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Symmetry-driven zero-frequency-pulling lasing via superradiant sidebands for active optical clocks

Mingyu Jeon¹, Jinuk Kim^2,*, and Kyungwon An ^1,†

¹Department of Physics and Astronomy & Institute of Applied Physics, Seoul National University, Seoul 08826, South Korea
²Korea Research Institute of Standards and Science, Daejeon 34113, South Korea

^*Contact author: jinuk.kim@kriss.re.kr
^†Contact author: kwan@phya.snu.ac.kr

Phys. Rev. Research 8, 023063 – Published 20 April, 2026

DOI: https://doi.org/10.1103/q6lc-f9b8

Abstract

Active optical clocks based on collective atomic emission promise narrow lasing linewidths as well as reduced sensitivity to cavity fluctuations, yet residual frequency pulling limits their ultimate precision. Here, we propose a laser scheme that simultaneously achieves vanishing frequency pulling and ultranarrow linewidths by exploiting symmetry in collective superradiant emission. Atoms in a dense beam traversing a bad cavity are prepared in controlled superposition states using a pump laser with a sinusoidally modulated Rabi frequency $Ω_{m}$ . The resulting emission spectrum consists of a central lasing peak at the atomic resonance and two superradiant sidebands at symmetric detunings $\pm Ω_{m}$ . Owing to their symmetric interaction, the central peak is protected against cavity-induced frequency shifts over detunings comparable to the cavity linewidth. As the atom number increases, its linewidth narrows far beyond the conventional gain-narrowing limit, reaching values as small as one millionth of the cavity linewidth. Small pump detunings break the symmetry of the sideband intensities, providing a robust error signal to stabilize the pump frequency without an external reference cavity. These results establish a symmetry-driven route toward ultrastable active optical clocks and collective-radiation sources with exceptional frequency stability.

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References (31)

S. Diddams, T. Udem, J. Bergquist, A. Curtis, R. Drullinger, L. Hollberg, W. Itano, W. Lee, C. Oates, K. Vogel, and D. Wineland, An optical clock based on a single trapped ${}^{199}{Hg}^{+}$ ion, Science 293, 825 (2001).
C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, Optical clock comparison for Lorentz symmetry testing, Nature (London) 567, 204 (2019).
A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Clock with $8 \times 10^{- 19}$ systematic uncertainty, Phys. Rev. Lett. 133, 023401 (2024).
S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, ${}^{27}{Al}^{+}$ quantum-logic clock with a systematic uncertainty below $10^{- 18}$ , Phys. Rev. Lett. 123, 033201 (2019).
P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, Spectroscopy using quantum logic, Science 309, 749 (2005).
T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Frequency ratio of ${Al}^{+}$ and ${Hg}^{+}$ single-ion optical clocks; metrology at the 17th decimal place, Science 319, 1808 (2008).
P. Micke, T. Leopold, S. A. King, E. Benkler, L. J. Spieß, L. Schmöger, M. Schwarz, J. R. C. López-Urrutia, and P. O. Schmidt, Coherent laser spectroscopy of highly charged ions using quantum logic, Nature (London) 578, 60 (2020).
M. Steinel, H. Shao, M. Filzinger, B. Lipphardt, M. Brinkmann, A. Didier, T. E. Mehlstäubler, T. Lindvall, E. Peik, and N. Huntemann, Evaluation of a ${}^{88}{Sr}^{+}$ optical clock with a direct measurement of the blackbody radiation shift and determination of the clock frequency, Phys. Rev. Lett. 131, 083002 (2023).
H. N. Hausser, J. Keller, T. Nordmann, N. M. Bhatt, J. Kiethe, H. Liu, I. M. Richter, M. von Boehn, J. Rahm, S. Weyers, E. Benkler, B. Lipphardt, S. Dörscher, K. Stahl, J. Klose, C. Lisdat, M. Filzinger, N. Huntemann, E. Peik, and T. E. Mehlstäubler, ${}^{115}{In}^{+} − {}^{172}{Yb}^{+}$ coulomb crystal clock with $2.5 \times 10^{- 18}$ systematic uncertainty, Phys. Rev. Lett. 134, 023201 (2025).
G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, Optical clock with ultracold neutral atoms, Phys. Rev. Lett. 89, 230801 (2002).
H. Katori, M. Takamoto, V. G. Pal’chikov, and V. D. Ovsiannikov, Ultrastable optical clock with neutral atoms in an engineered light shift trap, Phys. Rev. Lett. 91, 173005 (2003).
M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, An optical lattice clock, Nature (London) 435, 321 (2005).
J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, A steady-state superradiant laser with less than one intracavity photon, Nature (London) 484, 78 (2012).
M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, Superradiance on the millihertz linewidth strontium clock transition, Sci. Adv. 2, e1601231 (2016).
J. Zhang, T. Shi, J. Miao, D. Yu, and J. Chen, An extremely bad-cavity laser, npj Quantum Inf. 10, 87 (2024).
Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, Frequency comparison of two ${}^{40}{Ca}^{+}$ optical clocks with an uncertainty at the $10^{- 17}$ level, Phys. Rev. Lett. 116, 013001 (2016).
K. Beloy, M. I. Bodine, T. Bothwell, S. M. Brewer, S. L. Bromley, J.-S. Chen, J.-D. Deschênes, S. A. Diddams, R. J. Fasano, T. M. Fortier, et al., Frequency ratio measurements at 18-digit accuracy using an optical clock network, Nature (London) 591, 564 (2021).
M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, Ultrastable optical clock with two cold-atom ensembles, Nat. Photon. 11, 48 (2017).
J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, et al., Geodesy and metrology with a transportable optical clock, Nat. Phys. 14, 437 (2018).
S. Origlia, M. S. Pramod, S. Schiller, Y. Singh, K. Bongs, R. Schwarz, A. Al-Masoudi, S. Dörscher, S. Herbers, S. Häfner, U. Sterr, and C. Lisdat, Towards an optical clock for space: Compact, high-performance optical lattice clock based on bosonic atoms, Phys. Rev. A 98, 053443 (2018).
H. Liu, S. B. Jäger, X. Yu, S. Touzard, A. Shankar, M. J. Holland, and T. L. Nicholson, Rugged mHz-linewidth superradiant laser driven by a hot atomic beam, Phys. Rev. Lett. 125, 253602 (2020).
J. R. K. Cline, V. M. Schäfer, Z. Niu, D. J. Young, T. H. Yoon, and J. K. Thompson, Continuous collective strong coupling of strontium atoms to a high finesse ring cavity, Phys. Rev. Lett. 134, 013403 (2025).
B. J. Larsen, H. Hensley, G. Martinez, A. Staron, W. R. McGehee, J. Kitching, and J. K. Thompson, A chip-scale atomic beam source for non-classical light, arXiv:2506.00199 [physics.atom-ph].
J. Kim, S.-H. Oh, D. Yang, J. Kim, M. Lee, and K. An, A photonic quantum engine driven by superradiance, Nat. Photon. 16, 707 (2022).
High-current ion beams at tens of keV with centimeter-scale diameters have been experimentally demonstrated. In particular, M. Zhang [31] reported extracted proton beams with energies of 50 keV and currents up to 100 mA, with measured beam diameters on the order of 20 mm. These experimentally achieved parameters support the feasibility of realizing high-flux ion beams in the tens-of-keV energy range relevant to the present proposal.
W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, Observation of sub-Poisson photon statistics in the cavity-QED microlaser, Phys. Rev. Lett. 96, 093603 (2006).
H.-G. Hong, W. Seo, Y. Song, M. Lee, H. Jeong, Y. Shin, W. Choi, R. R. Dasari, and K. An, Spectrum of the cavity-QED microlaser: Strong coupling effects in the frequency pulling at off resonance, Phys. Rev. Lett. 109, 243601 (2012).
M. Tavis and F. W. Cummings, Exact solution for an $N$ -molecule—Radiation-field Hamiltonian, Phys. Rev. 170, 379 (1968).
C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
A feasible candidate for an initial experimental test is the 397-nm transition of ${}^{40}{Ca}^{+}$ in a 50-keV, 100-mA ion beam. The relevant parameters are a cavity linewidth $κ / 2 π = 6 GHz$ , an atomic linewidth $2 γ_{a} / 2 π = 21.6 MHz$ , a single-ion coupling strength $g / 2 π = 190 kHz$ , and an ion transit time $τ = 1.4 ns$ . The number of ions interacting with the cavity mode is estimated to be $N = 1.5 \times 10^{8}$ , assuming a pump-cavity separation of 1.0 mm. The pump Rabi frequency is taken to be $Ω_{m} / 2 π = 10 MHz$ , with a pulse area $Ω τ_{p} = 0.936 π$ . Based on our numerical simulations, the projected collective decay rate is $Γ_{c} / 2 π \approx 23 Hz$ and the number of collective emission events is $N_{coll} \sim 31$ , leading to an expected linewidth on the order of 1 Hz. The proposed parameters satisfy the bad-cavity condition, $κ ≫ \sqrt{N} g, \sqrt{n} g$ , with an estimated mean intracavity photon number of $n \sim 1.4 \times 10^{6}$ .
M. Zhang et al., Upgrade of the extraction system of permanent magnet electron cyclotron resonance ion source, Rev. Sci. Instrum. 81, 02B715 (2010).

Phys. Rev. Research 8, 023063– Published 20 April, 2026

Vol. 8, Iss. 2 — April - June 2026

Received 14 December 2025
Accepted 1 April 2026

DOI: https://doi.org/10.1103/q6lc-f9b8

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Symmetry-driven zero-frequency-pulling lasing via superradiant sidebands for active optical clocks

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