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arXiv:1508.02480 · Physical Review A

Effects of molecular resonances on Rydberg blockade

Andrei Derevianko, P. Kómár, Türker Topçu, Ronen M. Kroeze, Mikhail D. Lukin

Published Dec 23, 2015• 39 citations
arXivHTMLPDF

Abstract

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 $100s$ 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.

DOI
10.1103/physreva.92.063419

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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.
Abstract The process of the Rydberg blockade, which is currently regarded as one of the most promising approaches to quantum computation, can become significantly less effective due to interatomic interactions that shift the excitation frequency of initially blocked particles to the region of resonance with external laser radiation. In this article, we develop an analytical theory of this effect based on a self-consistent model of two Rydberg atoms acting on each other with their dipole electric fields and experiencing a Stark splitting of energy levels under the action of these fields. It follows from our calculations that the typical interatomic distances at which the unblocking effect due to ‘‘parasitic’’ resonances begins to occur are in rough agreement with earlier qualitative estimates; however, the number of such resonances can be much larger than in recent numerical simulations of some particular systems. Therefore, the possibility of breaking the Rydberg blockade at small interatomic distances should be carefully taken into account in any future applications to quantum computing.
Interaction between Rydberg atoms can significantly modify Rydberg excitation dynamics. Under a resonant driving field the Rydberg-Rydberg interaction in high-lying states can induce shifts in the atomic resonance such that a secondary Rydberg excitation becomes unlikely leading to the Rydberg blockade effect. In a related effect, off-resonant coupling of light to Rydberg states of atoms contributes to the Rydberg anti-blockade effect where the Rydberg interaction creates a resonant condition that promotes a secondary excitation in a Rydberg atomic gas. Here, we study the light-matter interaction and dynamics of off-resonant two-photon excitations and include two- and three-atom Rydberg interactions and their effect on excited state dynamics in an ensemble of cold atoms. In an experimentally-motivated regime, we find the optimal physical parameters such as Rabi frequencies, two-photon detuning, and pump duration to achieve significant enhancement in the probability of generating doubly-excited collective atomic states. This results in large auto-correlation values due to the Rydberg anti-blockade effect and makes this system a potential candidate for a high-purity two-photon Fock state source.
We present evidence for molecular resonances in a cold dense gas of rubidium Rydberg atoms. Single UV photon excitation from the 5s ground state to np Rydberg states (n=50-90) reveals resonances at energies corresponding to excited atom pairs (n-1)d+ns. We attribute these normally forbidden transitions to avoided crossings between the long-range molecular potentials of two Rydberg atoms. These strong van der Waals interactions result in avoided crossings at extremely long range, e.g., approximately 58 000 times the Bohr radius (a(0)) for n=70.
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. ^
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.