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arXiv:2212.06349 · Physical Review A

Hyperentanglement of divalent neutral atoms by Rydberg blockade

Xiaofeng Shi

Published Oct 25, 2021• 14 citations
arXivHTMLPDF

Abstract

Hyperentanglement (HE), the simultaneous entanglement between two particles in more than one degree of freedom, is relevant to both fundamental physics and quantum technology. Previous study on HE has been focusing on photons. Here, we study HE in individual neutral atoms. In most alkaline-earth-like atoms with two valence electrons and a nonzero nuclear spin, there are two stable electronic states, the ground state and the long-lived clock state, which can define an electronic qubit. Meanwhile, their nuclear spin states can define a nuclear qubit. By the Rydberg blockade effect, we show that the controlled-$Z$ (cz) operation can be generated in the electronic qubits of two nearby atoms, and simultaneously in their nuclear qubits as well, leading to a cz$\ensuremath{\bigotimes}$cz operation which is capable to induce HE. The possibility to induce HE in individual neutral atoms offers opportunities to study quantum science and technology based on neutral atoms.

DOI
10.1103/physreva.104.042422

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Hyperentanglement (HE), the simultaneous entanglement between two particles in more than one degree of freedom, is relevant to both fundamental physics and quantum technology. Previous study on HE has been focusing on photons. Here, we study HE in individual neutral atoms. In most alkaline-earth-like atoms with two valence electrons and a nonzero nuclear spin, there are two stable electronic states, the ground state and the long-lived clock state, which can define an electronic qubit. Meanwhile, their nuclear spin states can define a nuclear qubit. By the Rydberg blockade effect, we show that the controlled-ZZZ (cz) operation can be generated in the electronic qubits of two nearby atoms, and simultaneously in their nuclear qubits as well, leading to a cz\ensuremath⨂\ensuremath{\bigotimes}\ensuremath⨂cz operation which is capable to induce HE. The possibility to induce HE in individual neutral atoms offers opportunities to study quantum science and technology based on neutral atoms.
Quantum information processing with neutral atoms relies on Rydberg excitation for entanglement generation. While the use of heavy divalent or open-shell elements, such as strontium or ytterbium, has benefits due to their optically active core and a variety of possible qubit encodings, their Rydberg structure is generally complex. For some isotopes in particular, hyperfine interactions are relevant even for highly excited electronic states. We employ multichannel quantum defect theory to infer the Rydberg structure of isotopes with nonzero nuclear spin and perform nonperturbative Rydberg-pair interaction calculations. We find that due to the high level density and sensitivities to external fields, experimental parameters must be precisely controlled. Specifically in Sr 87 , we study an intrinsic Förster resonance, unique to divalent atoms with hyperfine-split thresholds, which simultaneously provides line stability with respect to external field fluctuations and enhanced long-range interactions. Additionally, we provide parameters for pair states that can be effectively described by single-channel Rydberg series. The explored pair states provide exciting opportunities for applications in the blockade regime, as well as for more exotic long-range interactions such as largely flat, distance-independent potentials. Published by the American Physical Society 2024
Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states ∣0〉 and ∣1〉 are excited to Rydberg states ∣ r 〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state ∣1〉 can be fully excited to the Rydberg state while ∣0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.
We report the generation of entanglement between two individual 87Rb atoms in hyperfine ground states |F=1,M=1> and |F=2,M=2> which are held in two optical tweezers separated by 4 microm. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.
A neutral-atom system serves as a promising platform for realizing gate-based quantum computing because of its capability to trap and control several atomic qubits in different geometries and the ability to perform strong, long-range interactions between qubits; however, the two-qubit entangling gate fidelity lags behind competing platforms such as superconducting systems and trapped ions. The aim of our work is to design a fast, robust, high-fidelity controlled-ZZZ (cz) gate, based on the Rydberg-blockade mechanism, for neutral atoms. We propose a gate procedure that relies on simultaneous and transitionless quantum driving of a pair of atoms using broadband lasers. By simulating a system of two interacting cesium atoms, including spontaneous emission from excited levels and parameter fluctuations, we yield a Rydberg-blockade cz gate with fidelity 0.9985 over an operation time of $0.12\phantom{\rule{3.33333pt}{0ex}}\mathrm{\textmu{}s}$. Our gate procedure delivers cz gates that are superior than the state-of-the-art experimental cz gate and the simulated cz gates based on adiabatic driving of atoms. Our results show that our gate procedure carries significant potential for achieving scalable quantum computing using neutral atoms.
Neutral atoms trapped in arrays of optical tweezers are a versatile platform for multiple research efforts in quantum information science. In particular, alkaline-earth atoms like Yb offer many advantages including ultralong coherence nuclear spin states for quantum information storage and high-fidelity qubit operations, optical transitions to Rydberg states for generating strong, long-range interactions between atoms, and narrow optical transitions for efficient cooling and metrology. Additionally, optical transitions from the long-lived 3P0 nuclear spin state have frequencies in the telecommunications band making integration with fiber networks and silicon nanophotonics an attractive avenue of exploration for hybrid quantum systems and quantum communication. Finally, these optical tweezer platforms are well suited for investigating the cooperative response of an array of atoms, where the proximity of neighboring atoms fundamentally alters the systems optical response which has implications for quantum information storage. Here I will present efforts to investigate these research avenues using alkaline-earth atoms in optical tweezers.
Abstract In this brief review, the opportunities that the alkaline-earth elements offer for studying new aspects of Rydberg physics are discussed. For example, the bosonic alkaline-earth isotopes have zero nuclear spin which eliminates many of the complexities present in alkali Rydberg atoms, permitting simpler and more direct comparison between theory and experiment. The presence of two valence electrons allows the production of singlet and triplet Rydberg states that can exhibit a variety of attractive or repulsive interactions. The availability of weak intercombination lines is advantageous for laser cooling and for applications such as Rydberg dressing. Excitation of one electron to a Rydberg state leaves behind an optically active core ion allowing, for high- L states, the optical imaging of Rydberg atoms and their (spatial) manipulation using light scattering. The second valence electron offers the possibility of engineering long-lived doubly excited states such as planetary atoms. Recent advances in both theory and experiment are highlighted together with a number of possible directions for the future.