Abstract
ARC 3.0 is a modular, object-oriented Python library combining data and algorithms to enable the calculation of a range of properties of alkali and divalent atoms. Building on the initial version of the ARC library (Šibalić et al., 2017), which focused on Rydberg states of alkali atoms, this major upgrade introduces support for divalent atoms. It also adds new methods for working with atom–surface interactions, for modelling ultracold atoms in optical lattices and for calculating valence electron wave functions and dynamic polarisabilities. Such calculations have applications in a variety of fields, e.g., in the quantum simulation of many-body physics, in atom-based sensing of DC and AC fields (including in microwave and THz metrology) and in the development of quantum gate protocols. ARC 3.0 comes with an extensive documentation including numerous examples. Its modular structure facilitates its application to a wide range of problems in atom-based quantum technologies. Program summaryProgram Title: ARC 3.0CPC Library link to program files:https://doi.org/10.17632/c4z4n2cdf7.1Licencing provisions: BSD-3-ClauseProgramming language: PythonExternal Routines: NumPy [1], SciPy [1], Matplotlib [2], SymPy [3], LmFit [4]Nature of problem: The calculation of atomic properties of alkali and divalent atoms including energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated through a variety of means.Solution method: Dipole matrix elements are calculated using an analytical semi-classical approximation or wave functions obtained by numerical integration of the radial Schrödinger equation for a one-electron model potential. Interaction energies and shifts due to external fields are calculated using second order degenerate perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation.Additional comments including restrictions and unusual features: External electric and magnetic field must be parallel to the quantisation axis. The accuracy of short range (≲1μm) atom - atom interaction potentials is limited by the truncation of the basis. Only weak magnetic fields are supported as only linear Zeeman shifts are taken into account. Calculations for divalent atoms use a single-electron approximation and calculation of their wave functions is not supported.
Highlights
Neutral atoms are ideal building blocks for both fundamental research and technological applications exploiting quantum mechanics
By promoting atoms to highly-excited, long-lived Rydberg states, the sensitivity to applied electric fields can be enhanced by many orders of magnitude compared to the ground state [3], which has applications to electric field metrology over a wide range of frequencies from DC to THz fields [2, 4, 5, 6, 7]
ARC 3.0 is available from the online repository Python Package Index (PyPI) and can be installed from the command line by invoking pip install ARC-Alkali-Rydberg-Calculator
Summary
Neutral atoms are ideal building blocks for both fundamental research and technological applications exploiting quantum mechanics. While several groups have performed calculations of Stark maps [21, 22, 23] and interaction potentials [24, 25, 26], open-source codes like those provided by ARC 1.0 [18] and Pairinteraction [27] for the alkalis are not available for these species. To allow easy visualisation of different atomic states, a module Wavefunction provides sectional views of the atomic wave function for arbitrary atomic states These are important both for pedagogical and research purposes, especially since the size of Rydberg electron orbitals can be large enough to encompass other atoms, and may even approach the typical lengthscale over which external trapping potentials vary [30, 31]. The rest of the paper gives an overview of the newly implemented calculations, with comments on restrictions and implementation details
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