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arXiv:0705.4040 · Physical Review A

Many-body theory of excitation dynamics in an ultracold Rydberg gas

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

Published Jul 20, 2007• 122 citations
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Abstract

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.

DOI
10.1103/physreva.76.013413

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2009•0 citations
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.
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.
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. ^
We demonstrate the interaction-induced blockade effect in an ultracold 88Sr^{88}\mathrm{Sr}88Sr gas via studying the time dynamics of a two-photon excitation to the triplet Rydberg series 5sns3S15sns{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}5sns3S1​ for five different principal quantum numbers nnn ranging from 19 to 37. By using a multipulse excitation sequence to increase the detection sensitivity, we could identify Rydberg-excitation-induced atom losses as low as <1<1%<1. Based on an optical Bloch equation formalism, treating the Rydberg-Rydberg interaction on a mean-field level, the van der Waals coefficients are extracted from the observed dynamics, which agree fairly well with ab initio calculations.
The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose–Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure two-body interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas–Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results and point out possible solutions for future approaches. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.
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.
Summary form only given. Interactions between neutral atoms are generally weak, but exciting these atoms in a Rydberg state considerably enhances their interaction through a long-range dipole-dipole potential. An interesting application of this dipole-dipole interaction is the dipole blockade in Rydberg excitation. This effect offers exciting possibilities for manipulating quantum bits stored in a single collective excitations in mesoscopic ensembles, or for realizing scalable quantum logic gate. The dipole blockade effect has been demonstrated in atomic ensembles by different groups, and recently also with two independently trapped atoms, which shows the possibility of creating entangle states and quantum logic gates. To extend and continue these results with more atoms, a promising method is to use atoms trapped in an optical lattice in the Mott insulator phase. To excite atoms into a Rydberg state, and to control the interactions and the dipole blockade, a high resolution laser scheme is needed. We use a two-photon excitation scheme 5s1/2rarr 6p3/2rarr ns or nd. The first step, at 420 nm, is realized by doubling a MOPA laser, with the second step at ~ 1000 nm. Both lasers are locked to a Fabry-Perot cavity, and the total excitation bandwidth is less than 3 MHz. After the excitation into the Rydberg state, we apply a pulsed electric field to ionize and detect the Rydberg atoms with an ion detector. To characterize and improve the efficiency of our ion detection, we have explored the direct ionization of ultracold atoms in a magneto-optical trap, or in a Bose-Einstein condensate. This calibration will allows us to characterize precisely the Rydberg excitation and to monitor its time evolution. First results on the Rydberg excitation of ultracold atoms in dipole traps and optical lattices will be presented. The prospect for creating Rydberg excitations inside a Mott insulator will also be discussed.