Engineered spin–orbit coupling (SOC) in cold-atom systems can enable the study of new synthetic materials and complex condensed matter phenomena1,2,3,4,5,6,7,8. However, spontaneous emission in alkali-atom spin–orbit-coupled systems is hindered by heating, limiting the observation of many-body effects1,2,5 and motivating research into potential alternatives9,10,11. Here we demonstrate that spin–orbit-coupled fermions can be engineered to occur naturally in a one-dimensional optical lattice clock12. In contrast to previous SOC experiments1,2,3,4,5,6,7,8,9,10,11, here the SOC is both generated and probed using a direct ultra-narrow optical clock transition between two electronic orbital states in 87Sr atoms. We use clock spectroscopy to prepare lattice band populations, internal electronic states and quasi-momenta, and to produce spin–orbit-coupled dynamics. The exceptionally long lifetime of the excited clock state (160 seconds) eliminates decoherence and atom loss from spontaneous emission at all relevant experimental timescales, allowing subsequent momentum- and spin-resolved in situ probing of the SOC band structure and eigenstates. We use these capabilities to study Bloch oscillations, spin–momentum locking and Van Hove singularities in the transition density of states. Our results lay the groundwork for using fermionic optical lattice clocks to probe new phases of matter.
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We are grateful to N. R. Cooper for insights and discussions, and S. L. Campbell, N. Darkwah Oppong, A. Goban, R. B. Hutson, D. X. Reed, J. Robinson, L. Sonderhouse and W. Zhang for technical contributions and discussions. This research is supported by NIST, the NSF Physics Frontier Center at JILA (NSF-PFC-1125844), AFOSR-MURI, AFOSR, DARPA and ARO. S.K., M.L.W. and G.E.M. acknowledge the NRC postdoctoral fellowship programme.
The authors declare no competing financial interests.
Nature thanks L. Duan and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
a, Spectroscopy of atoms prepared in |g〉0 reveals the band spacing of the lattice, with inter-band transitions colour-coded by the final band. b, Spectroscopy of atoms in |e〉1, prepared by driving the |g〉0 → |e〉1 transition shown in a and then removing any remaining atoms in |g〉. The spectrum for atoms in |e〉0 from Fig. 1d is shown for comparison (dashed grey line).
a–e, Theoretical modelling of carrier line shapes starting from the |g〉0 (a–c) or |e〉1 (d, e) state. For the ground band transitions (a–c), all data were taken using a π pulse, and are well reproduced by a perturbative model (solid lines). Three specific cases are shown covering from the deep-lattice regime (Uz ≈ 65Er; a) to the moderate-lattice regime (Uz ≈ 10Er; b), and down to the shallow-lattice limit (Uz ≈ 3Er; c). For the first excited band transitions, the data in the deeper-lattice case (Uz ≈ 21.3Er), taken with a π pulse, are well reproduced by the perturbative model (d). However, for the case of Uz ≈ 16Er where a longer pulse was used, the perturbative theory, which ignores radial sideband transitions induced by the laser, captures only the width of the line shape and not its amplitude (e).
Theoretical probability distribution P(q, nr) of quasi-momentum and radial quantum number nr of |e〉 excitations resulting from exciting a thermal distribution in |g〉 with a 50-ms π pulse. The lattice depth is Uz ≈ 16Er, resulting in a tunnelling rate of J ≈ 17 Hz. The distribution of atoms among q is broadened owing to the fact that the Rabi frequency and tunnelling rates are comparable, but can be made narrower by decreasing the Rabi frequency.
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Kolkowitz, S., Bromley, S., Bothwell, T. et al. Spin–orbit-coupled fermions in an optical lattice clock. Nature 542, 66–70 (2017). https://doi.org/10.1038/nature20811
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