Diffusive to Nonergodic Dipolar Transport in a Dissipative Atomic Medium

We investigate the dipole-mediated transport of Rydberg impurities through an ultracold gas of atoms prepared in an auxiliary Rydberg state. In one experiment, we continuously probe the system by coupling the auxiliary Rydberg state to a rapidly decaying state that realizes a dissipative medium. In situ imaging of the impurities reveals diffusive spreading controlled by the intensity of the probe laser. By preparing the same density of hopping partners, but then switching off the dressing fields, the spreading is effectively frozen. This is consistent with numerical simulations, which indicate the coherently evolving system enters a nonergodic extended phase. This opens the way to study transport and localization phenomena in systems with long-range hopping and controllable dissipation.

Figure 1

Setup for studying dipolar-mediated excitation transport in a controllable dissipative medium. (a) Sketch of the experimental geometry and level scheme used to prepare the Rydberg impurities and background gas and to observe transport. (b) The experimental sequence starts exciting a small number of impurities at the center of an ultracold atomic gas. We then couple a larger volume of atoms to a second Rydberg state via an EIT resonance. The presence of impurities is signaled by increased absorption on the probe laser. Different transport behavior is observed depending on whether the probe laser is left on continuously or pulsed.

Figure 2

Transport of Rydberg impurities under continuous and pulsed observation. (a) Density plots of the spatial distribution of impurities along the axial $x$ direction as a function of time under continuous observation for $R_{\mathrm{sc}}/2\pi =250\mathrm{kHz}$. (Upper) The experimental measurements. (Lower) Corresponds to the solution to the classical diffusion law. (b) Corresponding density plots for the case of pulsed observation showing the absence of diffusion. (Lower) Gaussian distribution determined by the preparation and probe periods with no dynamics during the evolution period. The dotted green lines in (a) and (b) depict the time-dependent widths of the distribution from the respective time-evolution model. (c) Measured mean square deviation $⟨x^2⟩$ as a function of the total time, which is the sum of the free evolution time and the exposure time for imaging. The solid lines are fits to the diffusion law showing diffusive (linear) and frozen (constant) dynamical evolution. (Inset) The stationary density profile obtained averaging the data shown in (b). The dashed line shows a fit to a Gaussian distribution and the solid black line shows a fit to Gaussian with exponential wings expected from theory.

Figure 3

Linear dependence of the diffusion coefficient of the dissipative medium on the squared probe Rabi frequency ${\mathrm{\Omega }}_p$.

Figure 4

Numerical simulations of the dipolar hopping Hamiltonian showing the inverse participation ratio and fractal dimension at late times as a function of the system size assuming purely coherent evolution under dipolar exchange interactions. Different symbols correspond to the moments $I_q$ of the wave function defined in the text. (Inset) Fractal dimension $D_q$ as a function of $q$ obtained from power law fits to $I_q$ for large system sizes. The solid line corresponds to $D_q=1$ for ergodic states.