arXiv subjects

Daniel Brady

Publications and source records attributed to Daniel Brady.

9 recordsLinked to original sources

arXiv2026

Quantum Contact Processes on a Topological Lattice

Contact processes play an important role in classical non-equilibrium dynamics, describing the spreading of diseases, the dynamics of earthquakes and forest fires, and the distribution of information through the internet. Here we show that their quantum counterpart, where the spreading occurs through coherent couplings, displays even richer dynamics and offers new means of control. A quantum contact process on a topologically non-trivial lattice can be confined to a protected subspace corresponding to either a single site or a fully excited lattice. Furthermore, excitation spreading can be controlled to occur in quantized steps and on demand when employing topological pumps. We show that the many-body dynamics of excited domains can be mapped to an effective single-particle model, which also determines the topological properties. Throughout this work, we consider a specific type of contact process corresponding to coherent Rydberg facilitation in a tweezer array of trapped atoms in a one-dimensional lattice.

quant-ph↗

arXiv2025

Dephasing in Rydberg Facilitation Due to State-Dependent Dipole Forces

Rydberg atoms allow for the experimental study of open many-body systems and nonequilibrium phenomena. High dephasing rates are a generic feature of these systems, and therefore they can often be described by rate equations, i.e. in the classical limit. In this work, we analyze one potential origin of the decoherence in Rydberg atoms: dipole-force induced dephasing. As the wave function of the Rydberg (spin-up) state is repelled in the presence of another nearby Rydberg atom, while the ground (spin-down) state diffuses in place, the Franck-Condon overlap between the two spin components quickly decays causing a decoherence of the spin transition. With an analytic approach we obtain a simple expression for the dephasing rate of the Rydberg state depending on atomic and laser parameters, which agrees with numerical findings.

quant-ph↗

arXiv2025

Quantum-Noise Induced Localization and Motional Squeezing in a Rydberg Quantum Simulator

We investigate the interplay between mechanical forces and the internal-state dynamics of Rydberg excitations in atom-tweezer arrays. Dipole interactions between Rydberg atoms facilitate excitation spreading, but at the same time couple electronic (spin) degrees of freedom with motional (phonon) states. With increasing spin-phonon coupling, the growth dynamics of a cluster of excited Rydberg atoms changes from ballistic spreading to Bloch-like oscillations and eventually to Anderson-like localization. We show that these effects are caused by quantum fluctuations in the phonon field: The dynamics of a Rydberg cluster can be mapped to a single particle in a semi-infinite lattice subject to phonon-induced energy shifts. The mean-field contribution of this energy shift leads to a linear potential gradient, resulting into Bloch-like oscillations. In addition, quantum fluctuations of phonons create a random local potential causing a transition from a regime of Bloch oscillations to localization. The spin-phonon coupling leads furthermore to highly correlated and non-classical phonon states in the form of squeezed states of the position of the Rydberg atoms. Depending on the form of the dipolar interaction potential, either in- or out-of-phase correlated oscillations of atoms emerge.

cond-mat.quant-gas↗

arXiv2025

Nonequilibrium Universality of Rydberg-Excitation Spreading on a Dynamic Network

Understanding the universal properties of non-equilibrium phase transitions of spreading processes is a challenging problem. This applies in particular to irregular and dynamically varying networks. We here investigate an experimentally accessible model system for such processes, namely the absorbing-state phase transition (ASPT) of Rydberg-excitation spreading, known as Rydberg facilitation, in a laser-driven gas of mobile atoms. It occurs on an irregular graph, set by the random atom positions in the gas and, depending on temperature, changes its character from static to dynamic. By studying the behavior of the order parameter in [Phys. Rev. Lett. 133, 173401 (2024)] we showed numerical evidence for a crossover from directed percolation (DP) universality through various phases of anomalous directed percolation (ADP) to mean-field (MF) behavior when the temperature of the gas is increased. As the behavior of the order parameter is not sufficient to uniquely determine the universality class, we here analyze the distribution of avalanches - characteristic of non-equilibrium critical behavior - to fully characterize the ASPT. Performing extended numerical calculations and experiments on a cold $^{87}$Rb atom gas we confirm our earlier numerical findings and our phenomenological model that maps the dynamic network to a static one with power-law tails of the distribution of excitation distances. Furthermore we discuss the influence of dissipation, present in the experiment and a necessary ingredient for the self-organization of the system to the critical point. In particular we study the potential modification of the universality class by losses as a function of dissipation strength.

physics.atom-ph↗

arXiv2024

Anomalous Directed Percolation on a Dynamic Network using Rydberg Facilitation

The facilitation of Rydberg excitations in a gas of atoms provides an ideal model system to study epidemic evolution on (dynamic) networks and self organization of complex systems to the critical point of a non-equilibrium phase transition. Using Monte-Carlo simulations and a machine learning algorithm we show that the universality class of this phase transition can be tuned. The classes include directed percolation (DP), the most common class in short-range spreading models, and mean-field (MF) behavior, but also different types of anomalous directed percolation (ADP), characterized by rare long-range excitation processes. In a frozen gas, ground state atoms that can facilitate each other form a static network, for which we predict DP universality. Atomic motion then turns the network into a dynamic one with long-range (Levy-flight type) excitations. This leads to continuously varying critical exponents corresponding to the ADP universality class, eventually reaching MF behavior. These findings also explain the recently observed critical exponent of Rydberg facilitation in an ultra-cold gas experiment [Helmrich et al., Nature 577, 481 (2020)], which was in between DP and MF values.

cond-mat.quant-gas↗

arXiv2023

Mean-field approach to Rydberg facilitation in a gas of atoms at high and low temperatures

The excitation spread caused by Rydberg facilitation in a gas of laser driven atoms is an interesting model system for studying epidemic dynamics. We derive a mean-field approach to describe this facilitation process in the limits of high and low temperatures, which takes into account Rydberg blockade and the network character of excitation spreading in a low-temperature gas. As opposed to previous mean-field models, our approach accurately predicts all stages of the facilitation dynamics from the initial fast epidemic growth, an extended saturation period, to the final relaxation phase.

cond-mat.quant-gas↗

arXiv2023

Griffiths Phase in a Facilitated Rydberg Gas at Low Temperature

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte-Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. In this paper, we analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. While in the high-temperature limit a homogeneous mean-field behaviour is recovered, characteristic effects of heterogeneity can be seen in a frozen gas. At large temperatures the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erd\"os-Renyi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erd\"os-Renyi network taking into account Rydberg blockade. Furthermore, we expand upon an existing macroscopic Langevin equation to more accurately describe the density of Rydberg atoms in the frozen and finite temperature regimes.

cond-mat.quant-gas↗

arXiv2022

Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks

Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many, seemingly unrelated systems, such as forest fires, virus spreading or atomic excitation dynamics. SOC describes the buildup of large-scale and long-range spatio-temporal correlations as a result of only local interactions and dissipation. The simulation of SOC dynamics is typically based on Monte-Carlo (MC) methods, which are however numerically expensive and do not scale beyond certain system sizes. We investigate the use of Graph Neural Networks (GNNs) as an effective surrogate model to learn the dynamics operator for a paradigmatic SOC system, inspired by an experimentally accessible physics example: driven Rydberg atoms. To this end, we generalize existing GNN simulation approaches to predict dynamics for the internal state of the node. We show that we can accurately reproduce the MC dynamics as well as generalize along the two important axes of particle number and particle density. This paves the way to model much larger systems beyond the limits of traditional MC methods. While the exact system is inspired by the dynamics of Rydberg atoms, the approach is quite general and can readily be applied to other systems.

physics.atom-ph↗

arXiv2021

Hamiltonian active particles in an environment

We examine a Hamiltonian system which represents an active Brownian particle that can move against an external force by drawing energy from an internal depot while immersed in a noisy and dissipative environment. The Hamiltonian consists of two subsystems, one representing the active particle's motion and the other its depot of `fuel'. We show that although the active particle loses some of its energy to dissipation from the environment, dissipation can also help to stabilize the dynamical process that makes the particle active. Additionally we show how a Hamiltonian active particle can harvest energy from its environment.

nlin.AO↗