Bichromatic UV detection system for atomically-resolved imaging of ions.

We present a compact bichromatic imaging system, located outside of the vacuum chamber of a trapped ion apparatus that collects the fluorescence of 230.6 and 369.5 nm photons simultaneously on a shared electron-multiplying charge-coupled device (EMCCD) camera. The system contains two lens doublets, consisting of a sphere and an asphere. They provide a numerical aperture of 0.45 and 0.40 at 230.6 and 369.5 nm, respectively, and enable spatially resolved state detection with a large field of view of 300 µm for long 115In+/172Yb+ Coulomb crystals. Instead of diffraction-limited imaging for one wavelength, the focus in this system is on simultaneous single-ion resolved imaging of both species over a large field, with special attention to the deep UV wavelength (230.6 nm) and the low scattering rate of In+ ions. The introduced concept is applicable to other dual-species applications.

Evaluation of a

We report on an evaluation of an optical clock that uses the ^{2}S_{1/2}→^{2}D_{5/2} transition of a single ^{88}Sr^{+} ion as the reference. In contrast to previous work, we estimate the effective temperature of the blackbody radiation that shifts the reference transition directly during operation from the corresponding frequency shift and the well-characterized sensitivity to thermal radiation. We measure the clock output frequency against an independent ^{171}Yb^{+} ion clock, based on the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition, and determine the frequency ratio with a total fractional uncertainty of 2.3×10^{-17}. Relying on a previous measurement of the ^{171}Yb^{+} (E3) clock frequency, we find the absolute frequency of the ^{88}Sr^{+} clock transition to be 444 779 044 095 485.277(59) Hz. Our result reduces the uncertainty by a factor of 3 compared with the previously most accurate measurement and may help to resolve so far inconsistent determinations of this value. We also show that for three simultaneously interrogated ^{88}Sr^{+} ions, the increased number causes the expected improvement of the short-term frequency instability of the optical clock without degrading its systematic uncertainty.

Erratum: Coherent Excitation of the Highly Forbidden Electric Octupole Transition in

This corrects the article DOI: 10.1103/PhysRevLett.125.163001.

Sub-kelvin temperature management in ion traps for optical clocks.

The uncertainty of the ac Stark shift due to thermal radiation represents a major contribution to the systematic uncertainty budget of state-of-the-art optical atomic clocks. In the case of optical clocks based on trapped ions, the thermal behavior of the rf-driven ion trap must be precisely known. This determination is even more difficult when scalable linear ion traps are used. Such traps enable a more advanced control of multiple ions and have become a platform for new applications in quantum metrology, simulation, and computation. Nevertheless, their complex structure makes it more difficult to precisely determine its temperature in operation and thus the related systematic uncertainty. We present here scalable linear ion traps for optical clocks, which exhibit very low temperature rise under operation. We use a finite-element model refined with experimental measurements to determine the thermal distribution in the ion trap and the temperature at the position of the ions. The trap temperature is investigated at different rf-drive frequencies and amplitudes with an infrared camera and integrated temperature sensors. We show that for typical trapping parameters for In+, Al+, Lu+, Ca+, Sr+, or Yb+ ions, the temperature rise at the position of the ions resulting from rf heating of the trap stays below 700 mK and can be controlled with an uncertainty on the order of a few 100 mK maximum. The corresponding uncertainty of the trap-related blackbody radiation shift is in the low 10-19 and even 10-20 regime for 171Yb+(E3) and 115In+, respectively.

Coherent Excitation of the Highly Forbidden Electric Octupole Transition in

We report on the first coherent excitation of the highly forbidden ^{2}S_{1/2}→^{2}F_{7/2} electric octupole (E3) transition in a single trapped ^{172}Yb^{+} ion, an isotope without nuclear spin. Using the transition in ^{171}Yb^{+} as a reference, we determine the transition frequency to be 642 116 784 950 887.6(2.4) Hz. We map out the magnetic field environment using the forbidden ^{2}S_{1/2}→^{2}D_{5/2} electric quadrupole (E2) transition and determine its frequency to be 729 476 867 027 206.8(4.4) Hz. Our results are a factor of 1×10^{5} (3×10^{5}) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable ^{2}F_{7/2} state of Yb^{+}.

Towards a transportable aluminium ion quantum logic optical clock.

With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10-17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of 40Ca+. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40Ca+ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27Al+, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for 27Al+ has been determined to be δνEMMν=-0.4-0.3 +0.4×10-18 and the black-body radiation shift is δνBBR/ν = (-4.0 ± 0.4) × 10-18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ωrad,Ca+ ≈ 2π × 2.5 MHz (ωax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.

Probing nanofriction and Aubry-type signatures in a finite self-organized system.

Friction in ordered atomistic layers plays a central role in various nanoscale systems ranging from nanomachines to biological systems. It governs transport properties, wear and dissipation. Defects and incommensurate lattice constants markedly change these properties. Recently, experimental systems have become accessible to probe the dynamics of nanofriction. Here, we present a model system consisting of laser-cooled ions in which nanofriction and transport processes in self-organized systems with back action can be studied with atomic resolution. We show that in a system with local defects resulting in incommensurate layers, there is a transition from sticking to sliding with Aubry-type signatures. We demonstrate spectroscopic measurements of the soft vibrational mode driving this transition and a measurement of the order parameter. We show numerically that both exhibit critical scaling near the transition point. Our studies demonstrate a simple, well-controlled system in which friction in self-organized structures can be studied from classical- to quantum-regimes.

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals.

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble-Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.

Atomic clocks with suppressed blackbody radiation shift.

We develop a concept of atomic clocks where the blackbody radiation shift and its fluctuations can be suppressed by 1-3 orders of magnitude independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies ν1 and ν2) which are exposed to the same thermal environment, there exists a "synthetic" frequency ν(syn) ∝ (ν1 - ε12ν2) largely immune to the blackbody radiation shift. For example, in the case of 171Yb+ it is possible to create a synthetic-frequency-based clock in which the fractional blackbody radiation shift can be suppressed to the level of 10(-18) in a broad interval near room temperature (300±15 K). We also propose a realization of our method with the use of an optical frequency comb generator stabilized to both frequencies ν1 and ν2, where the frequency ν(syn) is generated as one of the components of the comb spectrum.

Doppler cooling and trapping on forbidden transitions.

Ultracold atoms at temperatures close to the recoil limit have been achieved by extending Doppler cooling to forbidden transitions. A cloud of (40)Ca atoms has been cooled and trapped to a temperature as low as 6 microK by operating a magnetooptical trap on the spin-forbidden intercombination transition. Quenching the long-lived excited state with an additional laser enhanced the scattering rate by a factor of 15, while a high selectivity in velocity was preserved. With this method, more than 10% of precooled atoms from a standard magnetooptical trap have been transferred to the ultracold trap. Monte Carlo simulations of the cooling process are in good agreement with the experiments.