Software for Calculating Trap Induced Broadening in Potential Hydrogen Lattice Clocks

Joseph P. Scott; David Carty; Matthew P. A. Jones

doi:10.5334/jors.504

Abstract

We present software for calculating the polarisability and atom-photon scattering rates of hydrogen atoms in S-states (orbital angular momentum l = 0). It can also calculate magic wavelengths between pairs of hydrogen S states. Such calculations are essential to the potential optical trapping of atomic hydrogen. Calculations proceed numerically via implicit summation over a basis of radial Sturmian functions. This naturally includes all contributions from both bound and unbound states. The software was developed with low-lying states in mind but applies to all S states and any hydrogen isotope. Extensions to other hydrogen-like systems or different orbital angular momentum states are possible. It is written in Python and uses NumPy and SciPy extensively. It is available via GitHub.

References

Scott JP, Potvliege RM, Carty D, Jones MPA. Trap induced broadening in a potential hydrogen lattice clock. Metrologia. 2024;61(2):025001. DOI: 10.1088/1681-7575/ad1e37
Open DOI Search in Google Scholar Back to article
Scott JP. Towards precision measurement with trapped hydrogen atoms. Doctoral thesis, Durham University. 2024. Available at: https://etheses.dur.ac.uk/15616/.
Search in Google Scholar Back to article
Crivelli P, Kolachevsky N. Optical trapping of antihydrogen towards an atomic anti-clock. Hyperfine Interactions. 2020;241(1):60. DOI: 10.1007/s10751-018-1549-4
Open DOI Search in Google Scholar Back to article
Vázquez-Carson SF, Sun Q, Dai J, Mitra D, Zelevinsky T. Direct laser cooling of calcium monohydride molecules. New Journal of Physics. 2022;24(8):083006. DOI: 10.1088/1367-2630/ac806c
Open DOI Search in Google Scholar Back to article
Grimm R, Weidemüller M, Ovchinnikov YB. Optical dipole traps for neutral atoms. Advances in Atomic, Molecular, and Optical Physics. 2000;42:95–170. DOI: 10.1016/S1049-250X(08)60186-X
Open DOI Search in Google Scholar Back to article
Klarsfeld S. Retardation Effects in Second-Order Radiative Transitions between Hydrogenic States. Lettere Nuovo Cimento. 1969;1:682–686. DOI: 10.1007/BF02752568
Open DOI Search in Google Scholar Back to article
Marian TA. Bound-bound two-photon transition matrix elements for the hydrogen atom in the dipole approximation. Physical Review A. 1989;39(8):3816. DOI: 10.1103/PhysRevA.39.3816
Open DOI Search in Google Scholar Back to article
Maquet A, Véniard V, Marian TA. The Coulomb Green’s function and multiphoton calculations. Journal of Physics B: Atomic, Molecular and Optical Physics. 1998;31(17):3743. DOI: 10.1088/0953-4075/31/17/004
Open DOI Search in Google Scholar Back to article
Šibalić N, Pritchard JD, Adams CS, Weatherill KJ. ARC: An open-source library for calculating properties of alkali Rydberg atoms. Computer Physics Communications. 2017;220:319–331. DOI: 10.1016/j.cpc.2017.06.015
Open DOI Search in Google Scholar Back to article
Grau M, Wipfli O. atomphys. 2021. Available at: https://github.com/mgrau/atomphys.
Search in Google Scholar Back to article
Mavromatis HA. The Dalgarno–Lewis summation technique: Some comments and examples. American Journal of Physics. 1991;59(8):738–744. DOI: 10.1103/RevModPhys.35.522
Open DOI Search in Google Scholar Back to article
Zernik W. Interaction of optical and infrared radiation with metastable hydrogen atoms. Physical Review. 1964;133(1A):A117. DOI: 10.1103/PhysRev.133.A117
Open DOI Search in Google Scholar Back to article
Gontier Y, Trahin M. Multiphoton processes in a hydrogen atom. Physical Review A. 1971;4(5):1896. DOI: 10.1103/PhysRevA.4.1896
Open DOI Search in Google Scholar Back to article
Potvliege RM. STRFLO: A program for time-independent calculations of multiphoton processes in one-electron atomic systems I. Quasienergy spectra and angular distributions. Computer Physics Communications. 1998;114:42–93. DOI: 10.1016/S0010-4655(98)00073-3
Open DOI Search in Google Scholar Back to article
Potvliege RM, Shakeshaft R. High-order harmonic generation and Raman scattering by hydrogen in perturbation theory. Zeitschrift fuer Physik D. 1989;11(1):93–94. DOI: 10.1007/BF01436589
Open DOI Search in Google Scholar Back to article
Dörr M, Potvliege RM, Shakeshaft R. Atomic hydrogen irradiated by a strong laser field: Sturmian basis calculations of rates for high-order multiphoton ionization, Raman scattering, and harmonic generation. JOSA B. 1990;7(4):433–448. DOI: 10.1364/JOSAB.7.000433
Open DOI Search in Google Scholar Back to article
McNamara K, Fursa DV, Bray I. Efficient calculation of Rayleigh and Raman scattering. Physical Review A. 2018;98(4):043435. DOI: 10.1103/PhysRevA.98.043435
Open DOI Search in Google Scholar Back to article
Berrington KA, Eissner WB, Norrington PH. RMATRX1: Belfast atomic R-matrix codes. Computer Physics Communications. 1995;92(2–3):290–420. DOI: 10.1016/0010-4655(95)00123-8
Open DOI Search in Google Scholar Back to article
Harris CR, Millman KJ, van der Walt SJ, et al. Array programming with NumPy. Nature. 2020;585:357–362. DOI: 10.1038/s41586-020-2649-2
Open DOI Search in Google Scholar Back to article
SciPy 1.6.0. DOI: 10.5281/zenodo.4406806
Open DOI Search in Google Scholar Back to article
Tiesinga E, Mohr PJ, Newell DB, Taylor BN. CODATA recommended values of the fundamental physical constants: 2018. Journal of Physical and Chemical Reference Data. 2021;50(3). DOI: 10.1063/5.0064853
Open DOI Search in Google Scholar Back to article
Drake GW, editor. Springer handbook of atomic, molecular, and optical physics. Springer Nature; 2023. DOI: 10.1007/978-3-030-73893-8
Open DOI Search in Google Scholar Back to article
Adhikari CM, Canales JC, Arthanayaka TP, Jentschura UD. Magic Wavelengths for 1S–nS and 2S–nS Transitions in Hydrogenlike Systems. Atoms. 2021;10(1):1. DOI: 10.3390/atoms10010001
Open DOI Search in Google Scholar Back to article
Klarsfeld S. Interaction of Metastable Hydrogenlike Atoms with Electromagnetic Radiation. Physical Review A. 1972;6(1):506. DOI: 10.1103/PhysRevA.6.506
Open DOI Search in Google Scholar Back to article
Heno Y, Maquet A, Schwarcz R. Raman-like scattering processes in metastable hydrogenic atoms. Journal of Applied Physics. 1980;51(1):11–14. DOI: 10.1063/1.327404
Open DOI Search in Google Scholar Back to article
Udem TD. Private communications. 2023.
Search in Google Scholar Back to article

Software for Calculating Trap Induced Broadening in Potential Hydrogen Lattice Clocks

Abstract

Paradigm

My account