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arXiv:2410.20901 · Physical Review A

Magic running- and standing-wave optical traps for Rydberg atoms

Lukas Ahlheit, Chris Nill, Daniil Svirskiy, Jan de Haan, Simon Schroers, Wolfgang Alt, Nina Stiesdal, Igor Lesanovsky, Sebastian Hofferberth

Published Jan 24, 2025• 4 citations
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Abstract

The authors present an experimental and theoretical study of how the geometry of an optical trap influences the magic wavelength for a collective Rydberg excitation, and find the magic trap wavelength where the coherence time in photon storage experiments is maximized. This magic wavelength depends not only on the Rydberg state, but also on the trap geometry due to the wave function of the almost-free Rydberg electron exploring the potential landscape surrounding the core. Hence, it is necessary to take the size of both Rydberg atom and trapping beams into account when trapping Rydberg atoms.

DOI
10.1103/physreva.111.013115

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Photonics•Feb 8, 2025•0 citations
The authors present an experimental and theoretical study of how the geometry of an optical trap influences the magic wavelength for a collective Rydberg excitation, and find the magic trap wavelength where the coherence time in photon storage experiments is maximized. This magic wavelength depends not only on the Rydberg state, but also on the trap geometry due to the wave function of the almost-free Rydberg electron exploring the potential landscape surrounding the core. Hence, it is necessary to take the size of both Rydberg atom and trapping beams into account when trapping Rydberg atoms.
We develop a theoretical understanding of the trapping of divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wave functions. The optical potential is proportional to the ac Stark polarizability. We find that in the independent-particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free-electron polarizability, the Rydberg contribution depends both on the laser intensity profile and on the rotational symmetry of the total electronic wave function. We focus on the J=0J=0J=0 Rydberg states of Sr and evaluate the dynamic polarizabilities of the 5sns5sns5sns(1S0{}^{1}{S}_{0}1S0​) and 5snp5snp5snp(3P0{}^{3}{P}_{0}3P0​) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [5s25{s}^{2}5s2(1S0{}^{1}{S}_{0}1S0​) and 5s5p5s5p5s5p(3P0{}^{3}{P}_{0}3P0​)] and the J=0J=0J=0 Rydberg states [5sns5sns5sns(1S0{}^{1}{S}_{0}1S0​) and 5snp5snp5snp(3P0{}^{3}{P}_{0}3P0​)] vanishes. We tabulate these wavelengths as a function of the principal quantum number nnn of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\ensuremath{\sim}$1000 nm are ``universal'' as they do not depend on the principal quantum number nnn.
We propose blue-detuned optical traps that are suitable for trapping of both ground-state and Rydberg excited atoms. The addition of a background compensation field or a suitable choice of the trap geometry provides a magic trapping condition for ground-state and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200-kHz differential trap shift between Cs ground states and 125s125s125s Rydberg states for 10 $\ensuremath{\mu}\mathrm{K}$ Cs atoms are presented. Consideration of the trapping potential and photoionization rates suggests that these traps will be useful for quantum-information experiments with atomic qubits.
Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ with exact values that depend on Ry-state quantum numbers.
We propose blue-detuned optical traps that are suitable for trapping of both ground state and Rydberg excited atoms. Addition of a background compensation field or suitable choice of the trap geometry provides a magic trapping condition for ground and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200 kHz differential trap shift between Cs ground and 125s Rydberg states for 10 {\mu}K Cs atoms are presented. Consideration of the trapping potential and photoionization rates
Abstract Long ground-Rydberg coherence lifetime is interesting for implementing high-fidelity quantum logic gates, many-body physics, and other quantum information protocols. However, the potential formed by a conventional far-off-resonance red-detuned optical-dipole trap (ODT) is usually repulsive for Rydberg atoms, which will result in fast atom loss and low repetition rate of the experimental sequence. These issues can be addressed by a magic ODT. We performed the calculation of ODT’s magic detuning for confinement of ground-state and Rydberg-state cesium atoms with the same potential well. We used a sum-over-states method to calculate the dynamic polarizabilities of 6S 1/2 ground state and highly-excited ( n S 1/2 and n P 3/2 ) Rydberg state of cesium atoms, and identify corresponding magic detuning for optical wavelengths in the range of 850–1950 nm. We estimated the trapping lifetime of cesium Rydberg atoms confined in the magic ODT by including different dissipative mechanisms. Furthermore, we have experimentally realized an 1879.43 nm single-frequency laser system with a watt-level output power for setting up the magic ODT for 6S 1/2 ground-state and 84P 3/2 Rydberg-state cesium cold atoms.
A magic optical dipole trap (ODT) can confine atoms in the ground state and a highly excited state with the same light shifts, resulting in a long-range coherent lifetime between them, which plays an important role in high-fidelity quantum logic gates, multi-body physics and other quantum information. Here, we use a sum-over-states model to calculate the dynamic polarizabilities of the 6S1/2 ground state and 46S1/2 Rydberg state of Cs atoms and identify corresponding magic wavelengths and magic detunings for trapping the two states in the range of 900–1950 nm. Then, we analyze the robustness of the magic condition and the feasibility of the experimental operation. Furthermore, we estimate the trapping lifetime of Cs Rydberg atoms by considering different dissipation mechanisms, such as photon scattering and photoionization in the magic ODT. The photoexcitation and photoionization of Cs atoms under the action of three-step laser pulses are calculated by the rate equation. The presented results for magic-wavelength ODTs are of great significance for quantum information and quantum computing based on Rydberg atoms.