Spectral backbone of excitation transport in ultracold Rydberg gases

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 inter-atomic 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.

Statistical benchmark for BosonSampling

“…The former concern all effects related to the structure of state space (e.g., bunching for bosons, and the Pauli exclusion principle for fermions), whereas the latter involve all sorts of interference effects. One can divide these interferences into the well-known single-particle interference [23], encoded within the matrix U, which arises due to the wave-like nature of quantum transport [24][25][26], and the far more intricate many-body interference [15,16,27]. Below, we shall scrutinise the interference exhibited by various particle types-bosons, fermions, distinguishable particles and simulated bosons.…”

Arrested relaxation in an isolated molecular ultracold plasma

“…Under these conditions, each Rydberg molecule undergoes an excitonic interaction with its nearest neighbour [48][49][50][51], either a Rydberg molecule in a different high-n, high-l electronic state or an ion in the field formed by the quasi-continuum of electrons bound to multiple charge centres. Importantly, every such interaction in the bifurcated plasma randomly pairs two molecules in different excited states to define a unique, resonant close-coupled interaction.…”

Charge and spin diffusion on the metallic side of the metal-insulator transition: A self-consistent approach

“…The symmetries (15)(16) of the hopping amplitude matrix V, from which the diagrammatic expansion forŨ is constructed, determine the abovestated transformation properties of the latter. Solving the linear system of equations (39) for the matrix elements ofŨ(ε, ω, 0), we obtain the general form…”