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Narrowline Laser Cooling and Spectroscopy of Molecules via Stark States

Kameron Mehling1,2, Justin J. Burau1,2, Logan E. Hillberry1,2, Mengjie Chen1,2, Parul Aggarwal1,2, Lan Cheng3, Jun Ye1,2,*, and Simon Scheidegger1,2

  • 1JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309-0440, USA
  • 2Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
  • 3Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA

  • *Contact author: ye@jila.colorado.edu
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PRX Quantum 6, 040370 – Published 23 December, 2025

DOI: https://doi.org/10.1103/9v1s-d6bd

Abstract

The electronic energy level structure of yttrium monoxide (YO) provides a long-lived, low-lying 2Δ state ideal for high-precision molecular spectroscopy, narrowline laser cooling at the single photon-recoil limit, and studying dipolar physics with unprecedented interaction strength. High-resolution laser spectroscopy of ultracold laser-cooled YO molecules is used to study the Stark effect in the A′2Δ3/2J=3/2 state. An immediate onset of the linear Stark effect is observed in the presence of weak applied electric fields due to the near-degenerate Λ doublet and the large electric dipole moment. By applying a small electric field the Stark-insensitive state is spectroscopically isolated and the absolute transition frequency to the X2Σ+ electronic ground state is determined with a fractional frequency uncertainty of 9×10−12. This electric field control is necessary to implement a quasi-closed photon-cycling scheme that preserves parity. With this scheme the first narrowline laser cooling of a molecule is demonstrated, reducing the temperature of sub-Doppler cooled YO in two dimensions.

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Popular Summary

Quantum state control over the rich internal structure of molecules provides platforms for studying long-range dipolar physics, cold chemistry, and violations of fundamental symmetries. Over the past decade molecular laser cooling has progressed to establish motional and internal state control, although all photon-cycling schemes have been limited to addressing short-lived excited states. Extending quantum state control to long-lived excited states enables previously inaccessible laser-cooling schemes and experimental applications.

In this work, small electric fields are used to manipulate the internal states of the long-lived first excited state of yttrium monoxide. This additional experimental control enables isolation of individual quantum states and provides an easily accessible quasi-closed photon-cycling scheme. Narrowline laser cooling of a molecule is achieved, along with measurements of electronic transition frequencies with state-of-the-art precision for a polar molecule.

Subsequent work will leverage narrowline cooling for molecules to reach their motional ground state within an optical trap. Additionally, an even-longer-lived excited state exists with stronger electric-field susceptibility than the metastable state under investigation. This prospective state could serve as an ideal platform for studying fundamental physics and exploring strongly interacting many-body dynamics. The desirable properties of these metastable states naturally extend to a broad class of molecules, expanding the arsenal of quantum control methods available to molecular laser cooling.

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References (126)

  1. J. P. Gordon, H. J. Zeiger, and C. H. Townes, Molecular microwave oscillator and new hyperfine structure in the microwave spectrum of NH3, Phys. Rev. 95, 282 (1954).
  2. J. J. Hudson, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, Measurement of the electron electric dipole moment using YbF molecules, Phys. Rev. Lett. 89, 023003 (2002).
  3. V. Andreev, D. G. Ang, D. DeMille, J. M. Doyle, G. Gabrielse, J. Haefner, N. R. Hutzler, Z. Lasner, C. Meisenhelder, B. R. O’Leary, C. D. Panda, A. D. West, E. P. West, and X. Wu (ACME Collaboration), Improved limit on the electric dipole moment of the electron, Nature 562, 355 (2018).
  4. T. S. Roussy, L. Caldwell, T. Wright, W. B. Cairncross, Y. Shagam, K. B. Ng, N. Schlossberger, S. Y. Park, A. Wang, J. Ye, and E. A. Cornell, An improved bound on the electron’s electric dipole moment, Science 381, 46 (2023).
  5. H. P. Büchler, E. Demler, M. Lukin, A. Micheli, N. Prokof’ev, G. Pupillo, and P. Zoller, Strongly correlated 2D quantum phases with cold polar molecules: Controlling the shape of the interaction potential, Phys. Rev. Lett. 98, 060404 (2007).
  6. K. Góral, L. Santos, and M. Lewenstein, Quantum phases of dipolar bosons in optical lattices, Phys. Rev. Lett. 88, 170406 (2002).
  7. T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, The physics of dipolar bosonic quantum gases, Rep. Progr. Phys. 72, 126401 (2009).
  8. L. Pollet, J. D. Picon, H. P. Büchler, and M. Troyer, Supersolid phase with cold polar molecules on a triangular lattice, Phys. Rev. Lett. 104, 125302 (2010).
  9. L. Christakis, J. S. Rosenberg, R. Raj, S. Chi, A. Morningstar, D. A. Huse, Z. Z. Yan, and W. S. Bakr, Probing site-resolved correlations in a spin system of ultracold molecules, Nature 614, 64 (2023).
  10. C. Miller, A. N. Carroll, J. Lin, H. Hirzler, H. Gao, H. Zhou, M. D. Lukin, and J. Ye, Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules, Nature 633, 332 (2024).
  11. D. DeMille, Quantum computation with trapped polar molecules, Phys. Rev. Lett. 88, 067901 (2002).
  12. S. F. Yelin, K. Kirby, and R. Côté, Schemes for robust quantum computation with polar molecules, Phys. Rev. A 74, 050301(R) (2006).
  13. M. Karra, K. Sharma, B. Friedrich, S. Kais, and D. Herschbach, Prospects for quantum computing with an array of ultracold polar paramagnetic molecules, J. Chem. Phys. 144, 094301 (2016).
  14. S. L. Cornish, M. R. Tarbutt, and K. R. A. Hazzard, Quantum computation and quantum simulation with ultracold molecules, Nat. Phys. 20, 730 (2024).
  15. C. Zhang and M. R. Tarbutt, Quantum computation in a hybrid array of molecules and Rydberg atoms, PRX Quantum 3, 030340 (2022).
  16. K.-K. Ni, S. Ospelkaus, D. Wang, G. Quéméner, B. Neyenhuis, M. H. G. de Miranda, J. L. Bohn, J. Ye, and D. S. Jin, Dipolar collisions of polar molecules in the quantum regime, Nature 464, 1324 (2010).
  17. R. Bause, A. Christianen, A. Schindewolf, I. Bloch, and X.-Y. Luo, Ultracold sticky collisions: Theoretical and experimental status, J. Phys. Chem. A 127, 729 (2023).
  18. I. I. Rabi, S. Millman, P. Kusch, and J. R. Zacharias, The molecular beam resonance method for measuring nuclear magnetic moments. The magnetic moments of 3Li6, 3Li7 and 9F19, Phys. Rev. 55, 526 (1939).
  19. H. Bennewitz, W. Paul, and C. Schlier, Fokussierung polarer moleküle, Z. Phys. 141, 6 (1955).
  20. N. Ramsey, Molecular Beams (Oxford University, Oxford, 1956), Vol. 20.
  21. Hendrick L. Bethlem, G. Berden, and G. Meijer, Decelerating neutral dipolar molecules, Phys. Rev. Lett. 83, 1558 (1999).
  22. S. Y. T. van de Meerakker, H. L. Bethlem, and G. Meijer, Taming molecular beams, Nat. Phys. 4, 595 (2008).
  23. D. Reens, H. Wu, A. Aeppli, A. McAuliffe, P. Wcisło, T. Langen, and J. Ye, Beyond the limits of conventional Stark deceleration, Phys. Rev. Res. 2, 033095 (2020).
  24. P. Jansen and F. Merkt, Manipulating beams of paramagnetic atoms and molecules using inhomogeneous magnetic fields, Prog. Nucl. Magn. Reson. Spectrosc. 120–121, 118 (2020).
  25. R. E. Drullinger and R. N. Zare, Optical pumping of molecules, J. Chem. Phys. 51, 5532 (1969).
  26. M. Viteau, A. Chotia, M. Allegrini, N. Bouloufa, O. Dulieu, D. Comparat, and P. Pillet, Optical pumping and vibrational cooling of molecules, Science 321, 232 (2008).
  27. L. D. Carr, D. DeMille, R. V. Krems, and J. Ye, Cold and ultracold molecules: Science, technology and applications, New J. Phys. 11, 055049 (2009).
  28. X. Wu, Z. Han, J. Chow, D. G. Ang, C. Meisenhelder, C. D. Panda, E. P. West, G. Gabrielse, J. M. Doyle, and D. DeMille, The metastable Q3Δ2 state of ThO: A new resource for the ACME electron EDM search, New J. Phys. 22, 023013 (2020).
  29. M. D. Rosa, Laser-cooling molecules: Concept, candidates, and supporting hyperfine-resolved measurements of rotational lines in the A-X(0,0) band of CaH, Eur. Phys. J. D 31, 395 (2004).
  30. Benjamin K. Stuhl, Brian C. Sawyer, D. Wang, and J. Ye, Magneto-optical trap for polar molecules, Phys. Rev. Lett. 101, 243002 (2008).
  31. N. Fitch and M. Tarbutt, Chapter three - laser-cooled molecules, Adv. At., Mol. Opt. Phys. 70, 157 (2021).
  32. V. Zhelyazkova, A. Cournol, T. E. Wall, A. Matsushima, J. J. Hudson, E. A. Hinds, M. R. Tarbutt, and B. E. Sauer, Laser cooling and slowing of CaF molecules, Phys. Rev. A 89, 053416 (2014).
  33. Matthew T. Hummon, M. Yeo, Benjamin K. Stuhl, Alejandra L. Collopy, Y. Xia, and J. Ye, 2D magneto-optical trapping of diatomic molecules, Phys. Rev. Lett. 110, 143001 (2013).
  34. B. Hemmerling, E. Chae, A. Ravi, L. Anderegg, G. K. Drayna, N. R. Hutzler, A. L. Collopy, J. Ye, W. Ketterle, and J. M. Doyle, Laser slowing of CaF molecules to near the capture velocity of a molecular MOT, J. Phys. B: At. Mol. Opt. Phys. 49, 174001 (2016).
  35. J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, Magneto-optical trapping of a diatomic molecule, Nature 512, 286 (2014).
  36. M. R. Tarbutt and T. C. Steimle, Modeling magneto-optical trapping of CaF molecules, Phys. Rev. A 92, 053401 (2015).
  37. L. Anderegg, Benjamin L. Augenbraun, E. Chae, B. Hemmerling, Nicholas R. Hutzler, A. Ravi, A. Collopy, J. Ye, W. Ketterle, and John M. Doyle, Radio frequency magneto-optical trapping of CaF with high density, Phys. Rev. Lett. 119, 103201 (2017).
  38. Alejandra L. Collopy, S. Ding, Y. Wu, Ian A. Finneran, L. Anderegg, Benjamin L. Augenbraun, John M. Doyle, and J. Ye, 3D magneto-optical trap of yttrium monoxide, Phys. Rev. Lett. 121, 213201 (2018).
  39. Z. Zeng, S. Deng, S. Yang, and B. Yan, Three-dimensional magneto-optical trapping of barium monofluoride, Phys. Rev. Lett. 133, 143404 (2024).
  40. J. E. Padilla-Castillo, J. Cai, P. Agarwal, P. Kukreja, R. Thomas, B. G. Sartakov, S. Truppe, G. Meijer, and S. C. Wright, Magneto-optical trapping of aluminum monofluoride, arXiv:2506.02266.
  41. S. Truppe, H. Williams, M. Hambach, L. Caldwell, N. Fitch, E. Hinds, B. Sauer, and M. Tarbutt, Molecules cooled below the Doppler limit, Nat. Phys. 13, 1173 (2017).
  42. K. N. Jarvis, J. A. Devlin, T. E. Wall, B. E. Sauer, and M. R. Tarbutt, Blue-detuned magneto-optical trap, Phys. Rev. Lett. 120, 083201 (2018).
  43. S. Ding, Y. Wu, Ian A. Finneran, Justin J. Burau, and J. Ye, Sub-Doppler cooling and compressed trapping of YO molecules at μK temperatures, Phys. Rev. X 10, 021049 (2020).
  44. Justin J. Burau, P. Aggarwal, K. Mehling, and J. Ye, Blue-detuned magneto-optical trap of molecules, Phys. Rev. Lett. 130, 193401 (2023).
  45. C. Hallas, G. K. Li, N. B. Vilas, P. Robichaud, L. Anderegg, and J. M. Doyle, High compression blue-detuned magneto-optical trap of polyatomic molecules, arXiv:2404.03636.
  46. S. S. Yu, J. You, Y. Bao, L. Anderegg, C. Hallas, G. K. Li, D. Lim, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, A conveyor-belt magneto-optical trap of CaF, arXiv:2409.15262.
  47. V. Jorapur, Thomas K. Langin, Q. Wang, G. Zheng, and D. DeMille, High density loading and collisional loss of laser-cooled molecules in an optical trap, Phys. Rev. Lett. 132, 163403 (2024).
  48. Justin J. Burau, K. Mehling, Matthew D. Frye, M. Chen, P. Aggarwal, Jeremy M. Hutson, and J. Ye, Collisions of spin-polarized YO molecules for single partial waves, Phys. Rev. A 110, L041306 (2024).
  49. M. Yeo, Matthew T. Hummon, Alejandra L. Collopy, B. Yan, B. Hemmerling, E. Chae, John M. Doyle, and J. Ye, Rotational state microwave mixing for laser cooling of complex diatomic molecules, Phys. Rev. Lett. 114, 223003 (2015).
  50. A. L. Collopy, M. T. Hummon, M. Yeo, B. Yan, and J. Ye, Prospects for a narrow line MOT in YO, New J. Phys. 17, 055008 (2015).
  51. S. Truppe, S. Marx, S. Kray, M. Doppelbauer, S. Hofsäss, H. C. Schewe, N. Walter, J. Pérez-Ríos, B. G. Sartakov, and G. Meijer, Spectroscopic characterization of aluminum monofluoride with relevance to laser cooling and trapping, Phys. Rev. A 100, 052513 (2019).
  52. J. Kobayashi, K. Aikawa, K. Oasa, and S. Inouye, Prospects for narrow-line cooling of KRb molecules in the rovibrational ground state, Phys. Rev. A 89, 021401(R) (2014).
  53. S. Yi, T. Li, and C. P. Sun, Novel quantum phases of dipolar Bose gases in optical lattices, Phys. Rev. Lett. 98, 260405 (2007).
  54. K. Matsuda, L. De Marco, J.-R. Li, W. G. Tobias, G. Valtolina, G. Quéméner, and J. Ye, Resonant collisional shielding of reactive molecules using electric fields, Science 370, 1324 (2020).
  55. G. Quéméner and John L. Bohn, Shielding 2Σ ultracold dipolar molecular collisions with electric fields, Phys. Rev. A 93, 012704 (2016).
  56. M. Schmidt, L. Lassablière, G. Quéméner, and T. Langen, Self-bound dipolar droplets and supersolids in molecular Bose-Einstein condensates, Phys. Rev. Res. 4, 013235 (2022).
  57. A. D. Brandt, S. F. Cooper, C. Rasor, Z. Burkley, A. Matveev, and D. C. Yost, Measurement of the 2S1/2–8D5/2 transition in hydrogen, Phys. Rev. Lett. 128, 023001 (2022).
  58. G. Clausen, P. Jansen, S. Scheidegger, Josef A. Agner, H. Schmutz, and F. Merkt, Ionization energy of the metastable 21S0 state of 4He from Rydberg-series extrapolation, Phys. Rev. Lett. 127, 093001 (2021).
  59. S. Scheidegger, Josef A. Agner, H. Schmutz, and F. Merkt, Metrology of Rydberg states of the hydrogen atom, Phys. Rev. A 108, 042803 (2023).
  60. R. Stringat, C. Athénour, and J. L. Féménias, Analyse Rotationnelle de la Bande (0,0) du Système Orange de ScO, Can. J. Phys. 50, 395 (1972).
  61. W. J. Childs and T. C. Steimle, A molecular-beam-optical and radio frequency-optical double-resonance study of the A2Πr–X2Σ+ band system of scandium monoxide, J. Chem. Phys. 88, 6168 (1988).
  62. Q.-S. Yang, Y.-F. Gao, Y. Yu, and T. Gao, Ab initio study of the feasibility of laser cooling of ScO molecule, Mol. Phys. 114, 870 (2016).
  63. A. Bernard and A. M. Sibaï, The spectrum of lanthanum oxide: A reanalysis of the rotational data, Z. Naturforschung A 35, 1313 (1980).
  64. C. Zhang, H. Korslund, Y. Wu, S. Ding, and L. Cheng, Towards accurate prediction for laser-coolable molecules: Relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies, Phys. Chem. Chem. Phys. 22, 26167 (2020).
  65. A. Bernard, R. Bacis, and P. Luc, Fourier transform spectroscopy: Extensive analysis of the A2Π-X2Σ+ and B2Σ+-X2Σ+ systems of yttrium oxide, Astrophys. J. 227, 338 (1979).
  66. R. D. Suenram, F. J. Lovas, G. T. Fraser, and K. Matsumura, Pulsed-nozzle Fourier-transform microwave spectroscopy of laser-vaporized metal oxides: Rotational spectra and electric dipole moments of YO, LaO, ZrO, and HfO, J. Chem. Phys. 92, 4724 (1990).
  67. P. F. Bernath, R. Dodangodage, and J. Liévin, S-type stars: LaO line list for the B2Σ+-X2Σ+ band system, Astrophys. J. 933, 99 (2022).
  68. P. F. Bernath, R. Dodangodage, and J. Liévin, S-type stars: Line list for the A2Π-X2Σ+ band system of LaO, Astrophys. J. 953, 181 (2023).
  69. C. L. Chalek and J. L. Gole, Chemiluminescence spectra of ScO and YO: Observation and analysis of the A′2-X2Σ+ band system, J. Chem. Phys. 65, 2845 (1976).
  70. J. M. Brown and A. Carrington, Rotational Spectroscopy of Diatomic Molecules, Cambridge Molecular Science (Cambridge University, 2003).
  71. J. K. Watson, Hönl–London factors for multiplet transitions in Hund’s case a or b, J. Mol. Spectrosc. 252, 5 (2008).
  72. J. H. Van Vleck, On σ-type doubling and electron spin in the spectra of diatomic molecules, Phys. Rev. 33, 467 (1929).
  73. R. S. Mulliken and A. Christy, Λ-type doubling and electron configurations in diatomic molecules, Phys. Rev. 38, 87 (1931).
  74. H. Lefebvre-Brion and R. W. Field, The Spectra and Dynamics of Diatomic Molecules (Elsevier, Amsterdam, 2004).
  75. J. M. Brown, A. S.-C. Cheung, and A. J. Merer, Λ-type doubling parameters for molecules in Δ electronic states, J. Mol. Spectrosc. 124, 464 (1987).
  76. J. M. Brown and B. J. Howard, An approach to the anomalous commutation relations of rotational angular momenta in molecules, Mol. Phys. 31, 1517 (1976).
  77. E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, Demonstration of 4.8×10−17 stability at 1 s for two independent optical clocks, Nat. Photonics 13, 714 (2019).
  78. A. Aeppli, K. Kim, W. Warfield, Marianna S. Safronova, and J. Ye, Clock with 8×10−19 systematic uncertainty, Phys. Rev. Lett. 133, 023401 (2024).
  79. F. Papoff, F. Mauri, and E. Arimondo, Transient velocity-selective coherent population trapping in one dimension, J. Opt. Soc. Am. B 9, 321 (1992).
  80. J. Devlin and M. Tarbutt, Three-dimensional Doppler, polarization-gradient, and magneto-optical forces for atoms and molecules with dark states, New J. Phys. 18, 123017 (2016).
  81. A. N. Smirnov, V. G. Solomonik, S. N. Yurchenko, and J. Tennyson, Spectroscopy of YO from first principles, Phys. Chem. Chem. Phys. 21, 22794 (2019).
  82. John W. Farley and William H. Wing, Accurate calculation of dynamic Stark shifts and depopulation rates of Rydberg energy levels induced by blackbody radiation. Hydrogen, helium, and alkali-metal atoms, Phys. Rev. A 23, 2397 (1981).
  83. C. J. Foot, Atomic Physics (Oxford University, USA, 2005), Chap. 9.
  84. P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, Optical molasses, J. Opt. Soc. Am. B 6, 2084 (1989).
  85. Thomas H. Loftus, T. Ido, Martin M. Boyd, Andrew D. Ludlow, and J. Ye, Narrow line cooling and momentum-space crystals, Phys. Rev. A—At. Mol. Opt. Phys. 70, 063413 (2004).
  86. K. H. Leung, I. Majewska, H. Bekker, C.-H. Lee, E. Tiberi, S. S. Kondov, R. Moszynski, and T. Zelevinsky, Transition strength measurements to guide magic wavelength selection in optically trapped molecules, Phys. Rev. Lett. 125, 153001 (2020).
  87. Y. Lu, S. J. Li, C. M. Holland, and L. W. Cheuk, Raman sideband cooling of molecules in an optical tweezer array, Nat. Phys. 20, 389 (2024).
  88. Y. Bao, Scarlett S. Yu, J. You, L. Anderegg, E. Chae, W. Ketterle, Kang K. Ni, and John M. Doyle, Raman sideband cooling of molecules in an optical tweezer array to the 3D motional ground state, Phys. Rev. X 14, 031002 (2024).
  89. S. Burchesky, L. Anderegg, Y. Bao, Scarlett S. Yu, E. Chae, W. Ketterle, Kang K. Ni, and John M. Doyle, Rotational coherence times of polar molecules in optical tweezers, Phys. Rev. Lett. 127, 123202 (2021).
  90. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9v1s-d6bd for computational details, which includes Refs. [112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126].
  91. A. Asthana, J. Liu, and L. Cheng, Exact two-component equation-of-motion coupled-cluster singles and doubles method using atomic mean-field spin-orbit integrals, J. Chem. Phys. 150, 074102 (2019).
  92. B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, and G. Pupillo, Quantum phases of cold polar molecules in 2D optical lattices, Phys. Rev. Lett. 104, 125301 (2010).
  93. M. Ciardi, K. R. Pedersen, T. Langen, and T. Pohl, Self-bound superfluid membranes and monolayer crystals of ultracold polar molecules, Phys. Rev. Lett. 135, 153401 (2025).
  94. A. N. Carroll, H. Hirzler, C. Miller, D. Wellnitz, S. R. Muleady, J. Lin, K. P. Zamarski, R. R. W. Wang, J. L. Bohn, A. M. Rey, and J. Ye, Observation of generalized t−j spin dynamics with tunable dipolar interactions, Science 388, 381 (2025).
  95. W. Yuan, S. Zhang, N. Bigagli, H. Kwak, C. Warner, T. Karman, I. Stevenson, and S. Will, Extreme loss suppression and wide tunability of dipolar interactions in an ultracold molecular gas, arXiv:2505.08773.
  96. J. A. Blackmore, L. Caldwell, P. D. Gregory, E. M. Bridge, R. Sawant, J. Aldegunde, J. Mur-Petit, D. Jaksch, J. M. Hutson, B. E. Sauer, M. R. Tarbutt, and S. L. Cornish, Ultracold molecules for quantum simulation: Rotational coherences in CaF and RbCs, Quantum Sci. Technol. 4, 014010 (2018).
  97. C. M. Holland, Y. Lu, and L. W. Cheuk, On-demand entanglement of molecules in a reconfigurable optical tweezer array, Science 382, 1143 (2023).
  98. B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Observation of dipolar spin-exchange interactions with lattice-confined polar molecules, Nature 501, 521 (2013).
  99. K.-K. Ni, T. Rosenband, and D. D. Grimes, Dipolar exchange quantum logic gate with polar molecules, Chem. Sci. 9, 6830 (2018).
  100. P. Aggarwal, H. L. Bethlem, A. Borschevsky, M. Denis, K. Esajas, P. A. B. Haase, Y. Hao, S. Hoekstra, K. Jungmann, T. B. Meijknecht, M. C. Mooij, R. G. E. Timmermans, W. Ubachs, L. Willmann, and A. Zapara, Measuring the electric dipole moment of the electron in BaF, Eur. Phys. J. D 72, 197 (2018).
  101. D. DeMille, N. R. Hutzler, A. M. Rey, and T. Zelevinsky, Quantum sensing and metrology for fundamental physics with molecules, Nat. Phys. 20, 741 (2024).
  102. M. G. Kozlov and L. N. Labzowsky, Parity violation effects in diatomics, J. Phys. B: At. Mol. Opt. Phys. 28, 1933 (1995).
  103. M. S. Safronova, D. Budker, D. DeMille, Derek F. Jackson Kimball, A. Derevianko, and Charles W. Clark, Search for new physics with atoms and molecules, Rev. Mod. Phys. 90, 025008 (2018).
  104. Edmund R. Meyer, John L. Bohn, and Michael P. Deskevich, Candidate molecular ions for an electron electric dipole moment experiment, Phys. Rev. A—At. Mol. Opt. Phys. 73, 062108 (2006).
  105. V. A. Dzuba, V. V. Flambaum, J. S. M. Ginges, and M. G. Kozlov, Electric dipole moments of Hg, Xe, Rn, Ra, Pu, and TlF induced by the nuclear Schiff moment and limits on time-reversal violating interactions, Phys. Rev. A 66, 012111 (2002).
  106. T. Chen, C. Zhang, L. Cheng, K. B. Ng, S. Malbrunot-Ettenauer, V. V. Flambaum, Z. Lasner, J. M. Doyle, P. Yu, C. J. Conn, C. Zhang, N. R. Hutzler, A. M. Jayich, B. Augenbraun, and D. DeMille, Relativistic exact two-component coupled-cluster study of molecular sensitivity factors for nuclear Schiff moments, J. Phys. Chem. A 128, 6540 (2024).
  107. V. V. Flambaum, Electric dipole moments of actinide atoms and RaO molecule, Phys. Rev. A 77, 024501 (2008).
  108. E. Verstraelen, A. Teigelhöfer, W. Ryssens, F. Ames, A. Barzakh, M. Bender, R. Ferrer, S. Goriely, P.-H. Heenen, M. Huyse, P. Kunz, J. Lassen, V. Manea, S. Raeder, and P. Van Duppen, Search for octupole-deformed actinium isotopes using resonance ionization spectroscopy, Phys. Rev. C 100, 044321 (2019).
  109. V. V. Flambaum and A. J. Mansour, Enhanced nuclear Schiff and electric dipole moments in nuclei with octupole deformation, Phys. Rev. C 111, 055501 (2025).
  110. M. Athanasakis-Kaklamanakis, M. Au, A. Kyuberis, C. Zülch, K. Gaul, H. Wibowo, L. Skripnikov, L. Lalanne, J. Reilly, A. Koszorús, et al., Laser spectroscopy and CP-violation sensitivity of actinium monofluoride, arXiv:2507.05224.
  111. K. Mehling, Narrowline Laser Cooling and Spectroscopy of Molecules Via Stark States Data. PRX Quantum. Zenodo, December 3, 2025, https://doi.org/10.5281/zenodo.17794963.
  112. D. A. Matthews, L. Cheng, M. E. Harding, F. Lipparini, S. Stopkowicz, T.-C. Jagau, P. G. Szalay, J. Gauss, and J. F. Stanton, Coupled-cluster techniques for computational chemistry: The CFOUR program package, J. Chem. Phys. 152, 214108 (2020).
  113. J. F. Stanton, J. Gauss, L. Cheng, M. E. Harding, D. A. Matthews, and P. G. Szalay, CFOUR, Coupled-Cluster techniques for Computational Chemistry, a quantum-chemical program package, With contributions from A.A. Auer, A. Asthana, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, S. Blaschke, Y. J. Bomble, S. Burger, O. Christiansen, D. Datta, F. Engel, R. Faber, J. Greiner, M. Heckert, O. Heun, M. Hilgenberg, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, T. Kirsch, K. Klein, G.M. KopperW.J. Lauderdale, F. Lipparini, J. Liu, T. Metzroth, L.A. Mück, D.P. O’Neill, T. Nottoli, D.R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, C. Simmons, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J.D. Watts, C. Zhang, X. Zheng, and the integral packages MOLECULE (J. Almlöf and P.R. Taylor), PROPS (P.R. Taylor), ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van Wüllen. For the current version, see http://www.cfour.de.
  114. K. G. Dyall, Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation, J. Chem. Phys. 106, 9618 (1997).
  115. M. Iliaš and T. Saue, An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation, J. Chem. Phys. 126, 064102 (2007).
  116. W. Liu and D. Peng, Exact two-component Hamiltonians revisited, J. Chem. Phys. 131, 031104 (2009).
  117. K. G. Dyall, Interfacing relativistic and nonrelativistic methods. IV. One- and two-electron scalar approximations, J. Chem. Phys. 115, 9136 (2001).
  118. B. A. Heß, C. M. Marian, U. Wahlgren, and O. Gropen, A mean-field spin-orbit method applicable to correlated wavefunctions, Chem. Phys. Lett. 251, 365 (1996).
  119. J. Liu and L. Cheng, An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling, J. Chem. Phys. 148, 144108 (2018).
  120. L. Visscher and K. G. Dyall, Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions, At. Data Nucl. Data Tables 67, 207 (1997).
  121. J. F. Stanton and R. J. Bartlett, The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties, J. Chem. Phys. 98, 7029 (1993).
  122. B. O. Roos, R. Lindh, P.-Å. Malmqvist, V. Veryazov, and P.-O. Widmark, New relativistic ANO basis sets for transition metal atoms, J. Phys. Chem. A 109, 6575 (2005).
  123. B. O. Roos, R. Lindh, P.-Å. Malmqvist, V. Veryazov, and P.-O. Widmark, New relativistic ANO basis sets for actinide atoms, Chem. Phys. Lett. 409, 295 (2005).
  124. R. A. Kendall, T. H. Dunning Jr., and R. J. Harrison, Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions, J. Chem. Phys. 96, 6796 (1992).
  125. J. Liu, Y. Shen, A. Asthana, and L. Cheng, Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals, J. Chem. Phys. 148, 034106 (2018).
  126. J. Liu, X. Zheng, A. Asthana, C. Zhang, and L. Cheng, Analytic evaluation of energy first derivatives for spin–orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties, J. Chem. Phys. 154, 064110 (2021).

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PRX Quantum 6, 040370– Published 23 December, 2025
  • Received 6 March 2025
  • Revised 17 September 2025
  • Accepted 10 November 2025
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