Rydberg Atoms & Quantum Integrability Depend on Initial State

Researchers at Université Paris-Saclay and the Institut Universitaire de France have demonstrated that the line between predictable and chaotic behavior in quantum systems isn’t fixed, but depends on how a system begins. The team’s work with Rydberg atom chains reveals that integrable and non-integrable dynamics can coexist within the same system, determined by the initial state of the atoms. They studied the dynamics generated by a protocol and found a sharp qualitative change in behavior as particle density varied, suggesting control over the degree of integrability breaking, allowing access to both weaker and stronger non-integrable dynamics within a single Hamiltonian. Their findings provide clear and concrete evidence that integrability breaking is not solely a property of the Hamiltonian and of the magnitude of the couplings that break integrability, but also of the state in which the system is prepared.

Integrable-Non-Integrable Coexistence in Rydberg-Atom Chains

Rydberg atom chains exhibit a surprising fluidity in their behavior, shifting between predictable and chaotic dynamics depending on how they are initially prepared. Researchers affiliated with Université Paris-Saclay and the Institut Universitaire de France have shown that these chains, composed of atoms excited to a high energy Rydberg state, can simultaneously display characteristics of both integrable and non-integrable systems, a finding that challenges conventional understanding of how complexity arises in quantum mechanics. This isn’t simply a matter of tuning the strength of interactions; the initial state of the system itself dictates the degree of order or disorder. The foundation of this behavior lies in the interactions between the Rydberg atoms. When modeled with only nearest-neighbor interactions, the system effectively behaves as with ballistic transport. However, the inclusion of longer-range couplings fundamentally alters this picture, introducing and breaking the conservation laws that define integrability.

We studied the dynamics generated by a bipartition protocol and revealed a sharp qualitative change in behavior as the particle density is varied, suggesting a precise control over the balance between order and chaos within the same physical system. Comparatively little attention has been paid to the role of the initial state in the relaxation process when addressing the long-standing problem of thermalization in quantum many-body systems. We identified the configurations whose dynamics exhibit a ballistic behavior that is well captured by effective free-fermion models; more generally, however, this simple picture breaks down.

Recent advances in manipulating Rydberg atom chains have opened new avenues for exploring the subtle boundary between quantum systems exhibiting integrable and non-integrable behaviors. Researchers affiliated with Université Paris-Saclay and the Institut Universitaire de France are showing that these two seemingly distinct dynamical regimes can, in fact, coexist within the same physical system, contingent upon the initial state used to prepare it. This challenges the conventional understanding of integrability as an inherent property solely dictated by the system’s Hamiltonian, the mathematical description of its total energy. The foundation of this work lies in the dipolar XY model, a framework successfully used to describe the dynamics of experimentally realized Rydberg atom chains. Within a simplified approximation, considering only nearest-neighbor interactions, the model’s behavior can be elegantly mapped onto an integrable Fermi gas with ballistic transport.

Integrability Breaking via Longer-Range Couplings

Gianluca Morettini and colleagues affiliated with Université Paris-Saclay are investigating how the boundaries between predictable and chaotic quantum systems can blur, specifically within chains of Rydberg atoms. Their recent work shows that within these systems, integrability, the property of a system to evolve predictably with ballistic transport, isn’t simply present or absent, but can coexist with non-integrability, depending on how the system is initially prepared. The foundation of this research lies in modeling Rydberg atoms, which experience strong dipolar interactions. When limited to nearest-neighbor interactions, the model behaves as an “integrable Fermi gas with ballistic transport.” However, the researchers found that incorporating even weak interactions between atoms further apart fundamentally alters this behavior.

These extended interactions introduce mechanisms that shift the system away from predictable ballistic motion, toward what is known as diffusive transport. The researchers emphasize that this isn’t simply about the strength of the interactions, but rather the system’s initial configuration. Researchers affiliated with Université Paris-Saclay and the Institut Universitaire de France identified the configurations whose dynamics exhibit a ballistic behavior that is well captured by effective free-fermion models; more generally, however, this simple picture breaks down.

Researchers affiliated with Université Paris-Saclay and the Institut Universitaire de France are discovering that the boundary between order and disorder isn’t a sharp line, but rather a complex region where both integrable and non-integrable behaviors can coexist, a phenomenon with echoes of the Kolmogorov, Arnold, Moser (KAM) theorem from classical mechanics. Specifically, researchers affiliated with a team led by Gianluca Morettini at Université Paris-Saclay have found that seemingly small changes in preparation can unlock fundamentally different behaviors within the same physical system. Their investigations center on Rydberg atoms, which interact strongly via dipolar forces, and they study the dynamics generated by a bipartition protocol. The ability to engineer initial states that promote or suppress integrability opens exciting possibilities for quantum simulation and a deeper understanding of the transition from order to chaos in isolated quantum systems.

Rydberg atom interactions reveal a surprising link between initial state and system integrability. Recent investigations into Rydberg atom chains demonstrate that whether a system exhibits predictable, integrable dynamics or chaotic, non-integrable behavior isn’t solely determined by the underlying physics, the Hamiltonian, but also by how the system is initially prepared. Researchers affiliated with Université Paris-Saclay and the Institut Universitaire de France have been studying the dynamics generated by a bipartition protocol and found a sharp qualitative change in behavior as the particle density is varied. A key aspect of this research lies in the analysis of two-particle scattering within the Rydberg atom chain. The study finds that, under certain conditions, incoming quasiparticles can scatter into multiple outgoing states, a phenomenon constrained by energy and momentum conservation, with ballistic transport.