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arXiv:2408.00195 · Physical Review A

Engineering Rydberg-pair interactions in divalent atoms with hyperfine-split ionization thresholds

Frederic Hummel, Sebastian Weber, Johannes Mögerle, Henri Menke, Jonathan P. King, Benjamin Bloom, Sebastian Hofferberth, Ming Li

Published Oct 18, 2024• 7 citations
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Abstract

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

DOI
10.1103/physreva.110.042821

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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
The theory is developed for one- and two-atom interactions when the atom has a Rydberg electron attached to a hyperfine-split core state. This situation is relevant for some of the rare-earth and alkaline-earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare-earth atoms, the core electrons can have a very substantial total angular momentum JJJ and a nonzero nuclear spin III. In the alkaline-earth atoms there is a single (sss) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions (C5{C}_{5}C5​ and C6{C}_{6}C6​ matrices).
Abstract A method for calculating the properties of Rydberg states and Rydberg–Rydberg interaction between two 87 Sr atoms is described. The method is based on a multichannel quantum defect theory description of the Rydberg states that accounts for the hyperfine splitting of the 87 Sr + ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the C 6 matrix for the 5 sns F T = 9/2 series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several couple Förster resonances above n = 50 unlike the case of 88 Sr which has none.
We present calculations of long-range interactions in Rydberg atoms, with a focus on the dipole-dipole interactions of strontium Rydberg states. The growing use of Rydberg states in the field of cold atoms necessitates a more detailed understanding of the effects of dipole-dipole interactions, which are currently being investigated in a number of research groups worldwide. Calculations of long-range interactions in Rydberg states of caesium, cal- cium, rubidium, strontium and ytterbium are presented. By taking the one active electron approximation we develop consistent models of these long- range interactions, and construct a survey of the Rydberg state dipole-dipole interactions and quadrupole-quadrupole interactions. We compare the inter- actions between series and between atoms, highlighting the importance of certain series for applications suggested in previous works. In order to include two-electron effects in the description of dipole-dipole interactions in divalent atoms, we use multichannel quantum defect theory (MQDT) to develop models of the Rydberg series of strontium. We use an empirical reactance matrix formalism, where the reactance matrix is fitted to reproduce experimentally measured values of the bound state energy levels. Models are found for all series of strontium with L ≤ 3. We extend the MQDT formalism to the description of the natural radiative lifetimes of strontium, where the perturbers are found to have a large quenching effect on these lifetimes. By incorporating the MQDT description of the Rydberg states of strontium into the calculation of dipole-dipole interactions, we find a spin-forbidden two-atom resonance in the 3D2 states of strontium. We consider a one- dimensional lattice of strontium atoms, and find that the internal dynamics of the Rydberg atoms demonstrates spin transport for large lattice spacings and a separation of the spin and total angular momentum dynamics for small lattice spacings. Spin-angular momentum separation (analogous to spin-charge separation in condensed matter) in strontium Rydberg atoms may have uses in the investigation of one-dimensional Fermi gases and their description using Luttinger liquid theory.
We investigate the effect of series perturbation on the second-order dipole-dipole interactions between strontium atoms in the 5sns(1S0)5sns({^1}S_0)5sns(1S0​) and 5snp(1P1)5snp({^1}P_1)5snp(1P1​) Rydberg states as a means of engineering long-range interactions between atoms. The series perturbation in these atoms enables modifying the strength and the sign of the interaction by varying the principal quantum number nnn of the Rydberg electron. We utilize experimentally available data to estimate the importance of perturber states, and find that van der Waals interaction between two strontium atoms in the 5snp(1P1)5snp({^1}P_1)5snp(1P1​) states shows strong peaks outside the anticipated hydrogenic n11n^{11}n11 scaling. We identify this to be the result of the perturbation of 5snd(1D2)5snd({^1}D_2)5snd(1D2​) intermediate states by the 4d2(1D2)4d^2({^1}D_2)4d2(1D2​) and 4dn′s(1D2)4dn's({^1}D_2)4dn′s(1D2​) states in the n<20n<20n<20 range. This demonstrates that divalent atoms offer a unique advantage for generating substantially stronger or weaker inter-atomic interactions than those that can be achieved using alkali metal atoms. This is due to the highly perturbed spectra of divalent atoms and other multivalent atoms that can persist up to high nnn. Such irregularities can be especially useful in engineering asymmetric Ry blockade requiring the simultaneous presence of both ``weak'' and ``strong'' interactions.
A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet SSS and DDD Rydberg states in 87Sr^{87}\mathrm{Sr}87Sr is presented. 87Sr^{87}\mathrm{Sr}87Sr has a large nuclear spin I=9/2I=9/2I=9/2, and at high-nnn the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-nSn SnS states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the I=0I=0I=0 isotope 88Sr^{88}\mathrm{Sr}88Sr, which results in good agreement with the present measurements. For the DDD states, this procedure is reversed by first extracting from the present 87Sr^{87}\mathrm{Sr}87Sr measurements the energies of the 3D1,2,3{}^{3}{D}_{1,2,3}3D1,2,3​ states to be expected for isotopes without hyperfine structure (88Sr^{88}\mathrm{Sr}88Sr), which allows the determination of corrected quantum defects in the high-nnn limit.
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$\ensuremath{\bigotimes}$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.