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arXiv:1202.2871 · Journal of Physics B Atomic Molecular and Optical Physics

An experimental and theoretical guide to strongly interacting Rydberg gases

Robert Löw, Hendrik Weimer, Johannes Nipper, Jonathan B Balewski, Björn Butscher, Hans Peter Büchler, Tilman Pfau

Published May 22, 2012• 289 citations
arXivHTMLPDF

Abstract

We review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, high-lying Rydberg states. The major part is dedicated to highly excited S-states of rubidium, which feature an isotropic van der Waals potential. Nevertheless, the setup and the methods presented are also applicable to other atomic species used in the field of laser cooling and atom trapping.

DOI
10.1088/0953-4075/45/11/113001

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We review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, high-lying Rydberg states. The major part is dedicated to highly excited S-states of rubidium, which feature an isotropic van der Waals potential. Nevertheless, the setup and the methods presented are also applicable to other atomic species used in the field of laser cooling and atom trapping.
New phenomena have been observed by exciting ultracold ground-state atoms to Rydberg states. Starting with a dense sample of Rb atoms in a magneto-optical trap, we excite them to high Rydberg states (n = 30 - 90) with a single UV excitation pulse. Long-range molecular resonances with interatomic distances exceeding 104 a0 have been discovered. We have also observed the Rydberg excitation blockade, crucial for the implementation of quantum phase gates using neutral atoms. The physics behind these observations is attributed to the strong long-range van der Waals interactions among the Rydberg atoms. In addition, we have seen dipole (E1) forbidden but quadrupole (E2) allowed 5s → nd transitions, allowing us to determine the E2 oscillator strengths to these high Rydberg states. Our narrow-band UV pulsed laser system, with ∼100 MHz bandwidth, also allows us to measure the ratios of j-dependent oscillator strengths to the p and d Rydberg states. ^
Rydberg atoms are used in a wide range of applications due to their peculiar properties like strong dipolar and van der Waals interactions. The choice of Rydberg state has a huge impact on the strength and angular dependence of the interactions, and so a detailed understanding of the underlying processes and resulting properties of the interactions is therefore key to select the most suitable states for experiments. We study the van der Waals interactions in alkali-metal atoms in detail and highlight the structures which allow an understanding and exploitation of the various interaction properties. A particular theme is the identification of Förster resonances with n 1 ≠ n 2 , which offer interaction potentials with a wide range of properties that make them particularly interesting for experimental applications. A second theme is a focus on the underlying structures that shape the angular dependency and sign of the interactions. This understanding — instead of brute-force calculations — allows for a much simpler and more systematic search for suitable pair states. These insights can be used for the selection of tailored interaction potentials subject to experimental constraints and requirements. We use rubidium as an example species in this work and also provide data for cesium and pair states that are coupled via two- or three-photon transitions, i.e. up to F states, in the Appendix.
Summary form only given. We report on recent experimental and theoretical investigations of highly excited atoms prepared from a dense atomic sample in a magneto-optical trap (MOT). The goals of the work are two-fold. First, by exciting atoms above the ionization potential (IP) we can study the properties of an ultracold plasma of electrons (T<1 K) and ions (T<1 mK). Second, tuning the excitation below the IP, we can populate high-lying Rydberg states whose atomic radii are comparable to the interparticle spacing, possibly spawning new collective phenomena. In our initial experiments we study Rydberg states. We collect 10/sup 7/ /sup 85/Rb atoms in the MOT at a density of 10/sup 10//cm/sup 3/. Atoms in the 5s ground state are excited into Rydberg states using single photon 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.
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. ^
Van der Waals interactions between ultracold atoms excited to high-lying Rydberg states can lead to \nstrongly correlated excitation dynamics [1]. In my talk I will present a direct observation in real space \nof the mechanical effect of the van der Waals force on individual Rydberg atoms excited at close range \n[2]. Clusters of Rydberg atoms are created by first generating a small number of seed excitations in a \nmagneto-optical trap, followed by off-resonant excitation that leads to a chain of facilitated excitation \nevents. Our experimental results agree well with a numerical simulation of the van der Waals explosion.