Tutorial: Calculation of Rydberg interaction potentials

Abstract

The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation, and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be fine-tuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipole-dipole interaction term are no longer sufficient. In this tutorial, we review all relevant aspects of the full calculation of Rydberg interaction potentials. We discuss the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments, and the inclusion of electromagnetic fields with arbitrary direction. We focus specifically on symmetry arguments and selection rules, which greatly reduce the size of the Hamiltonian matrix, enabling the direct diagonalization of the Hamiltonian up to higher multipole orders on a desktop computer. Finally, we present example calculations showing the relevance of the full interaction calculation to current experiments. Our software for calculating Rydberg potentials including all features discussed in this tutorial is available as open source.

accepted in J. Phys. B

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• Coherent Excitation Transfer in a Spin Chain of Three Rydberg Atoms
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• Long-range interactions and entanglement of slow single-photon pulses
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• Spectroscopy of strontium Rydberg states using electromagnetically induced transparency
• Controlling the interactions of a few cold Rb Rydberg atoms by radiofrequency-assisted Förster resonances
• Observation of Rydberg-atom macrodimers: micrometer-sized diatomic molecules
• Observation of dipole-quadrupole interaction in an ultracold gas of Rydberg atoms
• Long-range potentials and $(n-1)d+ns$ molecular resonances in an ultracold rydberg gas
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Cited by in corpus (114)

• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• ARC: An open-source library for calculating properties of alkali Rydberg atoms
• Quantum simulation and computing with Rydberg-interacting qubits
• Long-range interacting quantum systems
• A concise review of Rydberg atom based quantum computation and quantum simulation
• A room temperature single-photon source based on strongly interacting Rydberg atoms
• Trapped arrays of alkaline earth Rydberg atoms in optical tweezers
• Detailed Balance of Thermalization dynamics in Rydberg atom quantum simulators
• Ultrafast energy exchange between two single Rydberg atoms on the nanosecond timescale
• Quench Dynamics of a Fermi Gas with Strong Non-Local Interactions
• Local optical control of the resonant dipole-dipole interaction between Rydberg atoms
• Quantum Computing with Circular Rydberg Atoms
• Realization of a density-dependent Peierls phase in a synthetic, spin-orbit coupled Rydberg system
• A dual-species Rydberg array
• Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity
• Universal quantum operations and ancilla-based readout for tweezer clocks
• Quantum gas microscopy of Rydberg macrodimers
• Accurate mapping of multilevel Rydberg atoms on interacting spin-$1/2$ particles for the quantum simulation of Ising models
• Realizing distance-selective interactions in a Rydberg-dressed atom array
• Asymmetric blockade and multi-qubit gates via dipole-dipole interactions
• Rydberg superatoms: An artificial quantum system for quantum information processing and quantum optics
• Controlling Rydberg excitations using ion core transitions in alkaline earth atom tweezer arrays
• Rydberg atom entanglements in the weak coupling regime
• Spatially tunable spin interactions in neutral atom arrays
• Programmable Quantum Annealing Architectures with Ising Quantum Wires
• Interactions between Rydberg excitons in Cu${}_2$O
• Observation of three-body correlations for photons coupled to a Rydberg superatom
• Robust control and optimal Rydberg states for neutral atom two-qubit gates
• Spatial imaging of a novel type of molecular ions
• The interplay between thermal Rydberg gases and plasmas
• Long-Lived Circular Rydberg Qubits of Alkaline-Earth Atoms in Optical Tweezers
• Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays
• Observation of Rydberg blockade due to the charge-dipole interaction between an atom and a polar molecule
• High-fidelity interconversion between Greenberger-Horne-Zeilinger and $W$ states through Floquet-Lindblad engineering in Rydberg atom arrays
• Emergent Bloch oscillations in a kinetically constrained Rydberg spin lattice
• Observation of vibrational dynamics of orientated Rydberg-atom-ion molecules
• Landau-Forbidden Quantum Criticality in Rydberg Quantum Simulators
• Black-body radiation induced facilitated excitation of Rydberg atoms in optical tweezers
• RydIQule: A Graph-based Paradigm for Modelling Rydberg and Atomic Systems
• Precision measurement of the ionization energy and quantum defects of 39K I
• Scalable $W$-type entanglement resource in neutral-atom arrays with Rydberg-dressed resonant dipole-dipole interaction
• Rydberg Aggregates
• Single-Photon Rydberg Excitation and Trap-Loss Spectroscopy of Cold Cesium Atoms in a Magneto-Optical Trap by Using of a 319-nm Ultra-Violet Laser System
• Theory of long range interactions for Rydberg states attached to hyperfine split cores
• Ion Imaging via Long-Range Interaction with Rydberg Atoms
• One-step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping
• Plasma-enhanced interaction and optical nonlinearities of Cu${}_2$O Rydberg excitons
• Realization of a doped quantum antiferromagnet with dipolar tunnelings in a Rydberg tweezer array
• Simulating polaron biophysics with Rydberg atoms
• Quantum Optics with Rydberg Superatoms
• Proposal for simulating quantum spin models with the Dzyaloshinskii-Moriya interaction using Rydberg atoms and the construction of asymptotic quantum many-body scar states
• Quantum Phases from Competing Van der Waals and Dipole-Dipole Interactions of Rydberg Atoms
• Strong Spin-Motion Coupling in the Ultrafast Dynamics of Rydberg Atoms
• Microscopic electronic structure tomography of Rydberg macrodimers
• Self-generated quantum gauge fields in arrays of Rydberg atoms
• Coherence of the Borromean three-body Förster resonances in Rydberg atoms
• Rydberg blockade in an ultracold strontium gas revealed by two-photon excitation dynamics
• From coherent collective excitation to Rydberg blockade on an atom chip
• Quantum simulation of the central spin model with a Rydberg atom and polar molecules in optical tweezers
• Characterizing the local vectorial electric field near an atom chip using Rydberg state spectroscopy
• Strongly non-linear interaction between non-classical light and a blockaded Rydberg atomic ensemble
• Dissipative quantum state preparation and metastability in two-photon micromasers
• Interspecies Förster resonances of Rb-Cs Rydberg $d$-states for enhanced multi-qubit gate fidelities
• Rydberg Macrodimers: Diatomic molecules on the micrometer scale
• Precision millimetre-wave spectroscopy and calculation of the Stark manifolds in high Rydberg states of para-H${}_2$
• Benchmarking direct and indirect dipolar spin-exchange interactions between two Rydberg atoms
• Fast entangling gates for Rydberg atoms via resonant dipole-dipole interaction
• Spin-1 Haldane phase in a chain of Rydberg atoms
• Avalanche terahertz photon detection in a Rydberg tweezer array
• Driven-dissipative Rydberg blockade in optical lattices
• Parallel implementation of CNOT${}^N$ and C${}_2$NOT${}^2$ gates via homonuclear and heteronuclear Förster interactions of Rydberg atoms
• Tracking Rydberg atoms with Bose-Einstein Condensates
• Supersolidity in Rydberg tweezer arrays
• Experimental realization of a 3D long-range random hopping model
• Observation of effects due to an atom's electric quadrupole polarizability
• Microwave photo-association of fine-structure-induced Rydberg $(n+2)D_{5/2}n{F}_J$ macro-dimer molecules of cesium
• Spectral Signatures of Vibronic Coupling in Trapped Cold Ionic Rydberg Systems
• Casimir--Polder induced Rydberg macrodimers
• Engineering Rydberg-pair interactions in divalent atoms with hyperfine-split ionization thresholds
• Transport on flexible Rydberg aggregates using circular states
• Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks
• Observation of average topological phase in disordered Rydberg atom array
• Isolated-core quadrupole excitation of highly excited autoionizing Rydberg states
• Quantum simulation of extended electron-phonon coupling models in a hybrid Rydberg atom setup
• Tuning excitation transport in a dissipative Rydberg ring
• Near-unity indistinguishability of single photons emitted from dissimilar and independent atomic quantum nodes
• Extended Bose-Hubbard models with Rydberg macrodimer dressing
• Finite-temperature Rydberg arrays: quantum phases and entanglement characterization
• Quantum annealing of Cayley-tree Ising spins at small scales
• Error-budgeting for a controlled-phase gate with strontium-88 Rydberg atoms
• Strong zero-field Förster resonances in K-Rb Rydberg systems
• Determination of Quantum Defects and Core Polarizability of Atomic Cesium via Terahertz and Radio-Frequency Spectroscopy in Thermal Vapor
• Two-atom van-der-Waals forces with one atom excited: the identical atoms limit I
• Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
• Unravelling the Structures in the van der Waals Interactions of Alkali Rydberg Atoms
• Rydberg wire gates for universal quantum computation
• $In$ $situ$ observation of non-polar to strongly polar atom-ion collision dynamics
• Internal diffraction dynamics of trilobite molecules
• Delocalization in two and three-dimensional Rydberg gases
• Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
• Multi-Qubit Parity Gates for Rydberg Atoms in Various Configurations
• Nonconservative dipole forces in a two-atom system with one atom excited
• Tunable two-species spin models with Rydberg atoms in circular and elliptical states
• Probing spin-motion coupling of two Rydberg atoms by a Stern-Gerlach-like experiment
• Impact of micromotion and field-axis misalignment on the excitation of Rydberg states of ions in a Paul trap
• High-fidelity multiqubit Rydberg gates via two-photon adiabatic rapid passage
• Detecting dark matter using optically trapped Rydberg atom tweezer arrays
• Quantum science with arrays of metastable helium-3 atoms
• Non-destructive optical read-out and manipulation of circular Rydberg atoms
• Algebraic law of local correlations in a driven Rydberg atomic system
• The Stark effect in molecular Rydberg states: Calculation of Rydberg-Stark manifolds of H${}_2$ and D${}_2$ including fine and hyperfine structures
• Quantifying the impact of state mixing on the Rydberg excitation blockade
• Double Supersolid Phase in a Bosonic t-J-V Model with Rydberg Atoms