The Spectral Backbone of Excitation Transport in Ultra-Cold Rydberg Gases
arXiv:1409.5625 · doi:10.1103/PhysRevA.90.063415
Abstract
The spectral structure underlying excitonic energy transfer in ultra-cold Rydberg gases is studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are of short range, and is ultimately determined by the spectral and eigenvector structure. In the energy levels' spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the relative weight of localized states is reduced. At the same time, the spectral statistics -- in particular, the density of states and the nearest neighbor level spacing statistics -- exhibits a transition from approximately a 1-stable Lévy to a Gaussian orthogonal ensemble. Deviations from random matrix statistics are shown to stem from correlations between interatomic interaction strengths that lead to an asymmetry of the spectral density and profoundly affect localization properties. We discuss approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.
20 pages, 9 figures, accepted as is by Physical Review A
References in corpus (16)
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- Quantum walks of correlated particles
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Quasiclassical calculations of BBR-induced depopulation rates and effective lifetimes of Rydberg nS, nP and nD alkali-metal atoms with n < 80
- Evidence for coherent collective Rydberg excitation in the strong blockade regime
- Dipole blockade in a cold Rydberg atomic sample
- Quantum critical behavior in strongly interacting Rydberg gases
- Spatially resolved observation of dipole-dipole interaction between Rydberg atoms
- Many-body theory of excitation dynamics in an ultracold Rydberg gas
- Quantum Decoherence of the Central Spin in a Sparse System of Dipolar Coupled Spins
- Superfluidity versus Anderson localization in a dilute Bose gas
- On the localization transition in symmetric random matrices
- Eigenvalue distributions of large Euclidean random matrices for waves in random media
- Nonlinear coherent transport of waves in disordered media
- Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials
- Quantum and Classical Superballistic Transport in a Relativistic Kicked-Rotor System