Hölzl et al. (Phys. Rev. Research 5, 033093 (2023)) demonstrated 'chirp cooling' of single 88Sr atoms in state-dependent optical tweezers, where the ground state is more strongly trapped than the excited state (αg/αe>1\alpha_g/\alpha_e>1): a linear frequency chirp of narrow-line cooling light sequentially addresses successive red sidebands, reaching radial ground-state fractions of 73–97% without magic trapping conditions. The paper explicitly leaves the completion of this scheme open: detailed investigation and optimization of cooling along the weakly confined axial direction, implementation of individually controlled radial and axial cooling beams in pulsed sequences to reach the full three-dimensional trap ground state, optimal-control design of the chirp waveforms, and exploitation of simultaneous cooling during narrow-line imaging to reach higher scattering rates in the so-far unexplored αg/αe>1\alpha_g/\alpha_e>1 regime. These tasks remain unaddressed in the literature to date: a 2025 dysprosium implementation of the same scheme remains radial-only with axial cooling explicitly left to future work, chirped cooling in three dimensions has been realized only in magic-wavelength optical lattices, and neighboring goals (3D ground-state atoms in tweezers, concurrent cooling-during-imaging) have been achieved by other mechanisms in magic traps, not in the state-dependent regime.

Background

An optical tweezer is a tightly focused, far-detuned laser beam whose dipole potential traps a single neutral atom at its focus, with motional trap frequencies of order 2π×100 2\pi\times100\,kHz in the tightly confined radial directions and typically an order of magnitude less along the weakly confined axial direction (the beam propagation axis). Resolved sideband cooling prepares the atom's motional ground state by driving laser transitions on the red motional sidebands (transitions that lower the vibrational quantum number by one) followed by spontaneous emission; it works most cleanly in so-called magic traps, where the AC Stark polarizabilities of the ground and excited states of the cooling transition are equal (αe=αg\alpha_e=\alpha_g), so the transition frequency is independent of the atom's position in the trap. This magic condition strongly constrains the usable trapping wavelength. Hölzl et al. (2023) studied the opposite, state-dependent regime αg/αe>1\alpha_g/\alpha_e>1, in which the ground state is more strongly trapped than the excited state and the sideband frequencies shift with motional quantum number. Their 'chirp cooling' scheme sweeps the frequency of cooling light on the narrow 1S0–3P1 intercombination line of 88Sr (a weak, narrow transition between states of different total spin, with linewidth γ=2π×7.4 \gamma=2\pi\times7.4\,kHz) linearly from −2π×4.1 -2\pi\times4.1\,MHz over 100 ms, sequentially resonating with successive red sidebands. In a 539.91 nm tweezer (waist 564(5) nm, radial trap frequency ωg=2π×126(5) \omega_g=2\pi\times126(5)\,kHz, polarizability ratios αg/αe≈1.13\alpha_g/\alpha_e\approx1.13 and ≈1.90\approx1.90 on the two accessible excited sublevel transitions) they reached radial ground-state fractions of 73–97% (from sideband spectroscopy with shelving into metastable states, cross-checked by release-and-recapture thermometry, a method that infers the motional temperature from the probability of recapturing the atom after a brief free expansion), comparable to sideband cooling in magic tweezers; the same light-assisted collisions (collisional loss of an atom pair triggered by optical excitation) provide parity projection, useful for deterministic assembly of large atom arrays. The platform is practically motivated: the chosen wavelength is magic for the 3P0 and 3P2 clock states (enabling clock-qubit encodings), and the scheme applies at wavelengths offering magic trapping of Rydberg states or to species incompatible with resolved-sideband conditions. However, the quantitative ground-state demonstration is radial: the axial direction enters only through an upper-bound estimate (the axial temperature is inferred not to exceed the radial one), and the source states that individually controlled radial and axial cooling beams applied in a pulsed sequence 'should allow for reaching the full three-dimensional trap ground-state', leaving a detailed investigation of the axial cooling dynamics for future work, together with optimal-control design of the chirps and higher-scattering-rate imaging in the αg/αe>1\alpha_g/\alpha_e>1 regime (the regime not explored by prior narrow-line imaging of strontium in shallow tweezers, which operated in the opposite case).

Problem Statement

In the state-dependent optical tweezer platform of Hölzl et al. — single atoms trapped more strongly in the ground state than in the excited state of the cooling transition, αg/αe>1\alpha_g/\alpha_e>1, cooled by frequency-chirped narrow-line light — can full three-dimensional motional ground-state preparation be achieved and quantitatively characterized? The source poses this as a set of connected open questions: (a) investigate and optimize the cooling dynamics along the weakly confined axial tweezer direction, where the demonstrated ground-state occupation is so far only radial and the axial temperature is merely bounded from above; (b) whether the full three-dimensional trap ground state can be reached, with the ground-state populations along all three axes determined (measured experimentally or modeled quantitatively); (c) in that context, whether the frequency-chirped cooling pulses can be optimized to increase the cooling efficiency of the scheme; and (d) as the detection-side extension of the same scheme, what photon scattering rate for atom detection can be achieved on the narrow intercombination transition in the hitherto unexplored αg/αe>1\alpha_g/\alpha_e>1 regime, with the achievable rate quantified. Together, questions (a)–(c) concern completing chirp cooling into a full three-dimensional ground-state preparation tool for state-dependent (non-magic) tweezers; (d) concerns the detection capability of the same scheme, stated in the source's outlook.

References

  1. C. Hölzl, A. Götzelmann, M. Wirth, M. S. Safronova, S. Weber, F. Meinert, 'Motional ground-state cooling of single atoms in state-dependent optical tweezers', Phys. Rev. Research 5, 033093 (2023), DOI 10.1103/PhysRevResearch.5.033093, arXiv:2302.03940, https://arxiv.org/abs/2302.03940
  2. A. Urech, I. H. A. Knottnerus, R. J. C. Spreeuw, F. Schreck, 'Narrow-line imaging of single strontium atoms in shallow optical tweezers', Phys. Rev. Research 4, 023245 (2022), DOI 10.1103/PhysRevResearch.4.023245, arXiv:2202.05727, https://arxiv.org/abs/2202.05727
  3. G. Biagioni, B. Hofer, N. Bonvalet, D. Bloch, A. Browaeys, I. Ferrier-Barbut, 'Narrowline cooling of dysprosium atoms in an optical tweezer array', Phys. Rev. A 112, 013316 (2025), DOI 10.1103/k4vn-y7mb, arXiv:2505.03456, https://arxiv.org/abs/2505.03456
  4. R. M. Kroeze, R. A. Villela, E. Zu, T. O. Höhn, M. Aidelsburger, 'Isotope-agnostic motional ground-state cooling of neutral Yb atoms', Phys. Rev. Research 7, L042061 (2025), DOI 10.1103/dts5-kxsx, arXiv:2506.09031, https://arxiv.org/abs/2506.09031
  5. A. L. Shaw, P. Scholl, R. Finkelstein, R. B.-S. Tsai, J. Choi, M. Endres, 'Erasure cooling, control, and hyperentanglement of motion in optical tweezers', Science 388, 845–849 (2025), DOI 10.1126/science.adn2618, arXiv:2311.15580, https://arxiv.org/abs/2311.15580
  6. Y. Song, K. Kim, J. H. Han, S. Oh, J. Mun, 'High performance imaging of 171Yb atom in shallow clock-magic tweezer by alternating dual-tone narrowline cooling', arXiv:2603.27498 (2026), https://arxiv.org/abs/2603.27498
  7. S. S. Phatak, K. N. Blodgett, D. Peana, M. R. Chen, J. D. Hood, 'Generalized theory for optical cooling of a trapped atom with spin', Phys. Rev. A 110, 043116 (2024), DOI 10.1103/PhysRevA.110.043116, arXiv:2406.19153, https://arxiv.org/abs/2406.19153
  8. K. N. Blodgett, S. S. Phatak, M. R. Chen, D. Peana, C. Pritts, J. D. Hood, 'Narrow-line electric quadrupole cooling and background-free imaging of a single Cs atom with spatially structured light', Phys. Rev. A 112, 043109 (2025), DOI 10.1103/vr4g-h995, arXiv:2505.10540, https://arxiv.org/abs/2505.10540
  9. O. Morandi, S. Nicoletti, V. Gavryusev, L. Fallani, 'Optimal control in phase space applied to minimal-time transfer of thermal atoms in optical traps', Phys. Rev. A 111, 063312 (2025), DOI 10.1103/d857-7cwr, https://doi.org/10.1103/d857-7cwr
  10. L. Kley, N. Heimann, A. Parvej, L. Broers, L. Mathey, 'Optimal recoil-free state preparation in an optical atom tweezer', arXiv:2411.02262 (2024), https://arxiv.org/abs/2411.02262
  11. R. B.-S. Tsai, L. R. B. Picard, X. Sun, Y. Le, K. H. Leung, M. Endres, 'Gate-based Readout and Cooling of Neutral Atoms', arXiv:2603.21643 (2026), https://arxiv.org/abs/2603.21643
  12. M. Venderbosch, R. van Herk, Z. Guo, J. del Pozo Mellado, M. Festenstein, D. Janse van Rensburg, I. Knottnerus, Y. C. Tseng, A. Urech, R. J. C. Spreeuw, F. Schreck, R. Lous, E. Vredenbregt, S. Kokkelmans, 'A robust strontium tweezer apparatus for quantum computing', AIP Advances 16, 075205 (2026), DOI 10.1063/5.0324304, arXiv:2601.16564, https://arxiv.org/abs/2601.16564