Rydberg atoms have strong and adjustable atomic interactions that can be tweaked by choosing different states with various principal quantum numbers or orbital angular momentum. They are highly used in quantum information applications. Furthermore, these atoms have long lifetimes and many possible energy levels, and their separations enable coupling to electromagnetic fields with frequencies ranging over six orders of magnitude. We studied some properties of these atoms and have developed a python program; the program gives two options. Firstly, it calculates energies of elements in s, p, d, and f orbitals and draws an energy level diagram of the element listed in the program. Secondly, it gives an option for calculating energy and quantum defects of atoms and ions, either listed or not listed in the program and generates their graphs accordingly. There are 21 elements in the database whose energy level diagrams could be drawn. The database can be extended by adding more elements.
Rydberg atoms have strong and adjustable atomic interactions that can be tweaked by choosing different states with various principal quantum numbers or orbital angular momentum. They are highly used in quantum information applications. Furthermore, these atoms have long lifetimes and many possible energy levels, and their separations enable coupling to electromagnetic fields with frequencies ranging over six orders of magnitude. We studied some properties of these atoms and have developed a python program; the program gives two options. Firstly, it calculates energies of elements in s, p, d, and f orbitals and draws an energy level diagram of the element listed in the program. Secondly, it gives an option for calculating energy and quantum defects of atoms and ions, either listed or not listed in the program and generates their graphs accordingly. There are 21 elements in the database whose energy level diagrams could be drawn. The database can be extended by adding more elements.
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/.
This topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground-states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics.
Abstract This topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics.
We present calculations of long-range interactions in Rydberg atoms, with a focus on the dipole-dipole interactions of strontium Rydberg states. The growing use of Rydberg states in the field of cold atoms necessitates a more detailed understanding of the effects of dipole-dipole interactions, which are currently being investigated in a number of research groups worldwide. Calculations of long-range interactions in Rydberg states of caesium, cal- cium, rubidium, strontium and ytterbium are presented. By taking the one active electron approximation we develop consistent models of these long- range interactions, and construct a survey of the Rydberg state dipole-dipole interactions and quadrupole-quadrupole interactions. We compare the inter- actions between series and between atoms, highlighting the importance of certain series for applications suggested in previous works. In order to include two-electron effects in the description of dipole-dipole interactions in divalent atoms, we use multichannel quantum defect theory (MQDT) to develop models of the Rydberg series of strontium. We use an empirical reactance matrix formalism, where the reactance matrix is fitted to reproduce experimentally measured values of the bound state energy levels. Models are found for all series of strontium with L ≤ 3. We extend the MQDT formalism to the description of the natural radiative lifetimes of strontium, where the perturbers are found to have a large quenching effect on these lifetimes. By incorporating the MQDT description of the Rydberg states of strontium into the calculation of dipole-dipole interactions, we find a spin-forbidden two-atom resonance in the 3D2 states of strontium. We consider a one- dimensional lattice of strontium atoms, and find that the internal dynamics of the Rydberg atoms demonstrates spin transport for large lattice spacings and a separation of the spin and total angular momentum dynamics for small lattice spacings. Spin-angular momentum separation (analogous to spin-charge separation in condensed matter) in strontium Rydberg atoms may have uses in the investigation of one-dimensional Fermi gases and their description using Luttinger liquid theory.
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
An operator that generates an approximate symmetry of long-range Rydberg molecules (LRRMs) formed by two alkali atoms, one in a Rydberg state and the other in the ground state, is identified. This is first done by evaluating the natural orbitals associated with a variational calculation of the binding wave function within the Born-Oppenheimer description of the molecule including s and p Fermi pseudopotential and the hyperfine structure energy terms. The resulting orbitals with the highest occupation number are shown to be identical to those obtained by a perturbative model for high angular momentum—trilobite and butterfly—LRRMs. Whenever the slight dependence of the quantum defects of the Rydberg electron on its total momentum j⃗=ℓ⃗+s⃗1 can be neglected, the symmetry operator of the high angular momentum LRRMs orbitals is identified as the sum of the spin of the Rydberg electron s⃗1 , spin of the valence electron s⃗2 , and the spin of nucleus i⃗ of the ground-state atom, N⃗=s1⃗+s2⃗+i⃗ . The spin orbitals that diagonalize N⃗ define compact basis sets for the description of LRRMs beyond the aforementioned approximations. The matrix elements of the Hamiltonian in these basis sets have simple expressions, so that the relevance of triplet and singlet contributions can be directly estimated. The expected consequences of this approximate spin-symmetry on the spectra of LRRMs are briefly described. Published by the American Physical Society 2024