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Physical Review Letters

Atom Counting Statistics in Ensembles of Interacting Rydberg Atoms

Tara Cubel Liebisch, Aaron Reinhard, P. R. Berman, Georg A. Raithel

Published Dec 13, 2005• 199 citations
Publisher

Abstract

We show that the probability distributions for the number of Rydberg excitations in small ensembles of cold atoms, excited using short (100 ns) laser pulses, can be highly sub-Poissonian. The phenomenon occurs if the atom density and the principal quantum number of the excited Rydberg level are sufficiently high. Our observations are attributed to a blockade of the Rydberg atom excitation.

DOI
10.1103/physrevlett.95.253002

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•Jan 1, 2007•0 citations
We show that the probability distributions for the number of Rydberg excitations in small ensembles of cold atoms, excited using short (100 ns) laser pulses, can be highly sub-Poissonian. The phenomenon occurs if the atom density and the principal quantum number of the excited Rydberg level are sufficiently high. Our observations are attributed to a blockade of the Rydberg atom excitation.
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.
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.
We provide evidence for the dipole blockade of Rydberg excitation by examining the distributions of the number of Rydberg excitations created in ensembles of interacting Rydberg atoms. We show that, over a range of densities, the Rydberg excitation number distributions become significantly narrower when an applied electric field is used to tune the 85Rb^{85}\mathrm{Rb}85Rb interaction channel $45{D}_{5∕2}+45{D}_{5∕2}\ensuremath{\rightarrow}43F+47{P}_{3∕2}$ into F\"orster resonance. Substantially sub-Poissonian distributions that agree with published theory were achieved using very dense atom samples tuned into F\"orster resonance.
Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly-excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of Rydberg excitations in jamming limits. This yields an explicit relationship between the Mandel Q parameter and the blockade effect, and comparison to measurement data shows strong agreement between theory and experiment.
Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of Rydberg excitations in jamming limits. This yields an explicit relationship between the Mandel Q parameter and the blockade effect, and comparison to measurement data shows strong agreement between theory and experiment.
Atoms excited into states of high principal quantum number, Rydberg atoms, have exaggerated properties such as large size and dipole moments, long lifetimes, and high polarizabilities. These properties can be used to realize a Rydberg excitation blockade in narrow-band photo-excitation (∼ 1 MHz bandwidth) of laser-cooled and trapped atoms. Under ideal conditions, the blockade phenomenon leads to an inhibition of more than one Rydberg excitation in dense samples of atoms. The blockade is useful in a number of applications including quantum information processing, quantum cryptography, and atomic clocks. In this thesis, I discuss experimental investigations of the dependence of the blockade effectiveness on the principal quantum number of the excited Rydberg level, and the Rydberg excitation laser's detuning and intensity. Rydberg-atom counting statistics is used as a technique for measuring the effectiveness of the Rydberg blockade. An important aspect in experiments on the blockade effect is the efficiency of the photo-excitation process used for Rydberg-atom generation. Therefore, the described work deals, in part, with methods of coherent excitation of atoms into and out of Rydberg states. I show that STIRAP (stimulated Raman adiabatic passage) allows us to transfer atoms into Rydberg levels with about 70% excitation efficiency, under the constraints of the present experiment. It is also seen that the excitation efficiency is insensitive to variations in laser pulse intensity and width, as expected for STIRAP. The experimental techniques used to measure the blockade effect using counting statistics and to achieve coherent excitation into Rydberg states, are important for future studies of small atomic systems blockaded to one Rydberg excitation.