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arXiv:2001.05579 · Journal of Physics B Atomic Molecular and Optical Physics

Three-level rate equations in cold, disordered Rydberg gases

R V Skannrup, T v Weerden, Y vd Werf, T Johri, E J D Vredenbregt, S. J. J. M. F. Kokkelmans

Published Feb 11, 2020• 1 citation
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Abstract

Abstract We have investigated formation of structures of Rydberg atoms excited from a disordered gas of ultracold atoms, using rate equations (REs) for two-photon Rydberg excitation in a single atom without eliminating the intermediate state. We have explored the validity range of these REs and defined a simple measure to determine, whether our model is applicable for a given set of laser parameters. We have applied these REs in Monte Carlo simulations of ultracold gases, for different laser beam profiles, and compared these simulations to experimental observations and find a general agreement.

DOI
10.1088/1361-6455/ab7525

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Abstract We have investigated formation of structures of Rydberg atoms excited from a disordered gas of ultracold atoms, using rate equations (REs) for two-photon Rydberg excitation in a single atom without eliminating the intermediate state. We have explored the validity range of these REs and defined a simple measure to determine, whether our model is applicable for a given set of laser parameters. We have applied these REs in Monte Carlo simulations of ultracold gases, for different laser beam profiles, and compared these simulations to experimental observations and find a general agreement.
We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases,with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in qualitative agreement with experiment. Possible sources of quantitative discrepancy are carefully examined. Based on the two-step excitation scheme, we predict the occurrence of an antiblockade effect and propose possible ways to detect this excitation enhancement experimentally in an optical lattice, as well as in the gas phase.
Inevitably present in many current experiments with ultracold Rydberg atoms, dissipative effects such as dephasing and decay modify the dynamics of the examined system. In this thesis, the dynamics of many-body Rydberg systems in the incoherent regime is studied numerically. Specifically, a wave function Monte Carlo (MCWF) technique is integrated into a coherent two-level many-body Rydberg model, allowing a numerical simulation of dissipative dynamics. This model is used to benchmark a steady-state rate equation model and assess its range of validity. In addition, incoherent, off-resonant excitation dynamics is studied in a one-dimensional disordered geometry. We find that our simulation results can essentially be explained by the equilibration time scale as well as — for positive laser detuning — resonant excitations arising when the laser detuning compensates the Rydberg interaction. Eventually, we employ a rate equation model to investigate excitation spectra for an experimental trap geometry, which we benchmark using the MCWF technique. Based on numerical data, we deduce that in the considered parameter regime the dominant excitation mechanism can be characterized as sequential growth of aggregates of Rydberg excitations around an initial seed. Our simulation results highlight the impact of incoherent effects on observables such as Rydberg population, excitation number fluctuation and pair correlation function.
It is shown that the two-step excitation scheme typically used to create an ultracold Rydberg gas can be described with an effective two-level rate equation, greatly reducing the complexity of the optical Bloch equations. This allows us to efficiently solve the many-body problem of interacting cold atoms with a Monte Carlo technique. Our results reproduce the observed excitation blockade effect. However, we demonstrate that an Autler-Townes double peak structure in the two-step excitation scheme, which occurs for moderate pulse lengths as used in the experiment, can give rise to an antiblockade effect. It is most pronounced for atoms arranged on a lattice. Since the effect is robust against a large number of lattice defects it should be experimentally realizable with an optical lattice created by CO2 lasers.
A statistical analysis of the laser excitation of cold and randomly distributed atoms to Rydberg states is developed. We first demonstrate with a hard-ball model that the distribution of energy level shifts in an interacting gas obeys L\'evy statistics in any dimension ddd and for any interaction $\ensuremath{-}{C}_{p}/{R}^{p}$ under the condition d/p<1d/p<1d/p<1. This result is confirmed with a Monte Carlo rate equations simulation of the actual laser excitation in the particular case p=6p=6p=6 and d=3d=3d=3. With this finding, we develop a statistical approach for the modeling of probe light transmission through a cold atom gas driven under conditions of electromagnetically induced transparency involving a Rydberg state. The simulated results are in good agreement with experiment.
We present extensive Monte Carlo calculations of electron-impact-induced transitions between highly excited Rydberg states and provide accurate rate coefficients. For moderate energy changes, our calculations confirm the widely applied expressions in P. Mansbach and J. Keck [Phys. Rev. 181, 275 (1969)] but reveal strong deviations at small energy transfer. Simulations of ultracold plasmas demonstrate that these corrections significantly impact the short-time dynamics of three-body Rydberg atom formation. The improved rate coefficients yield quantitative agreement with recent ultracold plasma experiments.