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  • Letter
  • Open Access

Prospects for thermalization of microwave-shielded ultracold molecules

Reuben R. W. Wang and John L. Bohn

  • JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

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Phys. Rev. Research 6, L022033 – Published 6 May, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022033

Abstract

Toward more efficient schemes for achieving deeply degenerate molecular Fermi gases, we study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng et al. [Phys. Rev. Lett. 130, 183001 (2023)] to obtain accurate two-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization.

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References (56)

  1. D. DeMille, Quantum computation with trapped polar molecules, Phys. Rev. Lett. 88, 067901 (2002).
  2. 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).
  3. D. S. Jin and J. Ye, Introduction to ultracold molecules: New frontiers in quantum and chemical physics, Chem. Rev. 112, 4801 (2012).
  4. G. Quéméner and P. S. Julienne, Ultracold molecules under control! Chem. Rev. 112, 4949 (2012).
  5. J. L. Bohn, A. M. Rey, and J. Ye, Cold molecules: Progress in quantum engineering of chemistry and quantum matter, Science 357, 1002 (2017).
  6. W. Ketterle and N. J. V. Druten, Evaporative Cooling of Trapped Atoms (Academic Press, Cambridge, USA, 1996).
  7. G. Quéméner and J. L. Bohn, Shielding Σ2 ultracold dipolar molecular collisions with electric fields, Phys. Rev. A 93, 012704 (2016).
  8. T. Xie, M. Lepers, R. Vexiau, A. Orbán, O. Dulieu, and N. Bouloufa-Maafa, Optical shielding of destructive chemical reactions between ultracold ground-state NaRb molecules, Phys. Rev. Lett. 125, 153202 (2020).
  9. K. Matsuda, L. D. 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).
  10. J.-R. Li, W. G. Tobias, K. Matsuda, C. Miller, G. Valtolina, L. De Marco, R. R. W. Wang, L. Lassablière, G. Quéméner, J. L. Bohn et al., Tuning of dipolar interactions and evaporative cooling in a three-dimensional molecular quantum gas, Nat. Phys. 17, 1144 (2021).
  11. B. Mukherjee, M. D. Frye, C. R. Le Sueur, M. R. Tarbutt, and J. M. Hutson, Shielding collisions of ultracold CaF molecules with static electric fields, Phys. Rev. Res. 5, 033097 (2023).
  12. A. V. Gorshkov, P. Rabl, G. Pupillo, A. Micheli, P. Zoller, M. D. Lukin, and H. P. Büchler, Suppression of inelastic collisions between polar molecules with a repulsive shield, Phys. Rev. Lett. 101, 073201 (2008).
  13. A. V. Avdeenkov, Dipolar collisions of ultracold polar molecules in a microwave field, Phys. Rev. A 86, 022707 (2012).
  14. L. Lassablière and G. Quéméner, Controlling the scattering length of ultracold dipolar molecules, Phys. Rev. Lett. 121, 163402 (2018).
  15. T. Karman and J. M. Hutson, Microwave shielding of ultracold polar molecules, Phys. Rev. Lett. 121, 163401 (2018).
  16. L. Anderegg, S. Burchesky, Y. Bao, S. S. Yu, T. Karman, E. Chae, K.-K. Ni, W. Ketterle, and J. M. Doyle, Observation of microwave shielding of ultracold molecules, Science 373, 779 (2021).
  17. A. Schindewolf, R. Bause, X.-Y. Chen, M. Duda, T. Karman, I. Bloch, and X.-Y. Luo, Evaporation of microwave-shielded polar molecules to quantum degeneracy, Nature (London) 607, 677 (2022).
  18. N. Bigagli, C. Warner, W. Yuan, S. Zhang, I. Stevenson, T. Karman, and S. Will, Collisionally stable gas of bosonic dipolar ground-state molecules, Nat. Phys. 19, 1579 (2023).
  19. J. Lin, G. Chen, M. Jin, Z. Shi, F. Deng, W. Zhang, G. Quéméner, T. Shi, S. Yi, and D. Wang, Microwave shielding of bosonic NaRb molecules, Phys. Rev. X 13, 031032 (2023).
  20. H. R. Sadeghpour, J. L. Bohn, M. J. Cavagnero, B. D. Esry, I. I. Fabrikant, J. H. Macek, and A. R. P. Rau, Collisions near threshold in atomic and molecular physics, J. Phys. B: At. Mol. Opt. Phys. 33, R93 (2000).
  21. K. Aikawa, A. Frisch, M. Mark, S. Baier, R. Grimm, J. L. Bohn, D. S. Jin, G. M. Bruun, and F. Ferlaino, Anisotropic relaxation dynamics in a dipolar Fermi gas driven out of equilibrium, Phys. Rev. Lett. 113, 263201 (2014).
  22. Y. Tang, A. G. Sykes, N. Q. Burdick, J. M. DiSciacca, D. S. Petrov, and B. L. Lev, Anisotropic expansion of a thermal dipolar Bose gas, Phys. Rev. Lett. 117, 155301 (2016).
  23. Y. Tang, A. Sykes, N. Q. Burdick, J. L. Bohn, and B. L. Lev, s-wave scattering lengths of the strongly dipolar bosons Dy162 and Dy164, Phys. Rev. A 92, 022703 (2015).
  24. A. Patscheider, L. Chomaz, G. Natale, D. Petter, M. J. Mark, S. Baier, B. Yang, R. R. W. Wang, J. L. Bohn, and F. Ferlaino, Determination of the scattering length of erbium atoms, Phys. Rev. A 105, 063307 (2022).
  25. J. L. Bohn, M. Cavagnero, and C. Ticknor, Quasi-universal dipolar scattering in cold and ultracold gases, New J. Phys. 11, 055039 (2009).
  26. J. L. Bohn and D. S. Jin, Differential scattering and rethermalization in ultracold dipolar gases, Phys. Rev. A 89, 022702 (2014).
  27. A. G. Sykes and J. L. Bohn, Nonequilibrium dynamics of an ultracold dipolar gas, Phys. Rev. A 91, 013625 (2015).
  28. R. R. W. Wang and J. L. Bohn, Anisotropic thermalization of dilute dipolar gases, Phys. Rev. A 103, 063320 (2021).
  29. O. J. Luiten, M. W. Reynolds, and J. T. M. Walraven, Kinetic theory of the evaporative cooling of a trapped gas, Phys. Rev. A 53, 381 (1996).
  30. K. B. Davis, M.-O. Mewes, and W. Ketterle, An analytical model for evaporative cooling of atoms, Appl. Phys. B 60, 155 (1995).
  31. F. Deng, X.-Y. Chen, X.-Y. Luo, W. Zhang, S. Yi, and T. Shi, Effective potential and superfluidity of microwave-shielded polar molecules, Phys. Rev. Lett. 130, 183001 (2023).
  32. X.-Y. Chen, A. Schindewolf, S. Eppelt, R. Bause, M. Duda, S. Biswas, T. Karman, T. Hilker, I. Bloch, and X.-Y. Luo, Field-linked resonances of polar molecules, Nature (London) 614, 59 (2023).
  33. G. Wang and G. Quéméner, Tuning ultracold collisions of excited rotational dipolar molecules, New J. Phys. 17, 035015 (2015).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022033 for details on the close-coupling calculations, frame transformations for Gaussian process regression, and a derivation of the Eikonal approximation and collision efficiency.
  35. L. P. Pitaevskii, E. M. Lifshitz, and J. B. Sykes, Physical Kinetics, Course of Theoretical Physics (Elsevier Science, Tarrytown, New Tork, 2017).
  36. G. A. Bird, Direct simulation and the Boltzmann equation, Phys. Fluids 13, 2676 (1970).
  37. The differential cross section suffers innate convergence issues due to singularities in the scattering amplitude [26]. Fortunately for us, forward scattering does not contribute to cross-dimensional thermalization, of which we are concerned with in this Letter. We leave addressing these issues to a future paper.
  38. J. Sacks, S. B. Schiller, and W. J. Welch, Designs for computer experiments, Technometrics 31, 41 (1989).
  39. J. Cui and R. V. Krems, Efficient non-parametric fitting of potential energy surfaces for polyatomic molecules with gaussian processes, J. Phys. B: At. Mol. Opt. Phys. 49, 224001 (2016).
  40. A. Christianen, T. Karman, R. A. Vargas-Hernández, G. C. Groenenboom, and R. V. Krems, Six-dimensional potential energy surface for NaKNaK collisions: Gaussian process representation with correct asymptotic form, J. Chem. Phys. 150, 064106 (2019).
  41. In the dipole frame, the differential cross section has scattering angles obey the symmetry relation Del(E,η,θs,ϕs)=Del(E,η,θs,−ϕs). Consequently, we only need to specify the differential cross section for angles within the domain η,θs,ϕs∈[0,π], to fully describe its global structure.
  42. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (The MIT Press, Cambridge, Massachusetts, 2005).
  43. The Matérn-52 kernel contains a parameter w that sets a length scale over which features of the data vary in coordinate space, which is optimized during the model training process.
  44. We utilize more points than usually necessary for GP fitting in this study, so as to obtain more accurate results of subsequently computed quantities in this Letter. We also optimize the model's hyperparameters [56] on top of just the kernel parameters. Even so, the Gaussian process model has issues faithfully reproducing the differential cross section around η,θs=90∘, known to have a discontinuity at threshold [26]. Fortunately, this angular segment corresponds to forward scattering, which does not contribute to the cross-dimensional thermalization process of interest here. We ignore this issue until necessary for consideration in future works.
  45. C. R. Monroe, E. A. Cornell, C. A. Sackett, C. J. Myatt, and C. E. Wieman, Measurement of Cs-Cs elastic scattering at T = 30 µK, Phys. Rev. Lett. 70, 414 (1993).
  46. D. W. Snoke and J. P. Wolfe, Population dynamics of a Bose gas near saturation, Phys. Rev. B 39, 4030 (1989).
  47. The Monte Carlo integration gives a ≲1% error, which is mostly imperceptible in the log-linear plot.
  48. E. L. Surkov, J. T. M. Walraven, and G. V. Shlyapnikov, Collisionless motion and evaporative cooling of atoms in magnetic traps, Phys. Rev. A 53, 3403 (1996).
  49. R. R. W. Wang and J. L. Bohn, Thermal conductivity of an ultracold paramagnetic Bose gas, Phys. Rev. A 106, 023319 (2022).
  50. R. R. W. Wang and J. L. Bohn, Thermoviscous hydrodynamics in nondegenerate dipolar Bose gases, Phys. Rev. A 106, 053307 (2022).
  51. R. R. W. Wang and J. L. Bohn, Anisotropic acoustics in dipolar Fermi gases, Phys. Rev. A 107, 033321 (2023).
  52. R. R. W. Wang and J. L. Bohn, Viscous dynamics of a quenched trapped dipolar Fermi gas, Phys. Rev. A 108, 013322 (2023).
  53. L. Lassablière and G. Quéméner, Model for two-body collisions between ultracold dipolar molecules around a Förster resonance in an electric field, Phys. Rev. A 106, 033311 (2022).
  54. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose-Einstein condensation of dipolar molecules, arXiv:2312.10965.
  55. B. DeMarco, J. L. Bohn, J. P. Burke, M. Holland, and D. S. Jin, Measurement of p-wave threshold law using evaporatively cooled fermionic atoms, Phys. Rev. Lett. 82, 4208 (1999).
  56. L. Yang and A. Shami, On hyperparameter optimization of machine learning algorithms: Theory and practice, Neurocomputing 415, 295 (2020).

Outline

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Phys. Rev. Research 6, L022033– Published 6 May, 2024
  • Received 26 October 2023
  • Revised 8 February 2024
  • Accepted 16 April 2024
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