Multichannel quantum-defect theory for ultracold atom-ion collisions

Abstract

We develop an analytical model for ultracold atom-ion collisions using the multichannel quantum-defect formalism. The model is based on the analytical solutions of the r^-4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of the atom-ion interaction in the ultracold domain in terms of three parameters only: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40Ca+ ion and a Na atom, and compared to numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes, and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.

39 pages, 21 figures

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Cited by in corpus (54)

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• Quantum theory of reactive collisions for 1/r^n potentials
• Description of ion motion in a Paul trap immersed in a cold atomic gas
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• Trapping Ions and Atoms Optically
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• Quantum dynamics of an atomic double-well system interacting with a trapped ion
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• Impact of Many-Body Correlations on the Dynamics of an Ion-Controlled Bosonic Josephson Junction
• Spin-orbit interactions and quantum spin dynamics in cold ion-atom collisions
• Quantum defect model of a reactive collision at finite temperature
• Generalised Kronig-Penney model for ultracold atomic quantum systems
• Ab initio electronic structure and prospects for the formation of ultracold calcium--alkali-metal-atom molecular ions
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• Observation of trap-assisted formation of atom-ion bound states
• Confinement-Induced Resonances in Ultracold Atom-Ion Systems
• Ultracold magnetically tunable interactions without radiative charge transfer losses between Ca${}^{+}$, Sr${}^{+}$, Ba${}^{+}$, and Yb${}^{+}$ ions and Cr atoms
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• Quantum-defect theory of resonant charge exchange
• Unveiling shape resonances in H + HF collisions at cold energies
• Buffer gas cooling of ions in time-dependent traps using ultracold atoms
• Ultracold ion-atom experiments: cooling, chemistry, and quantum effects
• High-energy-resolution measurement of ultracold atom-ion collisional cross section
• Dynamics of a trapped ion in a quantum gas: effects of particle statistics
• Multiscale quantum-defect theory and its application to atomic spectrum
• Beyond universality: parametrizing ultracold complex-mediated reactions using statistical assumptions
• Ion-induced interactions in a Tomonaga-Luttinger liquid
• Charge transfer in ultracold gases via Feshbach resonances
• Quantum-State Controlled Penning Ionization Reactions between Ultracold Alkali and Metastable Helium Atoms
• Integral representation for scattering phase shifts via the phase-amplitude approach
• Laser controlled charge-transfer reaction at low temperatures
• Universal behaviour of diatomic halo states and the mass sensitivity of their properties
• Interactions and charge transfer dynamics of an Al${}^{+}$ ion immersed in ultracold Rb and Sr atoms
• Universal behavior in complex-mediated reactions: Dynamics of S(1D)+ o-D2 --> D + SD at low collision energies
• Two-body loss rates for reactive collisions of cold atoms
• Vibrational quenching of cold molecular ions immersed in their parent gas
• Bound states of an ultracold atom interacting with a set of stationary impurities
• Multichannel quantum defect theory with a frame transformation for ultracold atom-molecule collisions in magnetic fields
• Singularities of Floquet Scattering and Tunneling
• Ultracold collisions of a neutral atom with a trapped ion in 1D
• Adiabatic and post-adiabatic hyperspherical treatment of the huge ungerade proton-hydrogen scattering length
• Universality and threshold laws for collision lifetimes at ultralow temperatures
• Multichannel Quantum Defect Theory with Numerical Reference Functions: Applications to Cold Atomic Collisions