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arXiv:2402.13398 · Science

Coherent evolution of superexchange interaction in seconds-long optical clock spectroscopy

William R. Milner, Stefan Lannig, Mikhail Mamaev, Lingfeng Yan, Anjun Chu, Ben Lewis, Max N. Frankel, Ross B. Hutson, Ana María Rey, Jun Ye

Published May 1, 2025• 11 citations
arXivHTMLPDF

Abstract

Scaling up the performance of atomic clocks requires understanding complex many-body Hamiltonians to ensure meaningful gains for metrological applications. Here we use a degenerate Fermi gas loaded into a three-dimensional optical lattice to study the effect of a tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit coupling spiral phase and breaks the isotropy of superexchange interactions, leading to XXZ-type spin anisotropy. By tuning the lattice confinement and applying imaging spectroscopy, we map out favorable atomic coherence regimes. We transition through various interaction regimes and observe coherent superexchange, tunable through on-site interaction and site-to-site energy shift, affecting the Ramsey fringe contrast over timescales >1 second. This study lays the groundwork for using a three-dimensional optical lattice clock to probe quantum magnetism and spin entanglement.

DOI
10.1126/science.ado5987

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Scaling up the performance of atomic clocks requires understanding complex many-body Hamiltonians to ensure meaningful gains for metrological applications. Here we use a degenerate Fermi gas loaded into a three-dimensional optical lattice to study the effect of a tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit coupling spiral phase and breaks the isotropy of superexchange interactions, leading to XXZ-type spin anisotropy. By tuning the lattice confinement and applying imaging spectroscopy, we map out favorable atomic coherence regimes. We transition through various interaction regimes and observe coherent superexchange, tunable through on-site interaction and site-to-site energy shift, affecting the Ramsey fringe contrast over timescales >1 second. This study lays the groundwork for using a three-dimensional optical lattice clock to probe quantum magnetism and spin entanglement.
Optical lattice clocks have set records in clock precision and accuracy. Continuing to advance their performance, via probing as many atoms as possible for the longest interrogation time affordable, requires experimentally and theoretically studying a many-body lattice system. Motivated by recent experimental results on a Fermi-degenerate three-dimensional optical lattice clock [W. R. Milner et al., Science 388, 503 (2025)], we present a theoretical overview of Ramsey and Rabi spectroscopy in one-dimensional chains. At realistic experimental temperatures and confinement conditions, atoms are spatially localized into small chains of approximately one to five atoms. We show that in the presence of spin-orbit coupling induced by the clock laser, the spectroscopy observables are modified by superexchange interactions within each chain, and depend strongly on the length of the chain. The thermal distribution of chain lengths thus plays a key role in the spectroscopy measurements. Our results offer insight into observable many-body effects in state-of-the-art lattice clocks and suggest new directions for optimizing clock performance.
Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a "magic" lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.
In this work we study the effect of interactions in an optical lattice clock based on fermionic Sr atoms. In current one-dimensional lattice clocks nuclear spin-polarized atoms are known to have contact interactions of p-wave character and collective in nature. Here we focus on interactions that will influence the design of future optical lattice clocks. We study the case where atoms are no longer confined to a single nuclear spin state. By using samples of atoms with different distributions among the ten nuclear spin states of Sr we show that these interactions are SU(N) symmetric up to a 3% uncertainty in our measurements. Through these measurements we are also able to determine all the s-wave and p-wave scattering lengths.\nWe also study the case of nuclear spin-polarized interacting atoms that are allowed to tunnel between different lattice sites where the electronic spin and the motion of these atoms become coupled. We observe spectroscopically the precession of the collective magnetization and evolution of spin locking effects arising from the interplay between p-wave interactions and interactions induced by the spin-orbit coupling. The many-body dynamics are captured by a spin model that describes a broad class of condensed matter systems ranging from superconductors to quantum magnets.\nBy loading a dense sample of atoms into a magneto-optical trap we are able to observe long-range dipole-dipole interactions between our Sr atoms. These interactions will be important for atomic clocks based on a three dimensional lattice, such as the one recently demonstrated in our lab. In these clocks it is possible to remove the contact interactions between the atoms by loading only one atom per lattice site. In this case the dominant interactions will be from the long-range dipole-dipole interactions that will take place between the atoms.
We propose the use of optical lattice clocks operated with fermionic alkaline-earth atoms to study spin-orbit coupling (SOC) in interacting many-body systems. The SOC emerges naturally during the clock interrogation, when atoms are allowed to tunnel and accumulate a phase set by the ratio of the "magic" lattice wavelength to the clock transition wavelength. We demonstrate how standard protocols such as Rabi and Ramsey spectroscopy that take advantage of the sub-Hertz resolution of state-of-the-art clock lasers can perform momentum-resolved band tomography and determine SOC-induced s-wave collisions in nuclear-spin-polarized fermions. With the use of a second counterpropagating clock beam, we propose a method for engineering controlled atomic transport and study how it is modified by p- and s-wave interactions. The proposed spectroscopic probes provide clean and well-resolved signatures at current clock operating temperatures.
Advances in ultra-stable lasers now permit sub-Hz resolution of optical atomic transitions. At this level, weak interactions by any ordinary scale can in fact dominate the dynamics of the interrogated atoms, even for spin polarized fermions at ultralow temperatures. Contrary to results obtained in radio frequency spectroscopy of alkali fermionic atoms, optical spectroscopy of 87 Sr and 171 Yb has revealed density dependent frequency shifts of the 1 S0 - 3 P 0 “clock” transition. Understanding interactions in these systems is necessary to improve their accuracy and stability. Moreover, such an understanding will enable optical lattice clock systems to serve as quantum simulators for open, driven, strongly-interacting quantum systems at the mesoscopic scale. In this talk we presented our progress towards a comprehensive evaluation and understanding of the interactions present during spectroscopy of the 87 Sr clock transition under various operating conditions. Our studies indicate that a mean-field solution of a master equation is sufficient to capture the many-body dynamics of alkaline earth atom clocks. Entering the regime in which a treatment beyond mean-field is required for a proper description of the clock dynamics is under immediate experimental reach.
We report on the observation of a high-density, band insulating state in a three-dimensional optical lattice clock. Filled with a nuclear-spin-polarized degenerate Fermi gas of 87Sr^{87}\mathrm{Sr}87Sr, the three-dimensional (3D) lattice has one atom per site in the ground motional state, thus guarding against frequency shifts due to contact interactions. At this high density where the average distance between atoms is comparable to the probe wavelength, conventional imaging techniques at saturation intensity suffer from large systematic errors. To spatially probe frequency shifts in the clock and measure thermodynamic properties of this system, accurate imaging techniques at high optical depths are required. Using a combination of highly saturated fluorescence and absorption imaging, we confirm the density distribution in our 3D optical lattice in agreement with a single spin band insulating state. Combining our clock platform with this high filling fraction opens the door to studying new classes of long-lived, many-body states arising from dipolar interactions.