New Methods for Testing Lorentz Invariance with Atomic Systems

Observation of an Inner-Shell Orbital Clock Transition in Neutral Ytterbium Atoms

We observe a weakly allowed optical transition of atomic ytterbium from the ground state to the metastable state 4f^{13}5d6s^{2} (J=2) for all five bosonic and two fermionic isotopes with resolved Zeeman and hyperfine structures. This inner-shell orbital transition has been proposed as a new frequency standard as well as a quantum sensor for new physics. We find magic wavelengths through the measurement of the scalar and tensor polarizabilities and reveal that the measured trap lifetime in a three-dimensional optical lattice is 1.9(1) s, which is crucial for precision measurements. We also determine the g factor by an interleaved measurement, consistent with our relativistic atomic calculation. This work opens the possibility of an optical lattice clock with improved stability and accuracy as well as novel approaches for physics beyond the standard model.

A fully fiber-integrated ion trap for portable quantum technologies

Trapped ions are a promising platform for the deployment of quantum technologies. However, traditional ion trap experiments tend to be bulky and environment-sensitive due to the use of free-space optics. Here we present a single-ion trap with integrated optical fibers directly embedded within the trap structure, to deliver laser light as well as to collect the ion's fluorescence. This eliminates the need for optical windows. We characterise the system's performance and measure the ion's fluorescence with signal-to-background ratios on the order of 50, which allows us to perform internal state readout measurements with a fidelity over 99% in 600 [Formula: see text]s. We test the system's resilience to thermal variations in the range between 22 and 53 [Formula: see text]C, and the system's vibration resilience at 34 Hz and 300 Hz and find no effect on its performance. The combination of compactness and robustness of our fiber-coupled trap makes it well suited for applications in, as well as outside, research laboratory environments, and in particular for highly compact portable quantum technologies, such as portable optical atomic clocks. While our system is designed for trapping ⁴⁰Ca⁺ ions the fundamental design principles can be applied to other ion species.

Improved bounds on Lorentz violation from composite pulse Ramsey spectroscopy in a trapped ion

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

Special Issue Editorial: “Symmetry and Geometry in Physics”

Nature organizes itself using the language of symmetries [...]

Coherent Excitation of the Highly Forbidden Electric Octupole Transition in ^{172}Yb^{+}

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^{+}.

A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement

A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature (m, 3) for all m ≥ 2. The resulting enriched special relativity provides the common symmetry group SO(1, 3) of the (1 + 3)-dimensional spacetime of individual particles, along with the symmetry group SO(m, 3) of the (m + 3)-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all m ≥ 2. A unified parametrization of the Lorentz groups SO(m, n) for all m, n ∈ N, shakes down the underlying matrix algebra into elegant and transparent results. The special case when (m, n) = (1, 3) is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when (m, n) = (m, 3) for all m ≥ 2.

Detection of the 5p - 4f orbital crossing and its optical clock transition in Pr9

Recent theoretical works have proposed atomic clocks based on narrow optical transitions in highly charged ions. The most interesting candidates for searches of physics beyond the Standard Model are those which occur at rare orbital crossings where the shell structure of the periodic table is reordered. There are only three such crossings expected to be accessible in highly charged ions, and hitherto none have been observed as both experiment and theory have proven difficult. In this work we observe an orbital crossing in a system chosen to be tractable from both sides: Pr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{9+}$$\end{document}9+. We present electron beam ion trap measurements of its spectra, including the inter-configuration lines that reveal the sought-after crossing. With state-of-the-art calculations we show that the proposed nHz-wide clock line has a very high sensitivity to variation of the fine-structure constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}α, and violation of local Lorentz invariance; and has extremely low sensitivity to external perturbations.

Atomic clocks are based on the frequency of optical transitions and offer high precision. Here the authors demonstrate a configuration crossing in the highly charged ion praseodymium (Pr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{9+}$$\end{document}9+) and determine the frequency of a potential reference transition for a highly charged ion clock.

Inner-shell clock transition in atomic thulium with a small blackbody radiation shift

One of the key systematic effects limiting the performance of state-of-the-art optical clocks is the blackbody radiation (BBR) shift. Here, we demonstrate unusually low sensitivity of a 1.14 μm inner-shell clock transition in neutral Tm atoms to BBR. By direct polarizability measurements, we infer a differential polarizability of the clock levels of -0.063(30) atomic units corresponding to a fractional frequency BBR shift of only 2.3(1.1) × 10^-18 at room temperature. This amount is several orders of magnitude smaller than that of the best optical clocks using neutral atoms (Sr, Yb, Hg) and is competitive with that of ion optical clocks (Al⁺, Lu⁺). Our results allow the development of lanthanide-based optical clocks with a relative uncertainty at the 10^-17 level.

Improved Test of Local Lorentz Invariance from a Deterministic Preparation of Entangled States

The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using ^{40}Ca^{+} ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe, for bipartite entangled states, the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using ^{40}Ca^{+} ions by a factor of two to four to about 5×10^{-19}.

Two Clock Transitions in Neutral Yb for the Highest Sensitivity to Variations of the Fine-Structure Constant

We propose a new frequency standard based on a 4f^{14}6s6p ^{3}P_{0}-4f^{13}6s^{2}5d (J=2) transition in neutral Yb. This transition has a potential for high stability and accuracy and the advantage of the highest sensitivity among atomic clocks to variation of the fine-structure constant α. We find its dimensionless α-variation enhancement factor to be K=-15, in comparison to the most sensitive current clock (Yb^{+}  E3, K=-6), and it is 18 times larger than in any neutral-atomic clocks (Hg, K=0.8). Combined with the unprecedented stability of an optical lattice clock for neutral atoms, this high sensitivity opens new perspectives for searches for ultralight dark matter and for tests of theories beyond the standard model of elementary particles. Moreover, together with the well-established ^{1}S_{0}-^{3}P_{0} transition, one will have two clock transitions operating in neutral Yb, whose interleaved interrogations may further reduce systematic uncertainties of such clock-comparison experiments.