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Optics Express

Rydberg-Rydberg interaction strengths and dipole blockade radii in the presence of Förster resonances

Chien‐Ting Wu, Teodora Kirova, Marcis P. Auzinsh, Yi‐Hsin Chen

Published Oct 10, 2023• 6 citations
Publisher

Abstract

Achieving a substantial blockade radius is crucial for developing scalable and efficient quantum communication and computation. In this theoretical study, we present the enhancement of the Rydberg blockade radius by utilizing Förster resonance. This phenomenon occurs when the energy difference between two initial Rydberg states closely matches that between the corresponding final Rydberg states, giving rise to a resonant energy transfer process. We employ quantum defect theory to numerically calculate the 87 Rb– 87 Rb Rydberg atomic pair, enabling us to accurately estimate the van der Waals interaction. Our investigation reveals that when the principal quantum numbers of two Rydberg states differ only slightly, the Förster transition is rarely able to achieve a large blockade radius. However, in cases where the principal quantum numbers differ significantly, we substantially improve the Rydberg blockade radius. Most notably, we identify transition channels exhibiting an extensive blockade radius, surpassing 50 μ m. This significant increase in the blockade radius enables larger-scale quantum operations and advances quantum technologies, with broad implications for achieving long-range quantum entanglement and robust quantum processes.

DOI
10.1364/oe.502183

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Achieving a substantial blockade radius is crucial for developing scalable and efficient quantum communication and computation. In this theoretical study, we present the enhancement of the Rydberg blockade radius by utilizing Förster resonance. This phenomenon occurs when the energy difference between two initial Rydberg states closely matches that between the corresponding final Rydberg states, giving rise to a resonant energy transfer process. We employ quantum defect theory to numerically calculate the 87 Rb– 87 Rb Rydberg atomic pair, enabling us to accurately estimate the van der Waals interaction. Our investigation reveals that when the principal quantum numbers of two Rydberg states differ only slightly, the Förster transition is rarely able to achieve a large blockade radius. However, in cases where the principal quantum numbers differ significantly, we substantially improve the Rydberg blockade radius. Most notably, we identify transition channels exhibiting an extensive blockade radius, surpassing 50 μ m. This significant increase in the blockade radius enables larger-scale quantum operations and advances quantum technologies, with broad implications for achieving long-range quantum entanglement and robust quantum processes.
Enhancing interactions between Rydberg atoms is a key challenge in contemporary quantum technologies. Stronger interactions enable faster Rydberg gates in digital processors and larger entangled states in analog simulation. Achieving the same interaction strength at lower principal quantum number addresses current constraints in available Rabi frequency and field sensitivity in large scale tweezer or cavity QED experiments. Here, we demonstrate a new technique using AC Stark shifts from a microwave drive to tune into a Förster resonance, thereby modifying the interaction scaling with distance from 1/R61/R^61/R6 to 1/R31/R^31/R3. We validate enhanced Rydberg interactions (in strength and range) by probing cavity Rydberg polariton blockade at n=44n=44n=44 in 87^{87}87Rb, improving from g(2)(0)=1.0(1)g^{(2)}(0) = 1.0 (1)g(2)(0)=1.0(1) in the Van-der-Waals regime to g(2)(0)=0.38(1)g^{(2)}(0) = 0.38 (1)g(2)(0)=0.38(1) in the dipolar regime on the Förster resonance. Importantly, our technique allows minimal shifts of the original Rydberg state, suppressing detuning errors in gate protocols while maintaining quadratic insensitivity to DC electric fields.
We analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum-information processing using the van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interaction is large compared to the atom-atom interactions. The results are presented for all potential angular momentum channels involving s\mathit{s}s, p\mathit{p}p, and d\mathit{d}d states. For most channels there are one or more combinations of Zeeman levels that have extremely small dipole-dipole interactions and are therefore poor candidates for effective blockade experiments. Channels with promising properties are identified and discussed. We also present numerical calculations of Rb and Cs dipole matrix elements and relevant energy levels using quantum defect theory, allowing for convenient quantitative estimates of the van der Waals interactions to be made for principal quantum numbers up to 100. Finally, we combine the blockade and van der Waals results to quantitatively analyze the angular distribution of the blockade shift and its consequence for angular momentum channels and geometries of particular interest for blockade experiments with Rb.
Abstract Förster resonances provide a highly flexible tool to tune both the strength and the angular shape of interactions between two Rydberg atoms. We give a detailed explanation about how Förster resonances can be found by searching through a large range of possible quantum number combinations. We apply our search method to SS , SD and DD pair states of 87 Rb with principal quantum numbers from 30 to 100, taking into account the fine structure splitting of the Rydberg states. We find various strong resonances between atoms with a large difference in principal quantum numbers. We quantify the strength of these resonances by introducing a figure of merit C ˜ 3 which is independent of the magnetic quantum numbers and geometry to classify the resonances by interaction strength. We further predict to what extent excitation exchange is possible on different resonances and point out limitations of the coherent hopping process. Finally, we discuss the angular dependence of the dipole–dipole interaction and its tunability near resonances.
Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e., simultaneous excitation of more than one Rydberg atom, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Rydberg atoms interacting via dipole-dipole exchange interactions. We study typical situations in current Rydberg atom experiments, where different types of dipole-dipole interactions can be achieved by varying Rydberg state couplings. An effective Hamiltonian governing underlying antiblockade dynamics is derived. We illustrate that geometric gates can be realized with the Rydberg antiblockade which is robust against the decay of Rydberg states. Our study may stimulate new experimental and theoretical exploration of quantum optics and strongly interacting many-body dynamics with Rydberg antiblockade driven by dipole-dipole interactions.
We calculate the interaction strength of the van der Waals force between two Rydberg atoms by applying the applications of quantum information processing using for Rydberg blockade. The alkali metals (Cs and K) in states of principal quantum number n were used to calculate the interaction strength. We use some possible angular momentum channels involving s, p, and d states for measuring interaction strength. The obtained results were then generalized for all angular momentum channels which mostly have small interactions and therefore a poor candidate for blockade experiments. The interaction strength in the atoms of Cs and K dipole matrix elements was calculated first and then relevant energy levels were determined by using the quantum defects theory. The radial wave function was calculated numerically with the integration of the radial Schrodinger equation. Also, the interaction coefficients of van der Waals for various channels were calculated here.
We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers nnn, $\ensuremath{\ell}$, jjj, and mj{m}_{j}mj​, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.