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arXiv:2507.11433 · Physical Review A

Effects of small-chain superexchange dynamics on spin-orbit-coupled clock spectroscopy

Mikhail Mamaev, Ana María Rey, William R. Milner

Published Nov 21, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/x7ly-x5vy

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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.
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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.
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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.
A recent realization of three-dimensional optical lattice clocks circumvents short-range collisional clock shifts which have been the bottle neck towards higher precision; the long-range electronic dipole-dipole interaction between the atoms becomes the primary source of clock shift due to interatomic interactions. We study the Rabi spectroscopy of three-dimensional optical lattice clocks with unity filling. From the Lindblad equation governing the time evolution of the density matrix of the atoms, we derive the Bloch equations in the presence of the external Rabi driving laser field, and solve the equations approximately to the first order of the coupling strength of the dipole-dipole interaction between the atoms. We find that the clock shift equals the product of the coupling strength, a factor determined by the parameters of the Rabi pulse, and another factor depending on the configuration of the three-dimensional optical lattice. Our result on the clock shift within the Rabi spectroscopy can be checked by measurements in a future experiment.
Rapid progress in the precision and accuracy of optical atomic clocks over the last decade has advanced the frontiers of timekeeping, metrology, and quantum science. However, the stabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves, leaving room for further progress. Here we implement a "multiplexed" one-dimensional optical lattice clock, in which spatially-resolved, movable ensembles of ultra-cold strontium atoms are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser, and read-out in parallel. By performing synchronized Ramsey interrogations of ensemble pairs we observe atom-atom coherence times up to 26 seconds, a 270-fold improvement over the atom-laser coherence time, demonstrate a relative stability of 9.7(4)×10−18/τ9.7(4)\times10^{-18}/\sqrtτ9.7(4)×10−18/τ​ (where τττ is the averaging time in seconds), and reach a fractional uncertainty of 8.9(3)×10−208.9(3)\times 10^{-20}8.9(3)×10−20 after 3.3 hours of averaging. These results demonstrate that applications requiring ultra-high-precision comparisons between optical atomic clocks need not be limited by the stability of the local oscillator. With multiple ensemble pairs, we realize a miniaturized clock network consisting of 6 atom ensembles, resulting in 15 unique pairwise clock comparisons with relative stabilities below 3×10−17/τ3\times10^{-17}/\sqrtτ3×10−17/τ​. Finally, we demonstrate the capability to simultaneously load spatially-resolved, heterogeneous ensemble pairs of all four stable isotopes of strontium in a lattice. The unique capabilities offered by this platform pave the way for future studies of precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, development of clock-based gravitational wave and dark matter detectors, and novel tests of relativity including measurements of the gravitational redshift at sub-centimeter scales.