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Journal of Physics B Atomic Molecular and Optical Physics

Strong interaction effects on the atom counting statistics of ultracold Rydberg gases

Cenap Ates, Thomas Pohl, Thomas Pattard, Jan Michael Rost

Published May 2, 2006• 61 citations
Publisher

Abstract

Based on simple rate equations for the Rydberg excitation process, we are able to model microscopically the dynamics of Rydberg excitation in ensembles of a large number of ultracold atoms, which is beyond the capabilities of fully ab initio approaches. Our results for the distribution of Rydberg atom numbers are in good agreement with recent experimental data, confirming the quenching of the distribution caused by Rydberg-Rydberg interactions.

DOI
10.1088/0953-4075/39/11/l02

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Based on simple rate equations for the Rydberg excitation process, we are able to model microscopically the dynamics of Rydberg excitation in ensembles of a large number of ultracold atoms, which is beyond the capabilities of fully ab initio approaches. Our results for the distribution of Rydberg atom numbers are in good agreement with recent experimental data, confirming the quenching of the distribution caused by Rydberg-Rydberg interactions.
The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states [M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010); D. Comparat and P. Pillet, J. Opt. Soc. Am. B 27, A208 (2010)]. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations, of which some evidence has been found in previous experiments. Here we present experimental results on the dynamics and the counting statistics of Rydberg excitations of ultracold rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We compare our results with numerical simulations using a novel theoretical model based on Dicke states of Rydberg atoms including dipole-dipole interactions, finding good agreement between experiment and theory.
In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^
Ultracold atomic gases excited to strongly interacting Rydberg states are a promising system for quantum simulations of many-body systems. The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states. We have measured the Rydberg excitation for rubidium ultracold atoms in magneto-optical traps and for Bose-Einstein condensates loaded into quasi one-dimensional traps. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations. We have obtained experimental results on the dynamics and the counting statistics of Rydberg excitations of ultra-cold Rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We have found strongly bimodal counting distributions in the offresonant regime.
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.
Ultracold gases excited to strongly interacting Rydberg states are a promising system for quantum simulations of many-body systems. For off-resonant excitation of such systems in the dissipative regime, highly correlated many-body states exhibiting, among other characteristics, intermittency and multimodal counting distributions are expected to be created. Here we report on the realization of a dissipative gas of rubidium Rydberg atoms and on the measurement of its full counting statistics and phase diagram for both resonant and off-resonant excitation. We find strongly bimodal counting distributions in the off-resonant regime that are compatible with intermittency due to the coexistence of dynamical phases. Our results pave the way towards detailed studies of many-body effects in Rydberg gases.