We present a computer program to calculate the quantised rotational and hyperfine energy levels of Σ1 diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to the bialkali molecules used in ongoing state-of-the-art experiments with ultracold molecular gases. We include functions for the calculation of space-fixed electric dipole moments, magnetic moments and transition dipole moments. Program Title: Diatomic-Py CPC Library link to program files: https://doi.org/10.17632/3yfxnh5bn5.1 Developer's repository link: https://doi.org/10.5281/zenodo.6632148 Licensing provisions: BSD 3-clause Programming language: Python ≥ 3.7 Nature of problem: Calculation of the rotational and hyperfine structure of Σ1 molecules in the presence of dc magnetic, dc electric, and off-resonant laser fields. Solution method: A matrix representation of the Hamiltonian is constructed in the uncoupled basis set. Eigenstates and eigenenergies are calculated by numerical diagonalization of the Hamiltonian. Additional comments including restrictions and unusual features: Restricted to calculating the Stark and Zeeman shifts with co-axial electric and magnetic fields.
We present a computer program to calculate the quantised rotational and hyperfine energy levels of Σ1 diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to the bialkali molecules used in ongoing state-of-the-art experiments with ultracold molecular gases. We include functions for the calculation of space-fixed electric dipole moments, magnetic moments and transition dipole moments. Program Title: Diatomic-Py CPC Library link to program files: https://doi.org/10.17632/3yfxnh5bn5.1 Developer's repository link: https://doi.org/10.5281/zenodo.6632148 Licensing provisions: BSD 3-clause Programming language: Python ≥ 3.7 Nature of problem: Calculation of the rotational and hyperfine structure of Σ1 molecules in the presence of dc magnetic, dc electric, and off-resonant laser fields. Solution method: A matrix representation of the Hamiltonian is constructed in the uncoupled basis set. Eigenstates and eigenenergies are calculated by numerical diagonalization of the Hamiltonian. Additional comments including restrictions and unusual features: Restricted to calculating the Stark and Zeeman shifts with co-axial electric and magnetic fields.
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 Title: ARC 3.0 CPC Library link to program files: https://doi.org/10.17632/c4z4n2cdf7.1 Licencing provisions: BSD-3-Clause Programming language: Python External 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. References [1] T.E. Oliphant, Comput. Sci. Eng. 9 (2007) 10. http://www.scipy.org/. [2] J.D. Hunter, Comput. Sci. Eng. 9 (2007) 90. http://matplotlib.org/. [3] A. Meurer et al., PeerJ Comput. Sci. 3 (2017) e103. https://doi.org/10.7717/peerj-cs.103 [4] M. Newville et al., lmfit/lmfit-py 1.0.0 (Version 1.0.0), Zenodo (2019). https://doi.org/10.5281/zenodo.3588521
We present an object-oriented Python library for the computation of properties of highly-excited Rydberg states of alkali atoms. These include single-body effects such as dipole matrix elements, excited-state lifetimes (radiative and black-body limited) and Stark maps of atoms in external electric fields, as well as two-atom interaction potentials accounting for dipole and quadrupole coupling effects valid at both long and short range for arbitrary placement of the atomic dipoles. The package is cross-referenced to precise measurements of atomic energy levels and features extensive documentation to facilitate rapid upgrade or expansion by users. This library has direct application in the field of quantum information and quantum optics which exploit the strong Rydberg dipolar interactions for two-qubit gates, robust atom-light interfaces and simulating quantum many-body physics, as well as the field of metrology using Rydberg atoms as precise microwave electrometers. Program Title: ARC: Alkali Rydberg Calculator Program Files doi: http://dx.doi.org/10.17632/hm5n8w628c.1 Licensing provisions: BSD-3-Clause Programming language: Python 2.7 or 3.5, with C extension External Routines: NumPy [1], SciPy [1], Matplotlib [2] Nature of problem: Calculating atomic properties of alkali atoms including lifetimes, energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated from radial wavefunctions. Solution method: Numerical integration of radial Schrödinger equation to obtain atomic wavefunctions, which are then used to evaluate dipole matrix elements. Properties are calculated using second order perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation. Restrictions: External electric field fixed to be parallel to quantisation axis. Supplementary material: Detailed documentation (.html), and Jupyter notebook with examples and benchmarking runs (.html and .ipynb). [1] T.E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/. [2] J.D. Hunter, Comput. Sci. Eng. 9, 90 (2007). http://matplotlib.org/.
We present a computer program and underlying model to calculate the electric susceptibility of a gas, which is essential to predict its absorptive and dispersive properties. Our program focuses on alkali-metal vapours where we use a matrix representation of the atomic Hamiltonian in the completely uncoupled basis in order to calculate transition frequencies and strengths. The program calculates various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field. This allows many optical devices to be designed, such as Faraday rotators/filters, optical isolators and circular polarisation filters. Fitting routines are also provided with the program which allows the user to perform optical metrology by fitting to experimental data. Program title: ElecSus Catalogue identifier: AEVD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVD_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Apache License, version 2 No. of lines in distributed program, including test data, etc.: 191 270 No. of bytes in distributed program, including test data, etc.: 309 4994 Distribution format: tar.gz Programming language: Python. Computer: Any single computer running Python 2. Operating system: Linux, Mac OSX, Windows. RAM: Depends on the precision required and size of the data set, but typically not larger than 50 MiB. Classification: 2.2, 2.3. External routines: SciPy library [1] 0.12.0 or later, NumPy [1], matplotlib [2] Nature of problem: Calculating the weak-probe electric susceptibility of an alkali-metal vapour. The electric susceptibility can be used to calculate spectra such as transmission and Stokes parameters. Measurements of experimental parameters can be made by fitting the theory to data. Solution method: The transition frequencies and wavelengths are calculated using a matrix representation of the Hamiltonian in the completely uncoupled basis. A suite of fitting methods are provided in order to allow user supplied experimental data to be fit to the theory, thereby allowing experimental parameters to be extracted. Restrictions: Only describes a magnetic field parallel to the laser beam propagation direction. Results are only valid in the weak-probe regime. Running time: At standard precision less than a second for a theory curve, fitting will take 10 s to 20 min depending on the method used, the number of parameters to fit and the number of data points. References: [1] T.E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/. [2] J.D. Hunter, Comput. Sci. Eng. 9, 10 (2007). http://matplotlib.org/.
We develop a program package named QS3 based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models on spatially uniform/non-uniform lattices near fully polarized states, which can be mapped to dilute hardcore Bose systems. All calculations in QS3, including eigenvalue problems, expectation values for one/two-point spin operators, and static/dynamical spin structure factors, are performed in the symmetry-adapted bases specified by the number N↓ of down spins and the wave number k associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS3 can support large-scale quantum systems containing more than 1000 sites with dilute N↓. We show the benchmark results of QS3 for the low-energy excitation dispersion of the isotropic Heisenberg model on the 10×10×10 cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the 10×10 square lattice, and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP). Theoretical backgrounds and the user interface of QS3 are also described. Program Title: QS3 CPC Library link to program files: https://doi.org/10.17632/yc6jytvf8v.1 Developer's repository link: https://github.com/QS-Cube/ED Licensing provisions: MIT Programming language: Fortran90 External routines/libraries: BLAS, LAPACK Nature of problem: Physical properties (such as total energy, magnetic moment, two-point spin correlation function, and dynamical structure factor) Solution method: Application software based on the full diagonalization method and the exact diagonalization method using the Lanczos and thick-restart Lanczos techniques for quantum spin S=1/2 models such as the XXZ model. Restrictions: Spin S=1/2 systems with U(1) symmetry. Unusual features: Massively large quantum spin systems with U(1) symmetry near the saturation field can be solved with or without considering translational symmetry, which is difficult to treat using standard exact diagonalization libraries with the bit representation for specifying spin configurations.
We present a major update to ElecSus, a computer program and underlying model to calculate the electric susceptibility of an alkali-metal atomic vapour. Knowledge of the electric susceptibility of a medium is essential to predict its absorptive and dispersive properties. In this version we implement several changes which significantly extend the range of applications of ElecSus, the most important of which is support for non-axial magnetic fields (i.e. fields which are not aligned with the light propagation axis). Supporting this change requires a much more general approach to light propagation in the system, which we have now implemented. We exemplify many of these new applications by comparing ElecSus to experimental data. In addition, we have developed a graphical user interface front-end which makes the program much more accessible, and have improved on several other minor areas of the program structure. Program Title: ElecSus Program Files doi: http://dx.doi.org/10.17632/h7cj8bz4bd.1 Licensing provisions: Apache License, Version 2.0 Programming language: Python External routines/libraries: SciPy library [1] 0.15.0 or later, NumPy [1], matplotlib [2], sympy [3], lmfit 0.9.5 or later [4], wxpython (required for GUI only) Nature of problem: Calculating the weak-probe electric susceptibility of an alkali-metal vapour. The electric susceptibility can be used to calculate spectra such as transmission and Stokes parameters. Measurements of experimental parameters can be made by fitting the theory to data. Solution method: The transition frequencies and wavelengths are calculated using a matrix representation of the Hamiltonian in the completely uncoupled basis. A suite of fitting methods are provided in order to allow user supplied experimental data to be fit to the theory, thereby allowing experimental parameters to be extracted. Restrictions: Results are only valid in the weak-probe regime. [1] T. E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/ [2] J. D. Hunter, Comput. Sci. Eng. 9, 10 (2007). http://matplotlib.org/ [3] A. Meurer et. al, PeerJ Comp. Sci. 3, e103 (2017) http://www.sympy.org/ [4] M. Newville et al., LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python, Zenodo (2014). DOI:10.5281/zenodo.11813 https://lmfit.github.io/lmfit-py/
The realization of rovibrationally stable dense samples of ultracold diatomic molecules remains one of the main stepping stones to achieve the next slate of major goals in the field of atomic and molecular physics. Though obtaining diatomic alkali molecules was seen as a logical next step following the optical cooling of atoms, many of the possible applications currently under investigation extend beyond atomic and molecular physics. For example, spectroscopy of ultracold molecules can help in testing extensions of the Standard Model via the search for a permanent electric dipole moment of the electron (1; 2), or the energy difference between enantiomers of chiral molecules (3). Various molecular transitions can be utilized to track the time dependence of fundamental constants, including the fine structure constant and the proton to electron mass ratio (4). They also open the way for cold and ultracold chemistry, where the interacting species and products are in a coherent quantum superposition state (5) and reactions can happen via quantum tunneling. Dipolar ultracold quantum gases promise to show a plethora of new phenomena due to anisotropic long-range dipole-dipole interactions (6). Dipolar molecules in optical lattices can be employed as a quantum simulator of condensed matter systems, and they are predicted to demonstrate new quantum phases such as a dipolar crystal, supersolid, checkerboard and collapse phases (7; 8). Ultracold polar molecules also represent an attractive platform for quantum computation (9). They offer a variety of long-lived states for qubit encoding, including rotational, spin and hyperfine (if electronic and nuclear spins are non-zero), Λ and Ω-doublet states (10) and scalability to a large number of qubits. Polar molecules can be easily controlled by DC electric and magnetic fields, as well as bymicrowave and optical fields, allowing the design of various traps (11; 12). The main appeal of polar molecules for quantum information processing, however, comes from their permanent electric dipole moment, permitting them to interact via a long-range dipole-dipole interaction. The dipole-dipole interaction offers a tool to construct two-qubit gates, required for universal quantum computation (9; 13). Ultracold molecules in their ground vibrational state v = 0 (and even in specific rotational, hyperfine or Zeeman states) are required formany of these applications since they have a large permanent electric dipole moment and are stable with respect to collisions and spontaneous emission. Currently translationally ultracold (100 nK 1 mK) molecules are produced by magneto(14) and photo-association (15) techniques. In a typical photoassociation scheme, 3