Peik and Tamm [Europhys. Lett. 61, 181 (2003)] proposed a nuclear clock based on the isomeric transition between the ground state and the first excited state of thorium-229. This transition was recognized as a potentially sensitive probe of possible temporal variation of the fine-structure constant, $α$. The sensitivity to such a variation can be determined from measurements of the mean-square charge radius and quadrupole moment of the different isomers. However, current measurements of the quadrupole moment are yet to achieve an accuracy high enough to resolve non-zero sensitivity. Here we determine this sensitivity using existing measurements of the change in the mean-square charge radius, coupled with the ansatz of constant nuclear density. The enhancement factor for $α$ variation is $K = -(0.82 \pm 0.25) \times 10^4$. For the current experimental limit, $δα/α\lesssim 10^{-17}$ per year, the corresponding frequency shift is $\sim\!200$ Hz per year. This shift is six orders of magnitude larger than the projected accuracy of the nuclear clock, paving the way for increased accuracy of the determination of $δα$ and interaction strength with low-mass scalar dark matter. We verify that the constant-nuclear-density ansatz is supported by nuclear theory and propose how to verify it experimentally. We also consider a possible effect of the octupole deformation on the sensitivity to $α$ variation, and calculate the effects of $α$ variation in a number of Mössbauer transitions.
The 7.6(5) eV nuclear magnetic-dipole transition in a single 229Th3+ ion may provide the foundation for an optical clock of superb accuracy. A virtual clock transition composed of stretched states within the 5F5/2 electronic ground level of both nuclear ground and isomeric manifolds is proposed. It is shown to offer unprecedented systematic shift suppression, allowing for clock performance with a total fractional inaccuracy approaching 1 x 10^-19.
The proposal for the development of a nuclear optical clock has triggered a multitude of experimental and theoretical studies. In particular the prediction of an unprecedented systematic frequency uncertainty of about $10^{-19}$ has rendered a nuclear clock an interesting tool for many applications, potentially even for a re-definition of the second. The focus of the corresponding research is a nuclear transition of the $^{229}$Th nucleus, which possesses a uniquely low nuclear excitation energy of only $8.12\pm0.11$ eV ($152.7\pm2.1$ nm). This energy is sufficiently low to allow for nuclear l…
We examine the effect of a parasitic rf magnetic field, attributed to ion trapping, on the highly anticipated nuclear clock based on $^{229}$Th$^{3+}$ [C. J. Campbell et al., Phys. Rev. Lett. 108, 120802 (2012)]. The rf magnetic field induces an ac Zeeman shift to the clock frequency. As we demonstrate, this shift threatens to be the dominant systematic frequency shift for the clock, exceeding other systematic frequency shifts and the projected systematic uncertainty of the clock by orders of magnitude. We propose practical means to suppress or eliminate this shift.
We consider the general class of theories in which there is a new ultralight scalar field that mediates an equivalence principle violating, long-range force. In such a framework, the sun and the earth act as sources of the scalar field, leading to potentially observable location dependent effects on atomic and nuclear spectra. We determine the sensitivity of current and next-generation atomic and nuclear clocks to these effects and compare the results against the existing laboratory and astrophysical constraints on equivalence principle violating fifth forces. We show that in the future, the a…
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 neutra…
Thorium-229 in its Highest Charge States: Single-Ion Nuclear Clocks for Tests of Fundamental Interactions
GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）；Helmholtz-Institut Jena（耶拿亥姆霍兹研究所）；Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学光学与量子电子学研究所）；Abbe Center of Photonics（阿贝光子学中心）；Deutsche Elektronen-Synchrotron DESY（德国电子同步辐射所DESY）；Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France（索邦大学卡斯勒-布罗塞尔实验室，法国国家科学研究中心，巴黎高等师范学院-PSL研究大学，法兰西学院）；Institut für Kernphysik, Universität zu Köln（科隆大学核物理研究所）
The low-energy, long-lived isomer in $^{229}$Th, first studied in the 1970s as an exotic feature in nuclear physics, continues to inspire a multidisciplinary community of physicists. Using the nuclear resonance frequency, determined by the strong and electromagnetic interactions inside the nucleus, it is possible to build a highly precise nuclear clock that will be fundamentally different from all other atomic clocks based on resonant frequencies of the electron shell. The nuclear clock will open opportunities for highly sensitive tests of fundamental principles of physics, particularly in sea…
Optical atomic clocks using highly-charged ions hold an intriguing promise of metrology at the 19th significant figure. Here we study transitions within the $4f^{12}$ ground-state electronic configuration of highly charged ions. We consider isotopes lacking hyperfine structure and show that the detrimental effects of coupling of electronic quadrupole moments to gradients of trapping electric field can be effectively reduced by using specially chosen virtual clock transitions. The estimated systematic fractional clock accuracy is shown to be below $10^{-19}$.
Investigation into thorium sulfate as a spinless crystal for a high-performance solid-state $^{229}Th$ nuclear clock
University of Manchester（曼彻斯特大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Nevada, Reno（内华达大学里诺分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
The 7.8 eV nuclear isomer transition in 229 Thorium has been suggested as an etalon transition in a new type of optical frequency standard. Here we discuss the construction of a "solid-state nuclear clock" from Thorium nuclei implanted into single crystals transparent in the vacuum ultraviolet range. We investigate crystal-induced line shifts and broadening effects for the specific system of Calcium fluoride. At liquid Nitrogen temperatures, the clock performance will be limited by decoherence due to magnetic coupling of the Thorium nucleus to neighboring nuclear moments, ruling out the common…
A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a non resonant radio-frequency field. For fermionic species as $^{87}$Sr, $^{171}$Yb, and $^{199}$Hg, particular ratios between the radiofrequency driving amplitude and frequency lead to "magic" magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first order magnetic variations are produced within a relative uncertainty below the $10^{-18}$ level. An Autler-Townes continued fraction describing a semi-classical radio-frequency dressed spin is numerically…
A thorium-229 optical nuclear clock with feedback loop
Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子研究所，维也纳工业大学）；Bundesamt für Eich- und Vermessungswesen (BEV)（奥地利联邦计量与测量局）；Wolfgang Pauli Institut（沃尔夫冈·泡利研究所）；Institut für Erdmessung, Leibniz Universität Hannover（汉诺威莱布尼茨大学大地测量研究所）；Institute of Scientific Instruments of the CAS, v.v.i.（中国科学院科学仪器研究所）；Physikalisch-Technische Bundesanstalt (PTB)（德国物理技术联邦研究院）；Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy（马克斯·玻恩非线性光学和超快光谱学研究所）
We review the ideas and concepts for a clock that is based on a radiative transition in the nucleus rather than in the electron shell. This type of clock offers advantages like an insensitivity against field-induced systematic frequency shifts and the opportunity to obtain high stability from interrogating many nuclei in the solid state. Experimental work concentrates on the low-energy (about 8 eV) isomeric transition in Th-229. We review the status of the experiments that aim at a direct optical observation of this transition and outline the plans for high-resolution laser spectroscopy experi…
Tsinghua University（清华大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；University of Chinese Academy of Sciences（中国科学院大学）
A new concept for narrow-band direct nuclear laser spectroscopy of $^{229\text{m}}$Th is proposed, using a single comb mode of a vacuum ultraviolet frequency comb generated from the 7th harmonic of an Yb-doped fiber laser system. In this concept more than $10^{14}$ $^{229}$Th atoms on a surface are irradiated in parallel and a successful nuclear excitation is probed via the internal-conversion (IC) decay channel. A net scanning time of 15 minutes for the most recent 1~$σ$ energy uncertainty interval of 0.34 eV appears to be achievable when searching for the nuclear transition. In case of succe…
The nucleus of 229Thorium presents a unique isomer state of very low energy and long lifetime, current estimates are around 7.8 eV and seconds to hours respectively. This nuclear transitions therefore is a promising candidate for a novel type of frequency standard and several groups worldwide have set out to investigate this system. Our aim is to construct a "solid state nuclear clock", i.e. a frequency standard where Thorium ions are implanted into Calciumfluoride crystals transparent in vacuum ultraviolet range. As a first step towards an accurate determination of the exact energy and lifeti…
Laser spectroscopy of the $^{\mathrm{229m}}$Th nuclear clock transition is necessary for the future construction of a nuclear-based optical clock. Precision laser sources with broad spectral coverage in the vacuum ultraviolet are needed for this task. Here, we present a tunable vacuum-ultraviolet frequency comb based on cavity-enhanced seventh-harmonic generation. Its tunable spectrum covers the current uncertainty range of the $^{\mathrm{229m}}$Th nuclear clock transition.
Probing Ultralight Dark Matter at the Mega-Planck Scale with the Thorium Nuclear Clock
University of Delaware（特拉华大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；JILA, NIST and University of Colorado（JILA、美国国家标准与技术研究院和科罗拉多大学）；University of Colorado（科罗拉多大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射研究所）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Physikalisch-Technische Bundesanstalt（德国物理技术联邦研究院）
Prospects for optical clocks combining high sensitivity to new physics with insensitivity to perturbations; the case of Sb$^{+}$, Au$^{+}$, and Hg$^{2+}$
The Dick effect can be a limitation of the achievable frequency stability of a passive atomic frequency standard when the ancillary frequency source is only periodically sampled. Here we analyze the Dick effect for a pulsed vapor cell clock using coherent population trapping (CPT). Due to its specific interrogation process without atomic preparation nor detection outside of the Ramsey pulses, it exhibits an original shape of the sensitivity function to phase noise of the oscillator. Numerical calculations using a three-level atom model are successfully compared with measurements; an approximat…
We demonstrate control of the differential Zeeman shift between clock states of ultracold rubidium atoms by means of non-resonant microwave dressing. Using the dc-field dependence of the microwave detuning, we suppress the first and second order differential Zeeman shift in magnetically trapped $^{87}$Rb atoms. By dressing the state pair 5S$_{1/2} F= 1, m_F = -1$ and $F= 2, m_F = 1$, a residual frequency spread of <0.1 Hz in a range of 100 mG around a chosen magnetic offset field can be achieved. This is one order of magnitude smaller than the shift of the bare states at the magic field of the…
Our calculations have shown that the 5f_5/2-7s_1/2 23131 cm^{-1} transition from the ground state in the ion Th^{3+} is very sensitive to the temporal variation of the fine structure constant alpha (q=-75300 cm^{-1}). The line is very narrow, the ion has been trapped and laser cooled and the positive shifter line 5f_5/2-5f_7/2 4325 cm^{-1} (q=+2900 cm^{-1}) may be used as a reference. A comparison may also be made with a positive shifter in another atom or ion. This makes Th^{3+} a good candidate to search for the alpha variation.
A solid-state nuclear clock based on VUV absorption spectroscopy of $^{229}$Th
Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理学院）
Compact and robust ion traps for thorium are enabling technology for the next generation of atomic clocks based on a low-energy isomeric transition in the thorium-229 nucleus. We aim at a laser ablation loading of single triply ionized thorium in a radio-frequency electromagnetic linear Paul trap. Detection of ions is based on a modified mass spectrometer and a channeltron with single-ion sensitivity. In this study, we successfully created and detected 232Th+ and 232Th2+ ions from plasma plumes, studied their yield evolution, and compared the loading to a quadrupole ion trap with Yb. We explor…
Quantum algorithms such as dynamical decoupling can be used to improve the sensitivity of a quantum sensor to a signal while suppressing sensitivity to noise. Atomic clocks are among the most sensitive quantum sensors, with recent improvements in clock technology allowing for unprecedented precision and accuracy. These clocks are highly sensitive to variations in fundamental constants, making them ideal probes for local ultralight scalar dark matter. Further improvements to the sensitivity is expected in proposed nuclear clocks based on the thorium 229m isomer. We investigate the use of variou…
Toward nanophotonic platforms for solid-state $^{229}$Th nuclear clocks
KU Leuven（荷语鲁汶大学）；Institute for Nuclear and Radiation Physics（核与辐射物理研究所）；Institute of Science and Technology Austria（奥地利科学技术研究所）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔兰根-纽伦堡弗里德里希·亚历山大大学）；Keio University（庆应义塾大学）；Ghent University（根特大学）
High accuracy measurements in Mössbauer transitions open up the possibility to use them in the search for temporal and spatial variation of the fine-structure constant $α$, quark mass $m_q$, and dark matter field which may lead to the variation of $α$ and $m_q$. We calculate the sensitivity of nuclear transitions to variation of $α$ and $m_q$. Mössbauer transitions have high sensitivity to variation of quark mass $m_q$ and the strong interaction scale $Λ_{QCD}$, to which atomic optical clocks are not sensitive. The enhancement factors $K$, defined by $\frac{δf}{f} =K_{α}\frac{δα}α$ and $\frac{…
Prediction of Nuclear Clock Transitions Frequency Difference between $^{229}$Th$^{3+}$ and $^{229}$Th$^{4+}$ via \textit{ab-initio} Self-Consistent Field Theory
We identify Ba$^{4+}$ (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a $^3P_J$ fine structure manifold with anomalous energy ordering, being non-monotonic in $J$. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground ($^3P_2$) and first-excited ($^3P_0$) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a sing…
The remarkable detection of a spatial variation in the fine-structure constant, alpha, from quasar absorption systems must be independently confirmed by complementary searches. In this letter, we discuss how terrestrial measurements of time-variation of the fundamental constants in the laboratory, meteorite data, and analysis of the Oklo nuclear reactor can be used to corroborate the spatial variation seen by astronomers. Furthermore, we show that spatial variation of the fundamental constants may be observable as spatial anisotropy in the cosmic microwave background, the accelerated expansion…
Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty demonstrating incredible control over external perturbations of the clock transition frequency. At the same time there is an increasing demand for atomic and ionic transitions with minimal sensitivity to external fields, with practical operational wavelengths and robust readout protocols. One of the goals is to simplify clock's operation maintaining its relative uncertainty at low 10-18 level. It is especially important for transportable and envisioned space-based optical clocks. We proved e…
