Abstract
Most ions 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$^{+}$-Ar$^{13+}$ 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 $T\lesssim200~\mathrm{\mu K}$ in each of the two modes, corresponding to a residual mean motional phonon number of $\langle n \rangle \lesssim 0.4$. Combined with the lowest observed electric field noise in a radiofrequency 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.
Highlights
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 Beþ-Ar13þ mixed Coulomb crystal close to their zero-point energies, despite the weak coupling between the ions
In conjunction with the ground-state cooling of the axial modes of the crystal, this is the coldest highly charged ions (HCI) prepared in a laboratory far
The technique demonstrated here is very general and could be applied to a plethora of ions that cannot be directly laser cooled and would have an unavoidably large charge-to-mass ratio mismatch with their cooling ion, as is the case forprotons [43,44], highly charged ions [11,12,17], and trapped charged macroscopic particles, such as nanospheres [45–47], graphene [48,49], or nanodiamonds [50,51]
Summary
Laser cooling has ushered in a new era of spectroscopic precision and accuracy. Atoms and ions can be brought practically to rest, greatly suppressing Doppler broadening and shifts. The required strong, cycling electronic transitions in the laser-accessible range only exist in a few species, which rendered a large number of interesting particles inaccessible to precision spectroscopy This limitation can be overcome using so-called sympathetic cooling, whereby a second ion, referred to as the “cooling ion” (or “logic ion,” depending on the application), is confined in the same trap together with the ion of interest, referred to as the “spectroscopy ion” or “computing ion.”. The control and manipulation of these modes via the cooling ion (e.g., for sideband cooling or thermometry) is challenging As such, these modes were expected to pose limitations to quantum protocols [16] and achievable spectroscopic accuracy [17]. We demonstrate the technique by cooling weakly coupled motional modes of a trapped, sympathetically cooled highly charged ion. Cooled systems with mismatched charge-to-mass ratios between the particles
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