Erratum: ^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18} [Phys. Rev. Lett. 123, 033201 (2019)]

This corrects the article DOI: 10.1103/PhysRevLett.123.033201.

Frequency-comb spectroscopy on pure quantum states of a single molecular ion

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state nondestructively, leaving the molecule ready for further manipulation. We can resolve rotational transitions to 11 significant digits and derive the rotational constant of 40CaH+ to be B R = 142 501 777.9(1.7) kilohertz. Our approach is suited for a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ²⁷Al⁺ clock to enable a total fractional systematic uncertainty below 10^-18. For this clock, with 38(19) nPa of room-temperature H₂ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10^-16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10^-19, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ±π/2 bound used for collisional phase shift of the ²⁷Al⁺ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18}

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.

An open source digital servo for atomic, molecular, and optical physics experiments

We describe a general purpose digital servo optimized for feedback control of lasers in atomic, molecular, and optical physics experiments. The servo is capable of feedback bandwidths up to roughly 1 MHz (limited by the 320 ns total latency); loop filter shapes up to fifth order; multiple-input, multiple-output control; and automatic lock acquisition. The configuration of the servo is controlled via a graphical user interface, which also provides a rudimentary software oscilloscope and tools for measurement of system transfer functions. We illustrate the functionality of the digital servo by describing its use in two example scenarios: frequency control of the laser used to probe the narrow clock transition of (27)Al(+) in an optical atomic clock, and length control of a cavity used for resonant frequency doubling of a laser.

Trapped-ion state detection through coherent motion

We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a spectroscopy ion (27Al+) to a control ion (25Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish clock states in 27Al+, which avoids ground-state cooling and sideband transitions. The second method reduces spontaneous emission and optical pumping on the spectroscopy ion, which we demonstrate by nondestructively distinguishing Zeeman sublevels in the (1)S0 ground state of 27Al+.

Ion crystal transducer for strong coupling between single ions and single photons

A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed.