative one-dimensional systems, a widely used observable to extract the winding number is the mean-chiral displacement. In many realistic photonic systems, however, losses can hardly be avoided, and little is known on how one can extend the mean-chiral displacement to a driven-dissipative context. Here we theoretically propose an experimentally viable method to directly detect the topological winding number of one-dimensional chiral photonic lattices. The method we propose is a generalization of the mean-chiral displacement to a driven-dissipative context with coherent illumination. By integrating the mean-chiral displacement of the steady state over the pump light frequency, one can obtain the winding number with a correction of the order of the loss rate squared. We demonstrate that this method can be successfully applied to lattices along synthetic frequency dimensions.

physics.optics↗

arXiv2024

Topological classification of driven-dissipative nonlinear systems

In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials. Moving beyond linear Hamiltonian systems, the study of topology in physics strives to characterize open (non-Hermitian) and interacting systems. Here, we establish a framework for the topological classification of driven-dissipative nonlinear systems. Specifically, we define a graph index for the Floquet semiclassical equations of motion describing such systems. The graph index builds upon topological vector analysis theory and combines knowledge of the particle-hole nature of fluctuations around each out-of-equilibrium stationary state. To test this approach, we divulge the topological invariants arising in a micro-electromechanical nonlinear resonator subject to forcing and a time-modulated potential. Our framework classifies the complete phase diagram of the system and reveals the topological origin of driven-dissipative phase transitions, as well as that of under- to over-damped responses. Furthermore, we predict topological phase transitions between symmetry-broken phases that pertain to population inversion transitions. This rich manifesting phenomenology reveals the pervasive link between topology and nonlinear dynamics, with broad implications for all fields of science.

cond-mat.mes-hall↗