We report the first operation of a Ra$^{+}$ optical clock, a promising high-performance clock candidate. The clock uses a single trapped $^{226}$Ra$^{+}$ ion and operates on the $7s\ ^2S_{1/2}\rightarrow$ $6d\ ^2D_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1$\times10^{-13}$/$\sqrtτ$, where $τ$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be ${Δν/ ν= 9 \times 10^{-16}}$. Using the clock, we realize the first measurement of the ratio of the $D_{5/2}$ state to the $S_{1/2}$ state Landé $g$-factors: $g_{D}/g_{S}$ = 0.5988053(11). A Ra$^{+}$ optical clock could improve limits on the time variation of the fine structure constant, $\dot α/ α$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.
We explore the potential of the electric quadrupole transitions $7s\,^2S_{1/2}$ - $6d\,^2D_{3/2}$, $6d\,^2D_{5/2}$ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive $^A$Ra$^+$ candidates with $A=$ 223 - 229 are identified. In particular, we show that the transition $7s\,^2S_{1/2}\,(F=2,m_F=0)$ - $6d\,^2D_{3/2}\,(F=0,m_F=0)$ at 828 nm in $^{223}$Ra$^+$, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case…
The unstable radium nucleus is appealing for probing new physics due to its high mass, octupole deformation and energy level structure. Ion traps, with long hold times and low particle numbers, are excellent for work with radioactive species, such as radium and radium-based molecular ions, where low activity, and hence low total numbers, is desirable. We address the challenges associated with the lack of stable isotopes in a tabletop experiment with a low-activity ($\sim 10 \ μ\mathrm{Ci}$) source where we laser-cool trapped radium ions. With a laser-cooled radium ion we measured the $7p\ ^2P_…
Single trapped and laser cooled Radium ion as a possible candidate for measuring the parity violation induced frequency shift has been discussed here. Even though the technique to be used is similar to that proposed by Fortson [1], Radium has its own advantages and disadvantages. The most attractive part of Radium ion as compared to that of Barium ion is its mass which comes along with added complexity of instability as well as other issues which are discussed here
The diatomic molecule radium monofluoride (RaF) has recently been proposed as a versatile probe for physics beyond the current standard model. Herein, a route towards production of a RaF molecular beam via radium ions is proposed. It takes advantage of the special electronic structure expected for group 2 halides and group 2 hydrides: The electronic ground state of neutral RaF and its monocation differ in occupation of a non-bonding orbital of $σ$ symmetry. This implies similar equilibrium distances and harmonic vibrational wavenumbers in the two charge states and thus favourable Franck--Condo…
We demonstrate an improvement in short-term stability by a factor of 10 over a previous generation miniature buffer gas cooled trapped ion clock. We describe the enhancement to detection SNR that has enabled this improvement, the method of clock operation, and the measurement of clock short-term stability. Additionally, we numerically investigate the magnitude of the Dick effect in our pulsed ion clock.
We report a measurement of the radium ion's $7p\,\, ^2\!P_{3/2}$ state branching fractions and improved theoretical calculations. With a single laser-cooled $^{226}\mathrm{Ra}^+$ ion we measure the $P_{3/2}$ branching fractions to the $7s\,\,^2\!S_{1/2}$ ground state 0.87678(20), the $6d\,\,^2\!D_{5/2}$ state 0.10759(10), and the $6d$ ${}^{2}D_{3/2}$ state 0.01563(21).
We report on the first frequency ratio measurement of an $^{115}$In+ single ion clock and a $^{87}$Sr optical lattice clock. A hydrogen maser serves as a reference oscillator to measure the ratio by independent optical combs. Over more than 90 000 seconds of measurement time, the frequency ratio $f_{\rm{In^+}}/f_{\rm{Sr}}$ is determined to be 2.952 748 749 874 863 4(21) with relative uncertainty of $7.0 \times 10^{-16}$. The measurement creates a new connection in the network of frequency ratios of optical clocks.
Al$^+$ ions optical clock is a very promising optical frequency standard candidate due to its extremely small blackbody radiation shift. It has been successfully demonstrated with indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al$^+$ ions optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme, two Al$^+$ ions traps are utilized. …
We study the Ho$^{14+}$ ion as a candidate for extremely accurate and stable optical atomic clock which is sensitive to the time variation of the fine structure constant. We demonstrate that the proposed system has all desired features including relatively strong optical electric dipole and magnetic dipole transitions which can be used for cooling and detection. Zero quadrupole moments for the relevant states in the clock transition allows interrogating multiple ions to improve the clock stability.
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.
For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below $10^{-17}$, finding applications in fundamental physics tests, relativistic geodesy, and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network ha…
Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly-charged ions (HCIs) made HCIs accessible for high resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in the Cf$^{15+}$ and Cf$^{17+}$ ions. Using a high-accuracy relativistic method of calculation we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric …
We identify laser-accessible transitions in group 16-like highly charged ions as candidates for high-accuracy optical clocks, including S-, Se-, and Te-like systems. For this class of ions, the ground $^{3}P_{J}$ fine structure manifold exhibits irregular (nonmonotonic in $J$) energy ordering for large enough ionization degree. We consider the $|^3P_2\rangle \longleftrightarrow |^3P_0\rangle$ (ground to first-excited state) electric quadrupole transition, performing relativistic many-body calculations of several atomic properties important for optical clock development. All ions discussed are …
We review a number of highly charged ions which have optical transitions suitable for building extremely accurate atomic clocks. This includes ions from Hf$^{12+}$ to U$^{34+}$, which have the $4f^{12}$ configuration of valence electrons, the Ir$^{17+}$ ion, which has a hole in almost filled $4f$ subshell, the Ho$^{14+}$, Cf$^{15+}$, Es$^{17+}$ and Es$^{16+}$ ions. Clock transitions in most of these ions are sensitive to variation of the fine structure constant, $α$ ($α= e^2/\hbar c$). E.g., californium and einsteinium ions have largest known sensitivity to $α$-variation while holmium ion look…
Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a non-perturbative framework based on a quantum channel description of the scattering process, and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the Sr$^+$ optical atomic clock transition due to elastic collisions with helium.
We report frequency measurement of the clock transition in an 115In+ ion sympathetically-cooled with Ca+ ions in a linear rf trap. The Ca+ ions are used as a probe of the external electromagnetic field and as the coolant for preparing the cold In+. The frequency is determined to be 1 267 402 452 901 049.9 (6.9) Hz by averaging 36 measurements using an optical frequency comb referenced to the frequency standards located in the same site.
We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have $I=J=F=0$, where $I$, $J$, and $F$ are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation…
Future transportable optical clocks require compact and reliable light sources. Here, broadband, unpolarized repumper and state clearout sources for Sr+ single-ion optical clocks are reported. These turn-key devices require no frequency stabilization nor external modulators. They are fiber based, inexpensive, and compact. Key characteristics for clock operation are presented, including optical spectra, induced light shifts and required extinction ratios. Tests with an operating single-ion standard show a clearout efficiency of 100%. Compared to a laser-based repumper, the achievable fluorescen…
We evaluate the electric quadrupole moments of the ${^1}\!S_0$ and ${^3}\!P_0$ clock states of $^{27}$Al$^+$ and $^{115}$In$^+$. To capture all dominant contributions, our analysis extends through third order of perturbation theory and includes hyperfine coupling of the electrons to both the magnetic dipole and electric quadrupole moments of the nucleus. For $^{27}$Al$^+$, a fortuitous cancellation leads to a suppressed frequency shift. This should allow for continued improvement of the clock without special techniques to control or cancel the shift, such as the averaging schemes that are crit…
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）
We present an experiment to characterize our new linear ion trap designed for the operation of a many-ion optical clock using 115-In^+ as clock ions. For the characterization of the trap as well as the sympathetic cooling of the clock ions we use 172-Yb^+. The trap design has been derived from finite element method (FEM) calculations and a first prototype based on glass-reinforced thermoset laminates was built. This paper details on the trap manufacturing process and micromotion measurement. Excess micromotion is measured using photon-correlation spectroscopy with a resolution of 1.1nm in moti…
This paper reports the direct temperature determination of sympathetically cooled 113Cd+ ions with laser-cooled 24Mg+ in a linear Paul trap. The sympathetically cooled ion species distribute in the outer shell of the large ensembles, which contain up to 3.3E5 ions. With optimized parameters, the minimum temperature of the sympathetically cooled 113Cd+ ions was measured to be tens of mK. These results indicate promising performance for microwave atomic clocks. The second order Doppler frequency shift is two orders of magnitudes lower and the Dick effect is suppressed.
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…
We propose here a few selective highly charged ions (HCIs), namely Ni$^{12+}$ and Cu$^{13+}$, Pd$^{12+}$ and Ag$^{13+}$, that not only promise to be very high accurate optical clocks below $10^{-19}$ uncertainties, but also offer quality factors larger than $10^{15}$ and yet possess simple atomic structures for the experimental set-up. Moreover, these ions have strong optical magnetic-dipole (M1) transitions than the previously proposed HCI clocks. They can be used for the cooling and detection techniques. To demonstrate the projected fractional uncertainties below $10^{-19}$ level, we have es…
An active optical clock based on highly charged Nd$^{9+}$ ion is proposed for the first time. The clock can offer ultra-narrow linewidth at the $\upmu$Hz-level which is more than two-order of magnitude below the currently recorded laser linewidth. Operating at 605(90) nm superradiation lasing transition between the $5p^2~4f$ ground state and one of the long-lived $5p~4f^2$ excited state, the proposed active clock is inherently immune against the cavity noise which provides high stability. The clock serves as a sensitive probe with high sensitivity to variation of the fine-structure constant wi…
A transportable optical clock refer to the $4s^2S_{1/2}-3d^2D_{5/2}$ electric quadrupole transition at 729 nm of single $^{40}Ca^+$ trapped in mini Paul trap has been developed. The physical system of $^{40}Ca^+$ optical clock is re-engineered from a bulky and complex setup to an integration of two subsystems: a compact single ion unit including ion trapping and detection modules, and a compact laser unit including laser sources, beam distributor and frequency reference modules. Apart from the electronics, the whole equipment has been constructed within a volume of 0.54 $m^3$. The systematic f…
Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. These systems have enabled relative frequency uncertainties at a level of a few parts in $10^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as variation of fundamental constants, violation of the local Lorentz invariance, and forces beyond the Standard Model of Physics. In addition, novel clocks are driving the development of so…
Attempts are made to unify gravity with the other three fundamental forces of nature. As suggested by higher dimensional models, this unification may require space and time variation of some dimensionless fundamental constants. In this scenario, probing temporal variation of the electromagnetic fine structure constant ($α= \frac{e^2} {\hbar c}$) in low energy regimes at the cosmological time scale is of immense interest. Atomic clocks are ideal candidates for probing $α$ variation because their transition frequencies are measured to ultra-high precision accuracy. Since atomic transition freque…
We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of th…
We study ultranarrow $5s_{1/2}$ - $4f_{5/2}$ transitions in Nd$^{13+}$ and Sm$^{15+}$ and demonstrate that they lie in the optical region. The transitions are insensitive to external perturbations. At the same time they are sensitive to the variation of the fine structure constant $α$. The fractional accuracy of the frequency of the transitions can be smaller than $10^{-19}$, which may provide a basis for atomic clocks of superb accuracy. Sensitivity to the variation of $α$ approaches $10^{-20}$ per year.
We report sympathetic cooling of $^{113}$Cd$^+$ by laser-cooled $^{40}$Ca$^+$ in a linear Paul trap for microwave clocks. Long-term low-temperature confinement of $^{113}$Cd$^+$ ions was achieved. The temperature of these ions was measured at $90(10)$ mK, and the corresponding uncertainty arising from the second-order Doppler shifts was estimated to a level of $2\times10^{-17}$. Up to $4.2\times10^5$ Cd$^+$ ions were confined in the trap, and the confinement time constant was measured to be 84 hours. After three hours of confinement, there were still $10^5$ Cd$^+$ ions present, indicating that…
The microwave clock frequency of the $|5s~^2S_{1/2}, F=0,m_F=0 \rangle \leftrightarrow |5s~^2S_{1/2}, F=1,m_F=0 \rangle$ transition in the $^{113}$Cd$^+$ ion has been reported as 15199862855.0192(10) Hz [Opt. Lett. {\bf 40}, 4249 (2015)]. Fractional systematic due to the black-body radiation (BBR) shift ($β$) arising from the Stark effect in the above clock transition was used as $-1.1 \times 10^{-16}$ from our unpublished preliminary estimation. We present here a precise value as $β=-1.815(77) \times 10^{-16}$ by carrying out rigorous calculations of third-order polarizabilities of the hyperf…
We report direct measurements of the frequency ratio of the 642 THz ${}^2S_{1/2} (F=0)$--${}^2F_{7/2} (F=3)$ electric octupole transition in ${}^{171}\mathrm{Yb}^+$ and the 429 THz ${}^1S_0$--${}^3P_0$ transition in ${}^{87}\mathrm{Sr}$. A series of 107 measurements has been performed at the Physikalisch-Technische Bundesanstalt between December 2012 and October 2019. Long-term variations of the ratio are larger than expected from the individual measurement uncertainties of few $10^{-17}$. The cause of these variations remains unknown. Even taking these into account, we find a fractional uncer…
We report the first driving of the $7s\ ^2S_{1/2}\rightarrow 6d\ ^2D_{3/2}$ and $7s\ ^2S_{1/2}\rightarrow 6d\ ^2D_{5/2}$ electric quadrupole (E2) transitions in Ra$^{+}$. We measure the frequencies of both E2 transitions, and two other low-lying transitions in $^{226}$Ra$^{+}$ that are important for controlling the radium ion's motional and internal states: $6d\ ^2D_{3/2}\rightarrow 7p\ ^2P_{3/2}^{0}$ and $6d\ ^2D_{5/2}\rightarrow 7p\ ^2P_{3/2}^{0}$.
This dissertation reports on the development of a low-power, high-stability miniature atomic frequency standard based on 171Yb+ ions. The ions are buffer-gas cooled and held in a linear quadrupole trap that is integrated into a sealed, getter-pumped vacuum package, and interrogated on the 12.6 GHz hyperfine transition. We hope to achieve a long-term fractional frequency stability of 10^-14 with a miniature clock that consumes only 50 mW of power and occupies a volume of 5 cm^3. I discuss our progress over several years of work on this project. We began by building a conventional tabletop clock…
We present additional magic wavelengths ($λ_{\rm{magic}}$) for the clock transitions in the alkaline-earth metal ions considering circular polarized light aside from our previously reported values in [J. Kaur et al., Phys. Rev. A {\bf 92}, 031402(R) (2015)] for the linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities ($α_d(ω)$) of the atomic states associated with the clock transitions play major roles in the evaluation of these $λ_{\rm{magic}}$, hence facilitating in choosing circular polarization of lasers in the experiments. Moreover, the …
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 $^{27}$Al$^+$ clock to enable a total fractional systematic uncertainty below $10^{-18}$. For this clock, with 38(19) nPa of room temperature H$_2$ 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 cont…
Quantum-logic-based ${}^{27}\textrm{Al}^+$ optical clock has been demonstrated in several schemes as there are different choices of the auxiliary ion species. In this paper, we present the first detailed evaluation of the systematic shift and the total uncertainty of an ${}^{27}\textrm{Al}^+$ optical clock sympathetically cooled by a ${}^{40}\textrm{Ca}^+$ ion. The total systematic uncertainty of the ${}^{40}\textrm{Ca}^+ - {}^{27}\textrm{Al}^+$ quantum logic clock has been estimated to be $7.9 \times 10^{-18}$, which was mainly limited by the uncertainty of the quadratic Zeeman shift. By comp…
We demonstrate that several metastable excited states in Hf$~$II, Hf$~$IV and W$~$VI ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. Cooling E1 transitions are available. Energy levels, Landé $g$-factors, transition amplitudes for electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transitions, lifetimes, and electric quadrupole moments for Hf$~$II, Hf$~$IV, and W$~$VI ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (…
We report a direct measurement of the $7s\ ^2S_{1/2}\rightarrow$ $7p\ ^2P_{3/2}$ electric dipole transition frequency in $^{226}$Ra$^{+}$. With a single laser-cooled radium ion we determine the transition frequency to be 785722.11(3) GHz by directly driving the transition with frequency-doubled light and measuring the frequency of the undoubled light with an iodine reference. This measurement addresses a discrepancy of five combined standard deviations between previously reported values.
We demonstrate experimentally the existence of magic wavelengths and determine the ratio of the oscillator strengths for a single trapped ion. For the first time, two magic wavelengths for the 40Ca+ clock-transition are measured simultaneously with high precision, giving Lamda|mj|=1/2 = 395.7992(7) nm and Lamda|mj|=3/2 = 395.7990(7) nm. By tuning a laser to an intermediate wavelength between two transitions (4s1/2-4p1/2 and 4s1/2-4p3/2) of 40Ca+, the sensitivity of the clock transition Stark shift to the oscillator strengths for the resonance transition has been greatly enhanced. With the meas…
We describe an optical atomic clock based on quantum-logic spectroscopy of the $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ transition in $^{27}$Al$^{+}$ with a systematic uncertainty of ${9.4 \times 10^{-19}}$ and a frequency stability of ${1.2\times10^{-15}/\sqrtτ}$. 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. Op…
