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arXiv:1705.01748

On the fidelity of quantum information processing with Rydberg atoms: Role of the non-molecular resonances

Yurii V. Dumin

Published May 4, 2017• 0 citations
arXivHTMLPDF

Abstract

Rydberg blockade of ultracold atoms is considered now as one of the most promising tools for the implementation of quantum computing, but its fidelity can be substantially compromised by detrimental excitation of the neighbouring atoms. This phenomenon has been investigated recently in detail for the particular case of molecular resonances (i.e., resulting in the formation of quasi-bound states). However, as will be shown in the present paper, an even greater effect can come from the non-molecular resonances, which therefore should be taken into account very carefully.

DOI
10.48550/arxiv.1705.01748

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Rydberg blockade of ultracold atoms is considered now as one of the most promising tools for the implementation of quantum computing, but its fidelity can be substantially compromised by detrimental excitation of the neighbouring atoms. This phenomenon has been investigated recently in detail for the particular case of molecular resonances (i.e., resulting in the formation of quasi-bound states). However, as will be shown in the present paper, an even greater effect can come from the non-molecular resonances, which therefore should be taken into account very carefully.
We study the effect of resonances associated with complex molecular interaction of Rydberg atoms on Rydberg blockade. We show that densely spaced molecular potentials between doubly excited atomic pairs become unavoidably resonant with the optical excitation at short interatomic separations. Such molecular resonances limit the coherent control of individual excitations in Rydberg blockade. As an illustration, we compute the molecular interaction potentials of Rb atoms near the 100s100s100s states asymptote to characterize such detrimental molecular resonances and determine the resonant loss rate to molecules and inhomogeneous light shifts. Techniques to avoid the undesired effect of molecular resonances are discussed.
We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.
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. ^
Crystalline structures of highly excited Rydberg atoms can be a model for dilute metallic solids with tunable parameters, and provide access to the regime of strongly coupled systems. In practice, crystal creation is made difficult by the 'Rydberg blockade', where one atom in the Rydberg state shifts the energy levels of its neighbours out of resonance with the excitation laser. In our experiment, we can spatially detect Rydberg atoms by a combination of field-ionization, and subsequent acceleration of the remaining ions onto a multi-channel plate. In this way, we were able to determine the blockade radius from measuring second-order correlations. We have also made small ordered Rydberg structures by optically imprinting local excitations in a disordered atomic gas using a spatial light modulator. With this diffractive optical element it is possible to control the intensity of light in the far ¿eld and create almost any desired intensity pattern. We found that a Rydberg system with a dissipative mechanism can be mapped onto a set of rate equations that describe a wireless computer network. In these networks neighbouring transmitters have a similar blockade effect on each other. For the Rydberg system, we used mathematical tools developed for wireless networks, and applied this to optically imprinted square lattices.
In the laser excitation of ultracold atoms to Rydberg states, we observe a dramatic suppression caused by van der Waals interactions. This behavior is interpreted as a local excitation blockade: Rydberg atoms strongly inhibit excitation of their neighbors. We measure suppression, relative to isolated atom excitation, by up to a factor of 6.4. The dependences of this suppression on both laser irradiance and atomic density are in good agreement with a mean-field model. These results are an important step towards using ultracold Rydberg atoms in quantum information processing.