Theory of quantum systems

Abstract:

We investigate the possibility of engineering dissipatively long-range order that is robust against heating in strongly interacting fermionic systems, relevant for atoms in cavity QED. It was previously shown [Tindall ] that it is possible to stabilize long-range order in a Hubbard model by exploiting a dissipative mechanism in the Lindblad limit, this latter being valid for spectrally unstructured baths. Here, we first show that this mechanism still holds when including additional spin-exchange interactions in the model, that is, for the tUJ model. Moreover, by means of a Redfield approach that goes beyond the Lindblad case, we show how the stability of the engineered state depends crucially on properties of the bath spectral density and discuss the feasibility of those properties in an experiment.

Abstract:

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D\propto 1/\rho$ at low densities $\rho$ . Our numerical approach generalizes the Dissipation-Assisted Operator Evolution algorithm: in the spirit of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we effectively approximate nonlocal operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low-temperature transport.

Abstract:

Disordered potentials fundamentally affect transport and coherence in quantum systems, giving rise to a Bose-glass phase in interacting bosonic systems—an insulating yet compressible phase lacking long-range coherence. Directly measuring a reduced coherence length of the Bose glass has been a outstanding challenge. We address this by employing Talbot interferometry combined with single-atom-resolved detection in a quantum-gas microscope. Using ultracold bosonic atoms in a two-dimensional lattice with site-resolved, reproducible disorder, we identify the Bose-glass phase through density distributions and particle-number fluctuations, quantified via the Edwards-Anderson parameter, and through the visibility of interference patterns after time of flight. By driving the system across the Bose-glass phase, we further observe signatures of nonergodic dynamics. Our studies provide a starting point to further explore disordered systems in and out of equilibrium, and are relevant for understanding the dynamics and stability of disordered and glasslike quantum states in solid-state systems.

Abstract:

Neutral atom arrays have emerged as a versatile candidate for the embedding of hard classical optimization problems. Prior work has focused on mapping problems onto finding the maximum independent set of weighted or unweighted unit disk graphs. In this paper we introduce a new approach to solving natively-embedded vertex graph coloring problems by performing coherent annealing with Rydberg-qudit atoms, where different same-parity Rydberg levels represent a distinct label or color. We demonstrate the ability to robustly find optimal graph colorings for chromatic numbers up to the number of distinct Rydberg states used, in our case k = 3. We analyze the impact of both the long-range potential tails and residual inter-state interactions, proposing encoding strategies that suppress errors in the resulting ground states. We discuss the experimental feasibility of this approach and propose extensions to solve higher chromatic number problems, providing a route towards direct solution of a wide range of real-world integer optimization problems using near-term neutral atom hardware.