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 searches for violations of Einstein's equivalence principle and for new particles and interactions beyond the standard model. It has been proposed to use the nuclear clock to search for variations of the electromagnetic and strong coupling constants and for dark matter searches.
The $^{229}$Th nuclear optical clock still represents a major challenge in view of the tremendous gap of nearly 17 orders of magnitude between the present uncertainty in the nuclear transition frequency and the natural linewidth. Significant experimental progress has been achieved in recent years, which will be briefly reviewed. Moreover, a research strategy will be outlined to consolidate our present knowledge about essential $^{229\rm{m}}$Th properties, to determine the nuclear transition frequency with laser spectroscopic precision, realize different types of nuclear clocks and apply them in precision frequency comparisons with optical atomic clocks to test fundamental physics. Two avenues will be discussed: laser-cooled trapped $^{229}$Th ions that allow experiments with complete control on the nucleus-electron interaction and minimal systematic frequency shifts, and Th-doped solids enabling experiments at high particle number and in different electronic environments.
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 $10^{-19}$.
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 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 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.
The quantum clock synchronization algorithm proposed by I. L. Chuang (Phys. Rev. Lett, 85, 2006(2000)) has been implemented in a three qubit nuclear magnetic resonance quantum system. The effective-pure state is prepared by the spatial averaging approach. The time difference between two separated clocks can be determined by reading out directly through the NMR spectra.
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…
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）
We discuss perspectives for new tests of general relativity which are based on recent technological developments as well as new ideas. We focus our attention on tests performed with atomic clocks and do not repeat arguments present in the other contributions to the present volume. In particular, we present the scientific motivations of the space projects ACES and SAGAS.
The ability to design quantum systems that decouple from environmental noise sources is highly desirable for development of quantum technologies with optimal coherence. The chemical tunability of electronic states in magnetic molecules combined with advanced electron spin resonance techniques provides excellent opportunities to address this problem. Indeed, so-called clock transitions (CTs) have been shown to protect molecular spin qubits from magnetic noise, giving rise to significantly enhanced coherence. Here we conduct a spectroscopic and computational investigation of this physics, focusi…
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…
A First Bound on the Moffat Energy and Thorium-229 Clock as a Probe of the Nonlocal Time-Energy Structure and a Proposed Experiment for the use of Nuclear Entanglement and Squeezed States to Test Nonlocal Quantum Field Theory
Wilfrid Laurier University（韦仕兰大学）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（基础物理研究所）
Origin of the inhomogeneous linewidth in a solid state $^{229}$Th:CaF$_2$ nuclear clock
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）；Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系）；Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系与量子物质理论中心）；Institute for Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）；Institute for Atomic and Subatomic Physics, TU Wien（维也纳工业大学原子与亚原子物理研究所）；Departments of Applied Physics and Physics, Yale University（耶鲁大学应用物理系与物理系）；Yale Quantum Institute, Yale University（耶鲁大学耶鲁量子研究所）
We report the existence of a sizeable quantum tunnelling splitting between the two lowest electronic spin levels of mononuclear Ni complexes. The level anti-crossing, or magnetic clock transition, associated with this gap has been directly monitored by heat capacity experiments. The comparison of these results with those obtained for a Co derivative, for which tunnelling is forbidden by symmetry, shows that the clock transition leads to an effective suppression of intermolecular spin-spin interactions. In addition, we show that the quantum tunnelling splitting admits a chemical tuning via the …
Whether a quantum bath can be approximated as classical noise is a fundamental issue in central spin decoherence and also of practical importance in designing noise-resilient quantum control. Spin qubits based on bismuth donors in silicon have tunable interactions with nuclear spin baths and are first-order insensitive to magnetic noise at so-called clock-transitions (CTs). This system is therefore ideal for studying the quantum/classical nature of nuclear spin baths since the qubit-bath interaction strength determines the back-action on the baths and hence the adequacy of a classical noise mo…
We observe two-body loss of ${}^3P_0$ ${}^{87}$Sr atoms trapped in a one-dimensional optical lattice. We measure loss rate coefficients for atomic samples between 1 and 6 $μ$K that are prepared either in a single nuclear-spin-sublevel or with equal populations in two sublevels. The measured temperature and nuclear spin preparation dependence of rate coefficients agree well with calculations and reveal that rate coefficients for distinguishable atoms are only slightly enhanced over those of indistinguishable atoms. We further observe a suppression of excitation and losses during interrogation o…
Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift (or universality of clock rates). Considering the atom as a clock operating at the Compton frequency associated…
We investigated the feasibility of quantum-correlation measurements in nuclear physics experiments. In a first approach, we measured spin correlations of singlet-spin (1S0) proton pairs, which were generated in 1H(d,2He) and 12C(d,2He) nuclear charge-exchange reactions. The experiment was optimized for a clean preparation of the 2He singlet state and offered a 2pi detection geometry for both protons in the exit channel. Our results confirm the effectiveness of the setup for theses studies, despite limitations of a small data sample recorded during the feasibility studies.
Optically addressable paramagnetic defects in wide-band-gap semiconductors are promising platforms for quantum communications and sensing. The presence of avoided crossings between the electronic levels of these defects can substantially alter their quantum dynamics and be both detrimental and beneficial for quantum information applications. Avoided crossings give rise to clock transitions, which can significantly improve protection from magnetic noise and favorably increase coherence time. However, the reduced coupling between electronic and nuclear spins at an avoided crossing may be detrime…
The clock transitions (CTs) of central spins have long coherence times because their frequency fluctuations vanish in the linear order of external field noise (such as Overhauser fields from nuclear spin baths). Therefore, CTs are useful for quantum technologies. Also, the quadratic dependence of frequencies on noises makes the CT decoherence an interesting physics problem. Thus we are motivated to study the decoherence of CTs. We consider noise from spin baths, which is one of the most relevant mechanisms of qubit decoherence. Various quantum many-body methods have been developed to study the…
