- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Collective light shifts of many longitudinal cavity modes induced by coupling to a cold-atom ensemble

Marin Ðujić1, Mateo Kruljac1, Lovre Kardum1, Neven Šantić1, Damir Aumiler1, Ivor Krešić1,2,*, and Ticijana Ban1

  • *Contact author: ikresic@ifs.hr
PDF

Phys. Rev. Research 8, 013288 – Published 17 March, 2026

DOI: https://doi.org/10.1103/fy4n-mj4d

Abstract

We experimentally study the interaction between a cold-atom cloud and many longitudinal modes of a high-quality Fabry-Perot cavity, by measuring signatures of collective light shifts in the cavity transmission spectrum of an optical frequency comb probe. Using a resonator coupled to more than 105 intracavity atoms, we detect significant shifts of ∼100 cavity modes simultaneously, which is a direct manifestation of physics beyond the hitherto explored regime of cavity-cold atom interaction with only single or few longitudinal modes at a time. For the cavity mode closest to the atomic resonance, we demonstrate a bistability in the transmission spectrum, arising due to a combined coupling of the cloud to an external pump laser and a cavity mode probed by the optical frequency comb. These results provide a first step toward deeper exploration of multifrequency cavity quantum electrodynamics, where ultrashort pulsed sources could be used for optical manipulation, cooling, and entanglement of cold atoms in a resonator.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (59)

  1. H. J. Kimble, Strong interactions of single atoms and photons in cavity QED, Phys. Scr. 1998, 127 (1998).
  2. J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).
  3. A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).
  4. P. Domokos and H. Ritsch, Collective cooling and self-organization of atoms in a cavity, Phys. Rev. Lett. 89, 253003 (2002).
  5. H. W. Chan, A. T. Black, and V. Vuletić, Observation of collective-emission-induced cooling of atoms in an optical cavity, Phys. Rev. Lett. 90, 063003 (2003).
  6. M. Xu, S. B. Jäger, S. Schütz, J. Cooper, G. Morigi, and M. J. Holland, Supercooling of atoms in an optical resonator, Phys. Rev. Lett. 116, 153002 (2016).
  7. M. Hosseini, Y. Duan, K. M. Beck, Y.-T. Chen, and V. Vuletić, Cavity cooling of many atoms, Phys. Rev. Lett. 118, 183601 (2017).
  8. I. D. Leroux, M. H. Schleier-Smith, and V. Vuletić, Implementation of cavity squeezing of a collective atomic spin, Phys. Rev. Lett. 104, 073602 (2010).
  9. K. C. Cox, G. P. Greve, J. M. Weiner, and J. K. Thompson, Deterministic squeezed states with collective measurements and feedback, Phys. Rev. Lett. 116, 093602 (2016).
  10. A. T. Black, H. W. Chan, and V. Vuletić, Observation of collective friction forces due to spatial self-organization of atoms: From rayleigh to bragg scattering, Phys. Rev. Lett. 91, 203001 (2003).
  11. C. von Cube, S. Slama, D. Kruse, C. Zimmermann, P. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Self-synchronization and dissipation-induced threshold in collective atomic recoil lasing, Phys. Rev. Lett. 93, 083601 (2004).
  12. K. J. Arnold, M. P. Baden, and M. D. Barrett, Self-organization threshold scaling for thermal atoms coupled to a cavity, Phys. Rev. Lett. 109, 153002 (2012).
  13. J. A. Muniz, D. Barberena, R. J. Lewis-Swan, D. J. Young, J. R. Cline, A. M. Rey, and J. K. Thompson, Exploring dynamical phase transitions with cold atoms in an optical cavity, Nature (London) 580, 602 (2020).
  14. Y. Guo, R. M. Kroeze, B. P. Marsh, S. Gopalakrishnan, J. Keeling, and B. L. Lev, An optical lattice with sound, Nature (London) 599, 211 (2021).
  15. C. Luo, H. Zhang, C. Maruko, E. A. Bohr, A. Chu, A. M. Rey, and J. K. Thompson, Realization of three-and four-body interactions between momentum states in a cavity, Science 390, 925 (2025).
  16. A. J. Kollár, A. T. Papageorge, V. D. Vaidya, Y. Guo, J. Keeling, and B. L. Lev, Supermode-density-wave-polariton condensation with a bose–einstein condensate in a multimode cavity, Nat. Commun. 8, 14386 (2017).
  17. R. M. Kroeze, B. P. Marsh, D. Atri Schuller, H. S. Hunt, A. N. Bourzutschky, M. Winer, S. Gopalakrishnan, J. Keeling, and B. L. Lev, Directly observing replica symmetry breaking in a vector quantum-optical spin glass, Science 389, 1122 (2025).
  18. B. P. Marsh, D. A. Schuller, Y. Ji, H. S. Hunt, G. Z. Socolof, D. P. Bowman, J. Keeling, and B. L. Lev, Multimode cavity QED Ising spin glass, Phys. Rev. Lett. 135, 160403 (2025).
  19. H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys. 85, 553 (2013).
  20. F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, Cavity QED with quantum gases: New paradigms in many-body physics, Adv. Phys. 70, 1 (2021).
  21. N. Masalaeva, H. Ritsch, and F. Mivehvar, Tuning photon-mediated interactions in a multimode cavity: From supersolid to insulating droplets hosting phononic excitations, Phys. Rev. Lett. 131, 173401 (2023).
  22. V. Torggler, S. Krämer, and H. Ritsch, Quantum annealing with ultracold atoms in a multimode optical resonator, Phys. Rev. A 95, 032310 (2017).
  23. V. Torggler, I. Krešić, T. Ban, and H. Ritsch, Self-ordering and cavity cooling using a train of ultrashort pulses, New J. Phys. 22, 063003 (2020).
  24. D. Kielpinski, Laser cooling of atoms and molecules with ultrafast pulses, Phys. Rev. A 73, 063407 (2006).
  25. W. Chen, J. Hu, Y. Duan, B. Braverman, H. Zhang, and V. Vuletić, Carving complex many-atom entangled states by single-photon detection, Phys. Rev. Lett. 115, 250502 (2015).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/fy4n-mj4d for more details about the experimental procedure (cavity and frequency comb characterization and stabilization) and theoretical modeling, which includes Refs. [51, 52, 53, 54, 55, 56, 57, 58, 59].
  27. M. Tavis and F. W. Cummings, Exact solution for an N-molecule—radiation-field Hamiltonian, Phys. Rev. 170, 379 (1968).
  28. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  29. R. H. Lehmberg, Radiation from an N-atom system. I. General formalism, Phys. Rev. A 2, 883 (1970).
  30. A. Wickenbrock, M. Hemmerling, G. R. M. Robb, C. Emary, and F. Renzoni, Collective strong coupling in multimode cavity QED, Phys. Rev. A 87, 043817 (2013).
  31. D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, Coherent accumulation in two-level atoms excited by a train of ultrashort pulses, Opt. Commun. 215, 69 (2003).
  32. A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, United time-frequency spectroscopy for dynamics and global structure, Science 306, 2063 (2004).
  33. A. Marian, M. C. Stowe, D. Felinto, and J. Ye, Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics, Phys. Rev. Lett. 95, 023001 (2005).
  34. A. M. Jayich, X. Long, and W. C. Campbell, Direct frequency comb laser cooling and trapping, Phys. Rev. X 6, 041004 (2016).
  35. N. Šantić, D. Buhin, D. Kovačić, I. Krešić, D. Aumiler, and T. Ban, Cooling of atoms using an optical frequency comb, Sci. Rep. 9, 2510 (2019).
  36. M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs, Opt. Express 13, 882 (2005).
  37. I. Krešić, M. Kruljac, T. Ban, and D. Aumiler, Electromagnetically induced transparency with a single frequency comb mode probe, J. Opt. Soc. Am. B 36, 1758 (2019).
  38. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Differential gain and bistability using a sodium-filled Fabry-Perot interferometer, Phys. Rev. Lett. 36, 1135 (1976).
  39. H. Gothe, T. Valenzuela, M. Cristiani, and J. Eschner, Optical bistability and nonlinear dynamics by saturation of cold YB atoms in a cavity, Phys. Rev. A 99, 013849 (2019).
  40. A. Lambrecht, E. Giacobino, and J.-M. Courty, Optical nonlinear dynamics with cold atoms in a cavity, Opt. Commun. 115, 199 (1995).
  41. G. Labeyrie, I. Kresic, R. Kaiser, and T. Ackemann, Optical pattern formation in self-focusing and self-defocusing diffractively thick media, Phys. Rev. A 111, 063506 (2025).
  42. C. J. Foot, Atomic Physics, 1st ed. (Oxford University Press, Oxford, 2005).
  43. F. Canella, J. Weitenberg, M. Thariq, F. Schmid, P. Dwivedi, G. Galzerano, T. W. Hänsch, T. Udem, and A. Ozawa, Low-repetition-rate optical frequency comb, Optica 11, 1 (2024).
  44. A. Lambrecht, T. Coudreau, A. Steinberg, and E. Giacobino, Squeezing with cold atoms, Europhys. Lett. 36, 93 (1996).
  45. M. Chen, N. C. Menicucci, and O. Pfister, Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb, Phys. Rev. Lett. 112, 120505 (2014).
  46. J. Roslund, R. M. De Araujo, S. Jiang, C. Fabre, and N. Treps, Wavelength-multiplexed quantum networks with ultrafast frequency combs, Nat. Photonics 8, 109 (2014).
  47. J. F. Barry, Cold results from fast lasers, Physics 9, 115 (2016).
  48. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, A frequency comb in the extreme ultraviolet, Nature (London) 436, 234 (2005).
  49. J. Davila-Rodriguez, A. Ozawa, T. W. Hänsch, and T. Udem, Doppler cooling trapped ions with a UV frequency comb, Phys. Rev. Lett. 116, 043002 (2016).
  50. M. Đujic, M. Kruljac, L. Kardum, N. Šantic, D. Aumiler, I. Kresic, and T. Ban, Collective light shifts of many longitudinal cavity modes induced by coupling to a cold-atom ensemble - dataset, [Data set], Zenodo (2026), https://doi.org/10.5281/zenodo.18833614.
  51. M. Kruljac, Cavity cooling and self-organization of atoms using an optical frequency comb, Ph.D. thesis, Faculty of Science, Zagreb, 2022.
  52. R. M. Wilcox, Exponential operators and parameter differentiation in quantum physics, J. Math. Phys. 8, 962 (1967).
  53. X. Wang, F. P. M. Méndez-Córdoba, D. Jaksch, and F. Schlawin, Floquet schrieffer-wolff transform based on Sylvester equations, Phys. Rev. B 110, 245108 (2024).
  54. F. Arecchi and R. Bonifacio, Theory of optical maser amplifiers, IEEE J. Quantum Electron. 1, 169 (1965).
  55. B. Gábor, D. Nagy, A. Dombi, T. W. Clark, F. I. B. Williams, K. V. Adwaith, A. Vukics, and P. Domokos, Ground-state bistability of cold atoms in a cavity, Phys. Rev. A 107, 023713 (2023).
  56. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  57. M. J. Thorpe and J. Ye, Cavity-enhanced direct frequency comb spectroscopy, Appl. Phys. B 91, 397 (2008).
  58. N. Ismail, C. C. Kores, D. Geskus, and M. Pollnau, Fabry-pérot resonator: spectral line shapes, generic and related airy distributions, linewidths, finesses, and performance at low or frequency-dependent reflectivity, Opt. Express 24, 16366 (2016).
  59. R. W. Boyd and D. Prato, Nonlinear Optics, 3rd ed. (Academic Press, Amsterdam, 2008).

Outline

Information

Phys. Rev. Research 8, 013288– Published 17 March, 2026
  • Received 14 May 2025
  • Revised 24 October 2025
  • Accepted 20 February 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation