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Trapping of individual circular Rydberg states and observation of singlet-triplet oscillations

Baptiste Muraz

Published Mar 19, 2026• 0 citations
OpenAlex

Abstract

In recent years, advances in optical tweezers arrays have enabled the trapping and control of individual atoms. This makes it possible to simulate condensed matter systems by arranging atoms in an array that mimics the crystalline structure of real materials. This approach, known as quantum simulation, was first envisioned by R. Feynman and is now being implemented by several research groups worldwide. In order to induce interactions between atoms, they are prepared in highly excited atomic states, known as Rydberg states. In particular, circular Rydberg states, which possess maximal angular momentum, exhibit lifetimes of several milliseconds, much longer than those of other Rydberg states. This property makes them particularly interesting for the development of new quantum technologies. In this work, we present the first building blocks of a quantum simulator based on circular Rydberg states of strontium atoms. This includes the development of a new cryogenic apparatus in which individual strontium atoms are trapped in optical tweezers. Using an alkaline-earth element allows us to exploit its two valence electrons for different tasks. One electron is excited to the circular state with principal quantum number n = 52, while the ionic core behaves as a Sr+ ion, which can be directly trapped by the tweezers. Moreover, we observe coherent oscillations between singlet and triplet spin states, due to the spin-orbit coupling of the electron in the circular state. These oscillations allow us to measure, with high precision, QED corrections to the Landé g5S1/2 factor of the ground state of Sr+.

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Neutral atom qubits with Rydberg-mediated interactions are a leading platform for developing large-scale coherent quantum systems. In the majority of experiments to date, the Rydberg states are not trapped by the same potential that confines ground state atoms, resulting in atom loss and constraints on the achievable interaction time. In this Letter, we demonstrate that the Rydberg states of an alkaline earth atom, ytterbium, can be stably trapped by the same red-detuned optical tweezer that also confines the ground state, by leveraging the polarizability of the Yb^{+} ion core. Using the previously unobserved ^{3}S_{1} series, we demonstrate trapped Rydberg atom lifetimes exceeding 100 μs, and observe no evidence of auto- or photoionization from the trap light for these states. We measure a coherence time of T_{2}=59 μs between two Rydberg levels, exceeding the 28 μs lifetime of untrapped Rydberg atoms under the same conditions. These results are promising for extending the interaction time of Rydberg atom arrays for quantum simulation and computing, and are vital to capitalize on the extended Rydberg lifetimes in circular states or cryogenic environments.

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In recent years, advances in optical tweezers arrays have enabled the trapping and control of individual atoms. This makes it possible to simulate condensed matter systems by arranging atoms in an array that mimics the crystalline structure of real materials. This approach, known as quantum simulation, was first envisioned by R. Feynman and is now being implemented by several research groups worldwide. In order to induce interactions between atoms, they are prepared in highly excited atomic states, known as Rydberg states. In particular, circular Rydberg states, which possess maximal angular momentum, exhibit lifetimes of several milliseconds, much longer than those of other Rydberg states. This property makes them particularly interesting for the development of new quantum technologies. In this work, we present the first building blocks of a quantum simulator based on circular Rydberg states of strontium atoms. This includes the development of a new cryogenic apparatus in which individual strontium atoms are trapped in optical tweezers. Using an alkaline-earth element allows us to exploit its two valence electrons for different tasks. One electron is excited to the circular state with principal quantum number n = 52, while the ionic core behaves as a Sr+ ion, which can be directly trapped by the tweezers. Moreover, we observe coherent oscillations between singlet and triplet spin states, due to the spin-orbit coupling of the electron in the circular state. These oscillations allow us to measure, with high precision, QED corrections to the Landé g5S1/2 factor of the ground state of Sr+.
Coherence time and gate fidelities in Rydberg atom quantum simulators and computers are fundamentally limited by the Rydberg state lifetime. Circular Rydberg states are highly promising candidates to overcome this limitation by orders of magnitude, as they can be effectively protected from decay due to their maximum angular momentum. We report the first realization of alkaline-earth circular Rydberg atoms trapped in optical tweezers, which provide unique and novel control possibilities due to the optically active ionic core. Specifically, we demonstrate creation of very high- n ( n = 79 ) circular states of Sr 88 . We measure lifetimes as long as 2.55 ms at room temperature, which are achieved via cavity-assisted suppression of black-body radiation. We show coherent control of a microwave qubit encoded in circular states of nearby manifolds, and characterize the qubit coherence time via Ramsey and spin-echo spectroscopy. Finally, circular-state tweezer trapping exploiting the Sr + core polarizability is quantified via measurements of the trap-induced light shift on the qubit. Our work opens routes for quantum simulations with circular Rydberg states of divalent atoms, exploiting the emergent toolbox associated with the optically active core ion. Published by the American Physical Society 2024
Measuring the Sr+^++ 5s1/2_{1/2}1/2​ Landé ggg-factor Using Singlet-Triplet Oscillations in a Circular Rydberg State of Strontium
Circular states of strontium are promising platforms for quantum technologies. They exhibit much longer lifetimes than laser-accessible Rydberg states and possess an optically active ionic core that can be manipulated with laser light. Here we trap circular states in optical tweezers by exploiting the dynamical polarizability of the ionic core. We measure the decay of the orbital component of a n=51 circular state and observe singlet-triplet spin oscillations arising from the interplay of vector light shifts induced by the optical tweezers, spin-orbit coupling associated with the Rydberg electron, and the difference in Landé ggg-factor between the ionic core and the Rydberg electrons. By observing the two electron spin dynamics, we measure the spin-orbit interaction and the correction δg∼δg \simδg∼ 10^(-5) of the Landé ggg-factor of the Sr+^++ 5s1/2_{1/2}1/2​ ionic core electron with respect to that of a free electron. This provides a first high-precision measurement of gSr+,5s1/2g_{\textrm{Sr}^+, 5s_{1/2}}gSr+,5s1/2​​ = 2.002290(1).
Quantum simulation offers interesting perspectives for the understanding of complex systems that are out of reach for numerical approaches. In this line, a new quantum simulation platform has recently been proposed. A spin-1/2 XXZ hamiltonian is thus realized in which the parameters can be controlled over a large range. The spin states are encoded by circular Rydberg states coupled through dipole-dipole interaction. These states benefit from longer lifetimes compared to the low angular momentum states used for current quantum simulations. In addition, they can be laser-trapped through the ponderomotive effect, and their lifetime can be further enhanced by spontaneous emission inhibition. We present in this thesis the first step towards the implementation of the proposed quantum simulator. We first prepare an array of rubidium 87 atoms trapped individually in optical tweezers. These atoms are subsequently excited to the circular Rydberg state n = 52 and transferred to hollow bottle-beam traps. We thus demonstrate the ponderomotive trapping of these states over durations of several milliseconds. We take advantage of the optical detection of the states thus prepared with various experiments. We characterize the trapping potential by measuring its transverse frequency. We finally conclude with the coherent manipulation of these trapped circular states through Rabi oscillations and Ramsey interferometry to determine their coherence.
Circular Rydberg atoms, with their long lifetimes and adjustable strong dipolar interactions, are promising candidates for the implementation of quantum simulations in regimes that were previously out of reach. A new quantum simulator paradigm, based on qubits encoded in circular states, would implement an XXZ spin-1/2 Hamiltonian with dynamically adjustable parameters over a wide range of values. This thesis addresses the preliminary steps in constructing such a quantum simulator. First, we present the realization of two-dimensional arrays of optically-trapped circular Rydberg atoms with arbitrary geometries. For this purpose, we prepare arrays of ultra-cold rubidium atoms, individually trapped in optical tweezers. An additional beam with adjustable position allows us to rearrange the atoms within the array to implement the desired geometry in a deterministic manner. We then excite the atoms to the circular state with principal quantum number n=52, while trapping them in hollow beams using the ponderomotive force. These experimental capabilities allowed us to control and characterize, for the first time, the dipolar interactions between circular states, within pairs of individually trapped atoms. We showed the good agreement of these measurements with theoretical expectations and highlighted their dependence on the system's geometry. This experimental study is coupled to an investigation of the motion of the circular atoms within their traps.
Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of Rydberg atoms and, notably, with a huge coupling to external fields or to other Rydberg atoms while the ionic core retains an optically active electron. However, low angular-momentum Rydberg states suffer almost immediate autoionization when the core is excited. Here, we demonstrate that strontium circular Rydberg atoms with a core excited in a 4D metastable level are impervious to autoionization over more than a few millisecond time scale. This makes it possible to trap and laser-cool Rydberg atoms. Moreover, we observe singlet to triplet transitions due to the core optical manipulations, opening the way to a microwave to optical quantum interface.
Neutral atom qubits with Rydberg-mediated interactions are a leading platform for developing large-scale coherent quantum systems. In the majority of experiments to date, the Rydberg states are not trapped by the same potential that confines ground state atoms, resulting in atom loss and constraints on the achievable interaction time. In this Letter, we demonstrate that the Rydberg states of an alkaline earth atom, ytterbium, can be stably trapped by the same red-detuned optical tweezer that also confines the ground state, by leveraging the polarizability of the Yb^{+} ion core. Using the previously unobserved ^{3}S_{1} series, we demonstrate trapped Rydberg atom lifetimes exceeding 100 μs, and observe no evidence of auto- or photoionization from the trap light for these states. We measure a coherence time of T_{2}=59 μs between two Rydberg levels, exceeding the 28 μs lifetime of untrapped Rydberg atoms under the same conditions. These results are promising for extending the interaction time of Rydberg atom arrays for quantum simulation and computing, and are vital to capitalize on the extended Rydberg lifetimes in circular states or cryogenic environments.