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Ultracold amplification proposal for parity violation in chiral molecules

Daniel Martínez-Gil* and Pedro Bargueño

Salvador Miret-Artés

  • *Contact author: daniel.martinez@ua.es

Phys. Rev. Research 8, 033056 – Published 13 July, 2026

DOI: https://doi.org/10.1103/54yp-6397

Abstract

We propose a theoretical mechanism to indirectly detect the small parity-violating energy difference (PVED) between chiral enantiomers through a macroscopic enantiomeric excess observed in an ultracold gas. We consider that chiral molecules are formed resonantly via ultracold collisions of achiral diatomic molecules, with PVED inducing a slight asymmetry in the resonance energies of right- and left-handed configurations. After formation, chiral molecules evolve within a Bose-Einstein condensate, incorporating nonlinear interactions, tunneling between enantiomeric states, intrinsic PVED, and thermal conversion rates. These collective dynamics enable amplification of the microscopic bias into a global population imbalance. Using coupled rate equations, we show that, under realistic regimes, a complete enantiomeric excess can be achieved even for extremely small intrinsic asymmetries. We illustrate the model with concrete examples (HSOH, H2Se2, H2Te2), predicting observable enantiomeric excesses under plausible experimental conditions. We also consider non-PVED effects that could be amplified under the proposed mechanism, including electric and magnetic fields as well as thermal fluctuations, the latter being illustrated through the aforementioned molecular examples. Overall, our results suggest that ultracold physics could provide a pathway to probe molecular parity violation, a fundamental weak effect that remains experimentally undetected.

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References (65)

  1. M. A. Bouchiat and C. Bouchiat, Parity violation induced by weak neutral currents in atomic physics, J. Phys. France 35, 899 (1974).
  2. M. Quack, G. Seyfang, and G. Wichmann, Perspectives on parity violation in chiral molecules: Theory, spectroscopic experiment and biomolecular homochirality, Chem. Sci. 13, 10598 (2022).
  3. M. Fujiki, Experimental tests of parity violation at helical polysilylene level, Macromol. Rapid Commun. 22, 669 (2001).
  4. M. Fujiki, Mirror symmetry breaking in helical polysilanes: Preference between left and right of chemical and physical origin, Symmetry 2, 1625 (2010).
  5. M. Fujiki, J. R. Koe, T. Mori, and Y. Kimura, Questions of mirror symmetry at the photoexcited and ground states of non-rigid luminophores raised by circularly polarized luminescence and circular dichroism spectroscopy: Part 1. Oligofluorenes, oligophenylenes, binaphthyls and fused aromatics, Molecules 23, 2606 (2018).
  6. M. P. Ledbetter, C. W. Crawford, A. Pines, D. E. Wemmer, S. Knappe, J. Kitching, and D. Budker, Optical detection of NMR J-spectra at zero magnetic field, J. Magn. Reson. 199, 25 (2009).
  7. B. Darquié, C. Stoeffler, A. Shelovnikov, C. Daussy, A. Amy-Klein, C. Chardonnet, S. Zrig, L. Guy, J. Crassous, P. Soulard, P. Asselin, T. R. Huet, P. Achwerdtfeger, R. Bast, and T. Saue, Progress toward the first observation of parity violation in chiral molecules by high-resolution laser spectroscopy, Chirality 22, 870 (2010).
  8. A. J. MacDermott and R. A. Hegstrom, Optical rotation of molecules in beams: The magic angle, Chem. Phys. 305, 47 (2004).
  9. A. J. MacDermott and R. A. Hegstrom, A proposed experiment to measure the parity-violating energy difference between enantiomers from the optical rotation of chiral ammonia-like “cat” molecules, Chem. Phys. 305, 55 (2004).
  10. M. Schnell and G. Meijer, Cold molecules: Preparation, applications, and challenges, Angew. Chem. Int. Ed. 48, 6010 (2009).
  11. A. S. Lahamer, S. M. Mahurin, R. N. Compton, D. House, J. K. Laerdahl, M. Lein, and P. Schwerdtfeger, Search for a parity-violating energy difference between enantiomers of a chiral iron complex, Phys. Rev. Lett. 85, 4470 (2000).
  12. E. Arimondo, P. Glorieux, and T. Oka, Observation of inverted infrared Lamb dips in separated optical isomers, Opt. Commun. 23, 369 (1977).
  13. M. Ziskind, C. Daussy, T. Marrel, and Ch. Chardonnet, Improved sensitivity in the search for a parity-violating energy difference in the vibrational spectrum of the enantiomers of CHFClBr, Eur. Phys. J. D 20, 219 (2002).
  14. M. Quack, On the measurement of the parity violating energy difference between enantiomers, Chem. Phys. Lett. 132, 147 (1986).
  15. C. Daussy, T. Marrel, A. Amy-Klein, C. T. Nguyen, C. J. Bordé, and C. Chardonnet, Limit on the parity nonconserving energy difference between the enantiomers of a chiral molecule by laser spectroscopy, Phys. Rev. Lett. 83, 1554 (1999).
  16. V. S. Letokhov, On difference of energy levels of left and right molecules due to weak interactions, Phys. Lett. A 53, 275 (1975).
  17. O. N. Kompanets, A. R. Kukudzhanov, V. S. Letokhov, and L. L. Gervits, Narrow resonances of saturated absorption of asymmetrical molecule CHFClBr and possibility of weak current detection in molecular physics, Opt. Commun. 19, 414 (1976).
  18. J. Eills, J. W. Blanchard, L. Bougas, M. G. Kozlov, A. Pines, and D. Budker, Measuring molecular parity nonconservation using nuclear magnetic resonance spectroscopy, Phys. Rev. A 96, 042119 (2017).
  19. A. Cournol et al., A new experiment to test parity symmetry in cold chiral molecules using vibrational spectroscopy, Quantum Electron. 49, 288 (2019).
  20. B. A. Stickler, M. Diekmann, R. Berger, and D. Wang, Enantiomer superpositions from matter-wave interference of chiral molecules, Phys. Rev. X 11, 031056 (2021).
  21. L. Satterthwaite, G. Koumarianou, D. Sorensen, and D. Patterson, Sub-Hz differential rotational spectroscopy of enantiomers, Symmetry 14, 28 (2022).
  22. I. Erez, E. R. Wallach, and Y. Shagam, Simultaneous enantiomer resolved Ramsey spectroscopy scheme for chiral molecules, Phys. Rev. X 13, 041025 (2023).
  23. N. Sahu, K. Gaul, A. Wilm, M. Schnell, and R. Berger, Towards detection of molecular parity violation by microwave spectroscopy of CpRe(CH3)(CO)(NO), arXiv:2303.08263.
  24. P. Dietiker, E. Miloglyadov, M. Quack, A. Schneider, and G. Seyfang, Infrared laser induced population transfer and parity selection in 14NH3: A proof of principle experiment towards detecting parity violation in chiral molecules, J. Chem. Phys 143, 244305 (2015).
  25. R. Berger, M. Gottselig, M. Quack, and M. Willeke, Parity violation dominates the dynamics of chirality in dichlorodisulfane, Angew. Chem. Int. Ed. 40, 4195 (2001).
  26. R. Prentner, M. Quack, J. Stohner, and M. Willeke, Wavepacket dynamics of the axially chiral molecule Cl-O-O-Cl under coherent radiative excitation and including electroweak parity violation, J. Phys. Chem. A 119, 12805 (2015).
  27. M. Quack, J. Stohner, and M. Willeke, High-resolution spectroscopic studies and theory of parity violation in chiral molecules, Annu. Rev. Phys. Chem. 59, 741 (2008).
  28. M. R. Fiechter, P. A. B. Haase, N. Saleh, P. Soulard, B. Tremblay, R. W. A. Havenith, R. G. E. Timmermans, P. Schwerdtfeger, J. Crassous, B. Darquié, L. F. Pasteka, and A. Borschwvsky, Toward detection of the molecular parity violation in chiral Ru(acac)3 and Os(acac)3, J. Phys. Chem. Lett. 13, 10011 (2022).
  29. A. Landau, Eduardus, D. Behar, E. R. Wallach, L. F. Pasteka, S. Faraji, A. Borschevsky, and Y. Shagam, Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation, J. Chem. Phys. 159, 114307 (2023).
  30. Eduardus, Y. Shagam, A. Landau, S. Faraji, P. Schwerdtfeger, A. Borschevsky, and L. F. Pašteka, Large vibrationally induced parity violation effects in CHDBrI+, Chem. Commun. 59, 14579 (2023).
  31. J.-H. Lee, E. Abdiha, B. G. Sartakov, G. Meijer, and S. Eibenberger-Arias, Near-complete chiral selection in rotational quantum states, Nat. Commun. 15, 7441 (2024).
  32. P. Bargueño, I. Gonzalo, and R. P. de Tudela, Detection of parity violation in chiral molecules by external tuning of electroweak optical activity, Phys. Rev. A 80, 012110 (2009).
  33. I. Gonzalo, P. Bargueño, R. P. de Tudela, and S. Miret-Artés, Towards the detection of parity symmetry breaking in chiral molecules, Chem. Phys. Lett. 489, 127 (2010).
  34. Q. Sallembien, L. Bouteiller, J. Crassous, and M. Raynal, Possible chemical and physical scenarios towards biological homochirality, Chem. Soc. Rev. 51, 3436 (2022).
  35. J. P. Ríos, An Introduction to Cold and Ultracold Chemistry: Atoms, Molecules, Ions and Rydbergs (Springer International Publishing, Cham, Switzerland, 2020).
  36. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. H. Denschlag, and R. Grimm, Bose–Einstein condensation of molecules, Science 302, 2101 (2003).
  37. Edited by R. V. Krems, W. C. Stwalley, and B. Friedrich, in Cold Molecules: Theory, Experiment, Applications (CRC Press, Boca Raton, FL, 2009).
  38. V. V. Flambaum and J. S. M. Ginges, Resonance reactions and enhancement of weak interactions in collisions of cold molecules, Phys. Rev. A 74, 025601 (2006).
  39. P. Bargueño, R. P. de Tudela, S. Miret-Artés, and I. Gonzalo, An alternative route to detect parity violating energy differences through Bose–Einstein condensation of chiral molecules, Phys. Chem. Chem. Phys. 13, 806 (2011).
  40. P. Bargueño and F. Sols, Macroscopic amplification of electroweak effects in molecular Bose–Einstein condensates, Phys. Rev. A 85, 021605(R) (2012).
  41. A. Vardi, On the role of intermolecular interactions in establishing chiral stability, J. Chem. Phys. 112, 8743 (2000).
  42. R. A. Harris and L. Stodolsky, Quantum beats in optical activity and weak interactions, Phys. Lett. B 78, 313 (1978).
  43. D. M. Gil, P. Bargueño, and S. Miret-Artés, Dissipative evolution of a two-level system through a geometry-based classical mapping, New J. Phys. 27, 124512 (2025).
  44. D. K. Kondepudi and G. W. Nelson, Weak neutral currents and the origin of biomolecular chirality, Nature (London) 314, 438 (1985).
  45. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose–Einstein condensation of dipolar molecules, Nature (London) 631, 289 (2024).
  46. D. K. Hoffmann, T. Paintner, W. Limmer, D. S. Petrov, and J. H. Denschlag, Reaction kinetics of ultracold molecule-molecule collisions, Nat. Commun. 9, 5244 (2018).
  47. Z. Idziaszek and P. S. Julienne, Universal rate constants for reactive collisions of ultracold molecules, Phys. Rev. Lett. 104, 113202 (2010).
  48. P. D. Gregory, J. A. Blackmore, M. D. Frye, L. M. Fernley, S. L. Bromley, J. M. Hutson, and S. L. Cornish, Molecule–molecule and atom–molecule collisions with ultracold RbCs molecules, New J. Phys. 23, 125004 (2021).
  49. P. D. Gregory, M. D. Frye, J. A. Blackmore, E. M. Bridge, R. Sawant, J. M. Hutson, and S. L. Cornish, Sticky collisions of ultracold RbCs molecules, Nat. Commun. 10, 3104 (2019).
  50. X.-Y. Chen, S. Biswas, S. Eppelt, A. Schindewolf, F. Deng, T. Shi, S. Yi, T. A. Hilker, I. Bloch, and X.-Y. Luo, Ultracold field-linked tetratomic molecules, Nature (London) 626, 283 (2024).
  51. P. D. Gregory, L. M. Fernley, A. L. Tao, S. L. Bromley, J. Stepp, Z. Zhang, S. Kotochigova, K. R. A. Hazzard, and S. L. Cornish, Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules, Nat. Phys. 20, 415 (2024).
  52. C.-C. Chen, R. G. Escudero, J. Minåř, B. Pasquiou, S. Bennetts, and F. Schreck, Continuous Bose–Einstein condensation, Nature (London) 606, 683 (2022).
  53. M. Egorov, R. P. Anderson, V. Ivannikov, B. Opanchuk, P. D. Drummond, and A. I. Sidorov, Long-lived periodic revivals of coherence in an interacting Bose-Einstein condensate, Phys. Rev. A 84, 021605(R) (2011).
  54. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates, Phys. Rev. Lett. 79, 4950 (1997).
  55. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Coherent oscillations between two weakly coupled Bose Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping, Phys. Rev. A 59, 620 (1999).
  56. I. Marino, S. Raghavan, S. Fantoni, S. R. Shenoy, and A. Smerzi, Bose-condensate tunneling dynamics: Momentum-shortened pendulum with damping, Phys. Rev. A 60, 487 (1999).
  57. M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction, Phys. Rev. Lett. 95, 010402 (2005).
  58. J. Herbig, T. Kraemer, M. Mark, T. Weber, C. Chin, H.-C. Nagerl, and R. Grimm, Preparation of a pure molecular quantum gas, Science 301, 1510 (2003).
  59. X. Chen and B. Fan, The emergence of picokelvin physics, Rep. Prog. Phys. 83, 076401 (2020).
  60. C. Deppner, W. Herr, M. Cornelius, P. Stromberger, T. Sternke, C. Grzeschik, A. Grote, J. Rudolph, S. Herrmann, M. Krutzik, A. Wenzlawski, R. Corgier, E. Charron, D. Guéry-Odelin, N. Gaaloul, C. Lämmerzahl, A. Peters, P. Windpassinger, and E. M. Rasel, Collective-mode enhanced matter-wave optics, Phys. Rev. Lett. 127, 100401 (2021).
  61. H. C. Peñate-Rodríguez, A. Dorta-Urra, P. Bargueño, G. Rojas-Lorenzo, and S. Miret-Artés, A Langevin canonical approach to the dynamics of chiral systems: Populations and coherences, Chirality 25, 514 (2013).
  62. J. Ruostekoski and D. F. Walls, Measurement scheme for relative phase diffusion between two Bose-Einstein condensates, Phys. Rev. A 59, R2571 (1999).
  63. D. Hochberg, T. Buhse, J.-C. Micheau, and J. M. Ribó, Resilience of parity-violation-induced chiral selectivity to nonequilibrium temperature fluctuations in open systems, Phys. Rev. Res. 4, 033183 (2022).
  64. D. Hochberg, T. Buhse, J.-C. Micheau, and J. M. Ribó, Chiral selectivity vs. noise in spontaneous mirror symmetry breaking, Phys. Chem. Chem. Phys. 25, 31583 (2023).
  65. D. DeMille, S. B. Cahn, D. Murphree, D. A. Rahmlow, and M. G. Kozlov, Using molecules to measure nuclear spin-dependent parity violation, Phys. Rev. Lett. 100, 023003 (2008).

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