TY - JOUR

T1 - Algorithmic Ground-State Cooling of Weakly Coupled Oscillators Using Quantum Logic

AU - King, Steven A.

AU - Spieß, Lukas J.

AU - Micke, Peter

AU - Wilzewski, Alexander

AU - Leopold, Tobias

AU - López-Urrutia, José R. Crespo

AU - Schmidt, Piet O.

N1 - Funding information: The authors would like to thank Erik Benkler and Thomas Legero for their contributions to the frequency stabilization of the HCI spectroscopy laser, Giorgio Zarantonello for fruitful discussions, and Ludwig Krinner for helpful comments on the manuscript. The project was supported by the Physikalisch-Technische Bundesanstalt, the Max-Planck Society, the Max-Planck–Riken–PTB–Center for Time, Constants and Fundamental Symmetries, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SCHM2678/5-1, the collaborative research centers SFB 1225 ISOQUANT and SFB 1227 DQ-mat, and under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967. This project 17FUN07 CC4C has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. S. A. K. acknowledges financial support from the Alexander von Humboldt Foundation.

PY - 2021/12/10

Y1 - 2021/12/10

N2 - The majority of ions and other charged particles of spectroscopic interest lack the fast, cycling transitions that are necessary for direct laser cooling. In most cases, they can still be cooled sympathetically through their Coulomb interaction with a second, coolable ion species confined in the same potential. If the charge-to-mass ratios of the two ion types are too mismatched, the cooling of certain motional degrees of freedom becomes difficult. This limits both the achievable fidelity of quantum gates and the spectroscopic accuracy. Here, we introduce a novel algorithmic cooling protocol for transferring phonons from poorly to efficiently cooled modes. We demonstrate it experimentally by simultaneously bringing two motional modes of a Be+−Ar13+ mixed Coulomb crystal close to their zero-point energies, despite the weak coupling between the ions. We reach the lowest temperature reported for a highly charged ion, with a residual temperature of only T≲200  μK in each of the two modes, corresponding to a residual mean motional phonon number of ⟨n⟩≲0.4. Combined with the lowest observed electric-field noise in a radio-frequency ion trap, these values enable an optical clock based on a highly charged ion with fractional systematic uncertainty below the 10−18 level. Our scheme is also applicable to (anti)protons, molecular ions, macroscopic charged particles, and other highly charged ion species, enabling reliable preparation of their motional quantum ground states in traps.

AB - The majority of ions and other charged particles of spectroscopic interest lack the fast, cycling transitions that are necessary for direct laser cooling. In most cases, they can still be cooled sympathetically through their Coulomb interaction with a second, coolable ion species confined in the same potential. If the charge-to-mass ratios of the two ion types are too mismatched, the cooling of certain motional degrees of freedom becomes difficult. This limits both the achievable fidelity of quantum gates and the spectroscopic accuracy. Here, we introduce a novel algorithmic cooling protocol for transferring phonons from poorly to efficiently cooled modes. We demonstrate it experimentally by simultaneously bringing two motional modes of a Be+−Ar13+ mixed Coulomb crystal close to their zero-point energies, despite the weak coupling between the ions. We reach the lowest temperature reported for a highly charged ion, with a residual temperature of only T≲200  μK in each of the two modes, corresponding to a residual mean motional phonon number of ⟨n⟩≲0.4. Combined with the lowest observed electric-field noise in a radio-frequency ion trap, these values enable an optical clock based on a highly charged ion with fractional systematic uncertainty below the 10−18 level. Our scheme is also applicable to (anti)protons, molecular ions, macroscopic charged particles, and other highly charged ion species, enabling reliable preparation of their motional quantum ground states in traps.

KW - physics.atom-ph

KW - quant-ph

UR - http://www.scopus.com/inward/record.url?scp=85122499027&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2102.12427

DO - 10.48550/arXiv.2102.12427

M3 - Article

VL - 11

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 4

M1 - 041049

ER -