Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Quantum sensing and metrology for fundamental physics with molecules

Abstract

Quantum sensing and metrology use coherent superposition states of quantum systems to detect and measure physical effects of interest. Their sensitivity is typically limited by the standard quantum limit, which bounds the achievable precision in measurements involving nominally identical but uncorrelated quantum systems. Fully quantum metrology involves entanglement in an array of quantum systems, enabling uncertainty reduction below the standard quantum limit. Although ultracold atoms have been widely used for applications such as atomic clocks or gravitational sensors, molecules show higher sensitivity to many interesting phenomena, including the existence of new, symmetry-violating forces mediated by massive particles. Recent advancements in molecular cooling, trapping and control techniques have enabled the use of molecules for quantum sensing and metrology. This Review describes these advancements and explores the potential of the rich internal structure and enhanced coupling strengths of molecules to probe fundamental physics and drive progress in the field.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: A typical quantum sensing protocol with molecules.
Fig. 2: CP violation effects.
Fig. 3: Molecular clock set-up.
Fig. 4: Quantum-enhanced sensing.

Similar content being viewed by others

References

  1. Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).

    ADS  MathSciNet  Google Scholar 

  2. DeMille, D. Diatomic molecules, a window onto fundamental physics. Phys. Today 68, 34–40 (2015).

    ADS  Google Scholar 

  3. Hutzler, N. R. Polyatomic molecules as quantum sensors for fundamental physics. Quantum Sci. Technol. 5, 044011 (2020).

    ADS  Google Scholar 

  4. Sushkov, P. & Flarnbaum, V. Parity breaking effects in diatomic molecules. Zh. Eksp. Teor. Fiz. 75, 1208–1213 (1978).

    Google Scholar 

  5. Salumbides, E. J. et al. Bounds on fifth forces from precision measurements on molecules. Phys. Rev. D 87, 112008 (2013).

    ADS  Google Scholar 

  6. Borkowski, M. et al. Weakly bound molecules as sensors of new gravitylike forces. Sci. Rep. 9, 14807 (2019).

    ADS  Google Scholar 

  7. Hutzler, N. R., Lu, H.-I. & Doyle, J. M. The buffer gas beam: an intense, cold, and slow source for atoms and molecules. Chem. Rev. 112, 4803–4827 (2012).

    Google Scholar 

  8. Shuman, E. S., Barry, J. F. & DeMille, D. Laser cooling of a diatomic molecule. Nature 467, 820–823 (2010).

    ADS  Google Scholar 

  9. Fitch, N. J. & Tarbutt, M. R. Laser-cooled molecules. Adv. Mol. Opt. Phys. 70, 157–262 (2021).

    ADS  Google Scholar 

  10. Augenbraun, B. L. et al. Direct laser cooling of polyatomic molecules. Adv. At. Mol. Opt. Phys. 72, 89–182 (2023).

    Google Scholar 

  11. Bohn, J. L., Rey, A. M. & Ye, J. Cold molecules: progress in quantum engineering of chemistry and quantum matter. Science 357, 1002–1010 (2017).

    ADS  MathSciNet  Google Scholar 

  12. De Marco, L. et al. A degenerate Fermi gas of polar molecules. Science 363, 853–856 (2019).

    ADS  Google Scholar 

  13. Schindewolf, A. et al. Evaporation of microwave-shielded polar molecules to quantum degeneracy. Nature 607, 677–681 (2022).

    ADS  Google Scholar 

  14. Bigagli, N. et al. Observation of Bose–Einstein condensation of dipolar molecules. Preprint at https://arxiv.org/abs/2302.10161 (2023).

  15. Langen, T., Valtolina, G., Wang, D. & Ye, J. Quantum state manipulation and cooling of ultracold molecules. Nat. Phys. https://doi.org/10.1038/s41567-024-02423-1 (2024).

  16. Dine, M. & Kusenko, A. Origin of the matter–antimatter asymmetry. Rev. Mod. Phys. 76, 1–30 (2003).

    ADS  Google Scholar 

  17. Baron, J. et al. Order of magnitude smaller limit on the electric dipole moment of the electron. Science 343, 269–272 (2014).

    ADS  Google Scholar 

  18. Andreev, V. et al. Improved limit on the electric dipole moment of the electron. Nature 562, 355–360 (2018).

    ADS  Google Scholar 

  19. Roussy, T. S. et al. An improved bound on the electron’s electric dipole moment. Science 381, 46–50 (2023).

    ADS  Google Scholar 

  20. Ema, Y., Gao, T. & Pospelov, M. Standard model prediction for paramagnetic electric dipole moments. Phys. Rev. Lett. 129, 231801 (2022).

    ADS  Google Scholar 

  21. Fleig, T. & Nayak, M. K. Electron electric dipole moment and hyperfine interaction constants for ThO. J. Mol. Spectrosc. 300, 16–21 (2014).

    ADS  Google Scholar 

  22. Skripnikov, L. V. Combined 4-component and relativistic pseudopotential study of ThO for the electron electric dipole moment search. J. Chem. Phys. 145, 214301 (2016).

    ADS  Google Scholar 

  23. Hudson, J. J. et al. Improved measurement of the shape of the electron. Nature 473, 493–496 (2011).

    ADS  Google Scholar 

  24. Brown, J. M. & Carrington, A. Rotational Spectroscopy of Diatomic Molecules (Cambridge Univ. Press, 2003); https://doi.org/10.1017/CBO9780511814808

  25. DeMille, D. et al. Search for the electric dipole moment of the electron using metastable PbO. AIP Conf. Proc. 596, 72–83 (2001).

  26. Wu, X. et al. Electrostatic focusing of cold and heavy molecules for the ACME electron EDM search. New J. Phys. 24, 073043 (2022).

    ADS  Google Scholar 

  27. Ang, D. G. et al. Measurement of the H 3Δ1 radiative lifetime in ThO. Phys. Rev. A 106, 022808 (2022).

    ADS  Google Scholar 

  28. Cho, D., Sangster, K. & Hinds, E. A. Search for time-reversal-symmetry violation in thallium fluoride using a jet source. Phys. Rev. A 44, 2783–2799 (1991).

    ADS  Google Scholar 

  29. Alarcon, R. et al. Electric dipole moments and the search for new physics. Preprint at https://arxiv.org/abs/2203.08103 (2022).

  30. Arrowsmith-Kron, G. et al. Opportunities for fundamental physics research with radioactive molecules. Rep. Prog. Phys. https://doi.org/10.1088/1361-6633/ad1e39 (2023).

  31. O Grasdijk, O. et al. CeNTREX: a new search for time-reversal symmetry violation in the 205Tl nucleus. Quantum Sci. Technol. 6, 044007 (2021).

    ADS  Google Scholar 

  32. Auerbach, N., Flambaum, V. V. & Spevak, V. Collective T- and P-odd electromagnetic moments in nuclei with octupole deformations. Phys. Rev. Lett. 76, 4316–4319 (1996).

    ADS  Google Scholar 

  33. Flambaum, V. Spin hedgehog and collective magnetic quadrupole moments induced by parity and time invariance violating interaction. Phys. Lett. B 320, 211–215 (1994).

    ADS  Google Scholar 

  34. Flambaum, V., DeMille, D. & Kozlov, M. Time-reversal symmetry violation in molecules induced by nuclear magnetic quadrupole moments. Phys. Rev. Lett. 113, 103003 (2014).

    ADS  Google Scholar 

  35. DeMille, D., Cahn, S. B., Murphree, D., Rahmlow, D. A. & Kozlov, M. G. Using molecules to measure nuclear spin-dependent parity violation. Phys. Rev. Lett. 100, 023003 (2008).

    ADS  Google Scholar 

  36. Altuntaş, E., Ammon, J., Cahn, S. B. & DeMille, D. Demonstration of a sensitive method to measure nuclear-spin-dependent parity violation. Phys. Rev. Lett. 120, 142501 (2018).

    ADS  Google Scholar 

  37. Norrgard, E. B. et al. Nuclear-spin dependent parity violation in optically trapped polyatomic molecules. Commun. Phys. 2, 77 (2019).

    Google Scholar 

  38. Karthein, J. et al. Electroweak nuclear properties from single molecular ions in a Penning trap. Preprint at https://arxiv.org/abs/2310.11192 (2023).

  39. Bothwell, T. et al. Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602, 420–424 (2022).

    ADS  Google Scholar 

  40. Leung, K. H. et al. Terahertz vibrational molecular clock with systematic uncertainty at the 10−14 level. Phys. Rev. X 13, 011047 (2023).

    Google Scholar 

  41. Barontini, G. et al. Measuring the stability of fundamental constants with a network of clocks. EPJ Quantum Technol. 9, 12 (2022).

    Google Scholar 

  42. Hanneke, D., Kuzhan, B. & Lunstad, A. Optical clocks based on molecular vibrations as probes of variation of the proton-to-electron mass ratio. Quantum Sci. Technol. 6, 014005 (2021).

    ADS  Google Scholar 

  43. Riehle, F., Gill, P., Arias, F. & Robertsson, L. The CIPM list of recommended frequency standard values: guidelines and procedures. Metrologia 55, 188 (2018).

    ADS  Google Scholar 

  44. Bertone, G. & Hooper, D. History of dark matter. Rev. Mod. Phys. 90, 045002 (2018).

    ADS  Google Scholar 

  45. Uzan, J.-P. Varying constants, gravitation and cosmology. Living Rev. Relativ. 14, 2 (2011).

    ADS  Google Scholar 

  46. Lange, R. et al. Improved limits for violations of local position invariance from atomic clock comparisons. Phys. Rev. Lett. 126, 011102 (2021).

    ADS  Google Scholar 

  47. Kobayashi, J., Ogino, A. & Inouye, S. Measurement of the variation of electron-to-proton mass ratio using ultracold molecules produced from laser-cooled atoms. Nat. Commun. 10, 3771 (2019).

    ADS  Google Scholar 

  48. Patra, S. et al. Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level. Science 369, 1238–1241 (2020).

    ADS  Google Scholar 

  49. Alighanbari, S., Giri, G. S., Constantin, F. L., Korobov, V. I. & Schiller, S. Precise test of quantum electrodynamics and determination of fundamental constants with HD+ ions. Nature 581, 152–158 (2020).

    ADS  Google Scholar 

  50. Germann, M. et al. Three-body QED test and fifth-force constraint from vibrations and rotations of HD+. Phys. Rev. Res. 3, 022028 (2021).

    Google Scholar 

  51. Heacock, B. et al. Pendellösung interferometry probes the neutron charge radius, lattice dynamics, and fifth forces. Science 373, 1239–1243 (2021).

    ADS  Google Scholar 

  52. Tiberi, E., Borkowski, M., Iritani, B. Moszynski, R. & Zelevinsky, T. Searching for New Fundamental Interactions via Isotopic Shifts in Molecular Lattice Clocks. Preprint at https://arxiv.org/abs/2403.07097 (2024).

  53. Wineland, D. J., Bollinger, J. J., Itano, W. M., Moore, F. L. & Heinzen, D. J. Spin squeezing and reduced quantum noise in spectroscopy. Phys. Rev. A 46, 6797–6800 (1992).

    ADS  Google Scholar 

  54. Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67–88 (1994).

    ADS  Google Scholar 

  55. Ma, J., Wang, X., Sun, C. P. & Nori, F. Quantum spin squeezing. Phys. Rep. 509, 89–165 (2011).

    ADS  MathSciNet  Google Scholar 

  56. Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993).

    ADS  Google Scholar 

  57. Ritsch, H., Domokos, P., Brennecke, F. & Esslinger, T. Cold atoms in cavity-generated dynamical optical potentials. Rev. Mod. Phys. 85, 553–601 (2013).

    ADS  Google Scholar 

  58. Hosten, O., Engelsen, N. J., Krishnakumar, R. & Kasevich, M. A. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).

    ADS  Google Scholar 

  59. Cox, K. C., Greve, G. P., Weiner, J. M. & Thompson, J. K. Deterministic squeezed states with collective measurements and feedback. Phys. Rev. Lett. 116, 093602 (2016).

    ADS  Google Scholar 

  60. Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).

    ADS  Google Scholar 

  61. Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

    ADS  MathSciNet  Google Scholar 

  62. Perlin, M. A., Qu, C. & Rey, A. M. Spin squeezing with short-range spin-exchange interactions. Phys. Rev. Lett. 125, 223401 (2020).

    ADS  Google Scholar 

  63. Bilitewski, T. et al. Dynamical generation of spin squeezing in ultracold dipolar molecules. Phys. Rev. Lett. 126, 113401 (2021).

    ADS  Google Scholar 

  64. Yan, B. et al. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature 501, 521–525 (2013).

    ADS  Google Scholar 

  65. Hazzard, K. R. A. et al. Many-body dynamics of dipolar molecules in an optical lattice. Phys. Rev. Lett. 113, 195302 (2014).

    ADS  Google Scholar 

  66. Christakis, L. et al. Probing site-resolved correlations in a spin system of ultracold molecules. Nature 614, 64–69 (2023).

    ADS  Google Scholar 

  67. Holland, C. M., Lu, Y. & Cheuk, L. W. On-demand entanglement of molecules in a reconfigurable optical tweezer array. Science 382, 1143–1147 (2023).

    ADS  MathSciNet  Google Scholar 

  68. Bao, Y. et al. Dipolar spin-exchange and entanglement between molecules in an optical tweezer array. Science 382, 1138–1143 (2023).

    ADS  MathSciNet  Google Scholar 

  69. Bornet, G. et al. Scalable spin squeezing in a dipolar Rydberg atom array. Nature 621, 728–733 (2023).

    ADS  Google Scholar 

  70. Eckner, W. J. et al. Realizing spin squeezing with Rydberg interactions in a programmable optical clock. Nature 621, 734–739 (2023).

    ADS  Google Scholar 

  71. Franke, J. et al. Quantum-enhanced sensing on optical transitions through finite-range interactions. Nature 621, 740–745 (2023).

    ADS  Google Scholar 

  72. Hines, J. A. et al. Spin squeezing by Rydberg dressing in an array of atomic ensembles. Phys. Rev. Lett. 131, 063401 (2023).

    ADS  Google Scholar 

  73. Gorshkov, A. V. et al. Tunable superfluidity and quantum magnetism with ultracold polar molecules. Phys. Rev. Lett. 107, 115301 (2011).

    ADS  Google Scholar 

  74. Hazzard, K. R. A., Manmana, S. R., Foss-Feig, M. & Rey, A. M. Far-from-equilibrium quantum magnetism with ultracold polar molecules. Phys. Rev. Lett. 110, 075301 (2013).

    ADS  Google Scholar 

  75. Wellnitz, D., Mamaev, M., Bilitewski, T. & Rey, A. M. Spin squeezing with itinerant dipoles: a case for shallow lattices. Phys. Rev. Res. 6, 012025 (2024).

    Google Scholar 

  76. Gorshkov, A. V. et al. Quantum magnetism with polar alkali-metal dimers. Phys. Rev. A 84, 033619 (2011).

    ADS  Google Scholar 

  77. Tscherbul, T. V., Ye, J. & Rey, A. M. Robust nuclear spin entanglement via dipolar interactions in polar molecules. Phys. Rev. Lett. 130, 143002 (2023).

    ADS  Google Scholar 

  78. Hermsmeier, R., Rey, A. M. & Tscherbul, T. V. Magnetically tunable electric dipolar interactions of ultracold polar molecules in the quantum ergodic regime. Preprint at https://arxiv.org/abs/2401.04902 (2024).

  79. Zhang, C., Yu, P., Jadbabaie, A. & Hutzler, N. R. Quantum-enhanced metrology for molecular symmetry violation using decoherence-free subspaces. Phys. Rev. Lett. 131, 193602 (2023).

    ADS  Google Scholar 

  80. Garcia Ruiz, R. F. et al. Spectroscopy of short-lived radioactive molecules. Nature 581, 396–400 (2020).

    ADS  Google Scholar 

  81. Piskorski, J., Patterson, D., Eibenberger, S. & Doyle, J. M. Cooling, spectroscopy and non-sticking of trans-stilbene and Nile Red. ChemPhysChem 15, 3800–3804 (2014).

    Google Scholar 

  82. Patterson, D. & Doyle, J. M. Sensitive chiral analysis via microwave three-wave mixing. Phys. Rev. Lett. 111, 023008 (2013).

    ADS  Google Scholar 

  83. Norrgard, E. B., Eckel, S. P., Holloway, C. L. & Shirley, E. L. Quantum blackbody thermometry. New J. Phys. 23, 033037 (2021).

    ADS  Google Scholar 

  84. Arvanitaki, A., Dimopoulos, S. & Van Tilburg, K. Resonant absorption of bosonic dark matter in molecules. Phys. Rev. X 8, 041001 (2018).

    Google Scholar 

  85. Eibenberger, S., Doyle, J. & Patterson, D. Enantiomer-specific state transfer of chiral molecules. Phys. Rev. Lett. 118, 123002 (2017).

    ADS  Google Scholar 

  86. Doyle, J. M., Lasner, Z. D. & Augenbraun, B. L. High sensitivity chiral detection in the gas phase via microwave spectroscopy and the possible frontier of ultracold chiral molecules. Chiral Matter 167, 195–207 (2023).

  87. Quack, M., Stohner, J. & Willeke, M. High-resolution spectroscopic studies and theory of parity violation in chiral molecules. Annu. Rev. Phys. Chem. 59, 741–769 (2008).

    ADS  Google Scholar 

  88. Cornish, S. L., Tarbutt, M. R. & Hazzard, K. R. A. Quantum computation and quantum simulation with ultracold molecules. Nat. Phys. https://doi.org/10.1038/s41567-024-02453-9 (2024).

  89. Baron, J. et al. Methods, analysis, and the treatment of systematic errors for the electron electric dipole moment search in thorium monoxide. New J. Phys. 19, 073029 (2017).

    ADS  Google Scholar 

  90. Fitch, N. J., Lim, J., Hinds, E. A., Sauer, B. E. & Tarbutt, M. R. Methods for measuring the electron’s electric dipole moment using ultracold YbF molecules. Quantum Sci. Technol. 6, 014006 (2021).

    Google Scholar 

  91. Kozyryev, I. & Hutzler, N. R. Precision measurement of time-reversal symmetry violation with laser-cooled polyatomic molecules. Phys. Rev. Lett. 119, 133002 (2017).

    ADS  Google Scholar 

  92. Takahashi, Y., Zhang, C., Jadbabaie, A. & Hutzler, N. R. Engineering field-insensitive molecular clock transitions for symmetry violation searches. Phys. Rev. Lett. 131, 183003 (2023).

    ADS  Google Scholar 

  93. Anderegg, L. et al. Quantum control of trapped polyatomic molecules for eEDM searches. Science 382, 665–668 (2023).

    ADS  MathSciNet  Google Scholar 

  94. Fleig, T. & DeMille, D. Theoretical aspects of radium-containing molecules amenable to assembly from laser-cooled atoms for new physics searches. New J. Phys. 23, 113039 (2021).

    ADS  Google Scholar 

  95. Kłos, J., Li, H., Tiesinga, E. & Kotochigova, S. Prospects for assembling ultracold radioactive molecules from laser-cooled atoms. New J. Phys. 24, 025005 (2022).

    ADS  Google Scholar 

  96. Singh, J. T. A new concept for searching for time-reversal symmetry violation using Pa-229 ions trapped in optical crystals. Hyperfine Interact. 240, 29 (2019).

    ADS  Google Scholar 

  97. Flambaum, V. V. & Dzuba, V. A. Electric dipole moments of atoms and molecules produced by enhanced nuclear Schiff moments. Phys. Rev. A 101, 042504 (2020).

    ADS  Google Scholar 

  98. Ramachandran, H. D. & Vutha, A. C. Nuclear T-violation search using octopole-deformed nuclei in a crystal. Phys. Rev. A 108, 012819 (2023).

    ADS  Google Scholar 

  99. Kozlov, M. G. & Derevianko, A. Proposal for a sensitive search for the electric dipole moment of the electron with matrix-isolated radicals. Phys. Rev. Lett. 97, 063001 (2006).

    ADS  Google Scholar 

  100. Li, S. J., Ramachandran, H. D., Anderson, R. & Vutha, A. C. Optical control of BaF molecules trapped in neon ice. New J. Phys. 25, 082001 (2023).

    ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge funding support from AFOSR MURI Grant FA9550-21-1-0069 (DD, AMR, and TZ), the Gordon and Betty Moore Foundation Grant 12330 (DD), and the Brown Foundation Grant CU22-1584 (TZ) We thank S. Park and C. Miller for careful reading of the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David DeMille.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

DeMille, D., Hutzler, N.R., Rey, A.M. et al. Quantum sensing and metrology for fundamental physics with molecules. Nat. Phys. 20, 741–749 (2024). https://doi.org/10.1038/s41567-024-02499-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-024-02499-9

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing