arXiv:2005.13659 · Physical Review A

Rydberg spectrum of a single trapped Ca+ ion: A Floquet analysis

Mariusz Pawlak, H. R. Sadeghpour

Published May 18, 2020• 11 citations

Abstract

We compute the Rydberg spectrum of a single ${\mathrm{Ca}}^{+}$ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in ${\mathrm{Ca}}^{+}$, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for ${e}^{\ensuremath{-}}+{\mathrm{Ca}}^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of ${\mathrm{Ca}}^{+}(23P)$ and ${\mathrm{Ca}}^{+}(52F)$ Rydberg lines.

DOI: 10.1103/physreva.101.052510

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arXiv:2005.13659 · Physical Review A

Rydberg spectrum of a single trapped Ca+ ion: A Floquet analysis

Mariusz Pawlak, H. R. Sadeghpour

Published May 18, 2020• 11 citations

arXiv HTML PDF

Abstract

We compute the Rydberg spectrum of a single

{\mathrm{Ca}}^{+}

ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in

{\mathrm{Ca}}^{+}

, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for

{e}^{\ensuremath{-}}+{\mathrm{Ca}}^{2+}

, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of

{\mathrm{Ca}}^{+}(23P)

and

{\mathrm{Ca}}^{+}(52F)

Rydberg lines.

DOI: 10.1103/physreva.101.052510

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Markus Müller, Lin-Mei Liang, Igor Lesanovsky +1 more

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arXiv:0709.2849New Journal of PhysicsSep 10, 2008106 citations

We compute the Rydberg spectrum of a single

{\mathrm{Ca}}^{+}

ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in

{\mathrm{Ca}}^{+}

{e}^{\ensuremath{-}}+{\mathrm{Ca}}^{2+}

{\mathrm{Ca}}^{+}(23P)

and

{\mathrm{Ca}}^{+}(52F)

Rydberg lines.

^{40}

^+

ion from the motional ground state into coherent states with

|α|

up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D

_{5/2}

state, is excited to a Rydberg S

_{1/2}

-state via the 5P

_{3/2}

state in a two-photon process. We probe the depletion of the 3D

_{5/2}

state owing to the Rydberg excitation followed by a decay into the internal ground 4S

_{1/2}

state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is easy-to-implement and applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.