Clock Transition Research Articles

Diode-pumped visible lasing in femtosecond-laser-written Pr:LiLuF4 waveguide.

In this Letter we report the realization of a femtosecond-laser-written diode-pumped Pr:LiLuF4 visible waveguide laser. The waveguide studied in this work consisted of a depressed-index cladding, whose design and fabrication were optimized to minimize the propagation loss. Laser emission has been achieved at 604 nm and 721 nm, with output power of 86 mW and 60 mW, respectively, and slope efficiencies of 16% and 14%. In addition, we obtained, for the first time in a praseodymium-based waveguide laser, stable continuous-wave laser operation at 698 nm (3 mW of output power and 0.46% of slope efficiency), corresponding to the wavelength necessary for the clock transition of the strontium-based atomic clock. The waveguide laser emission at this wavelength is mainly in the fundamental mode (i.e., the larger propagation constant mode) showing a nearly Gaussian intensity profile.

Suppressed electric quadrupole moment of thulium atomic clock states

A method for highly accurate calculations of atomic electric quadrupole moments (EQM) is presented, using relativistic general-excitation-rank configuration interaction wave functions based on Dirac spinors. Application to the clock transition states of the thulium atom employing up to full Quadruple excitations for the atomic wave function yields a final value of ${Q}_{zz}({^{2}F}_{7/2})=0.07\begin{array}{c}+0.07\\ \ensuremath{-}0.00\end{array}$ a.u., establishing that the thulium electronic ground state has an exceptionally small EQM. A detailed analysis of this result is presented which has implications for EQMs of other atoms with unpaired $f$ electrons.

Optical Stern–Gerlach effect via a single traveling-wave light

In this paper, we propose a simplified model of the optical Stern–Gerlach effect based on coherent coupling between the clock transition of alkaline-earth single atoms and a traveling-wave light. It is demonstrated that spin–orbit coupling-induced chiral motion in atom deflection appears under strong atom–light interaction. The strong optical driving removes the perturbation from the Doppler effect and back-action effect to access the coherent system. In this process, the superposition of distant matter waves connected to the arbitrary distribution of the atom internal state could be predicted, which is important for the realization of atom interferometry and quantum-state operation. The influence of atom relaxation and atom–atom interactions is discussed. The basic conditions for the experimental design are given at the end of this work.

Coherent optical-microwave interface for manipulation of low-field electronic clock transitions in 171Yb3+:Y2SiO5

The coherent interaction of solid-state spins with both optical and microwave fields provides a platform for a range of quantum technologies, such as quantum sensing, microwave-to-optical quantum transduction and optical quantum memories. Rare-earth ions with electronic spins are interesting in this context. In this work, we use a loop-gap microwave resonator to coherently drive optical and microwave clock transitions simultaneously in a 171Yb3+:Y2SiO5 crystal, achieving a Rabi frequency of 0.56 MHz at 2.497 GHz over a 1-cm long crystal. Furthermore, we provide insights into the spin dephasing at very low fields, showing that superhyperfine-induced collapse of the Hahn echo plays an important role. Our calculations and measurements reveal that the effective magnetic moment can be manipulated in 171Yb3+:Y2SiO5, which suppresses the superhyperfine interaction at the clock transition. At a doping concentration of 2 ppm and 3.4 K, we achieve spin coherence time of 10.0 ± 0.4 ms.

Electron-nuclear decoupling at a spin clock transition

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 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, focusing on the role of the nuclear bath. Away from the clock transition, linear coupling to the nuclear degrees of freedom causes a modulation and decay of electronic coherence, as quantified via electron spin echo signals generated experimentally and in silico. Meanwhile, the effective hyperfine interaction vanishes at the clock transition, resulting in electron-nuclear decoupling and an absence of quantum information leakage to the nuclear bath, providing opportunities to characterize other decoherence sources.

Vibronic Relaxation Pathways in Molecular Spin Qubit Na9[Ho(W5O18)2]·35H2O under Pressure

In order to explore how spectral sparsity and vibronic decoherence pathways can be controlled in a model qubit system with atomic clock transitions, we combined diamond anvil cell techniques with synchrotron-based far infrared spectroscopy and first-principles calculations to reveal the vibrational response of Na9[Ho(W5O18)2]·35H2O under compression. Because the hole in the phonon density of states acts to reduce the overlap between the phonons and f manifold excitations in this system, we postulated that pressure might move the HoO4 rocking, bending, and asymmetric stretching modes that couple with the MJ = ±5, ±2, and ±7 levels out of resonance, reducing their interactions and minimizing decoherence processes, while a potentially beneficial strategy for some molecular qubits, pressure slightly hardens the phonons in Na9[Ho(W5O18)2]·35H2O and systematically fills in the transparency window in the phonon response. The net result is that the vibrational spectrum becomes less sparse and the overlap with the various MJ levels of the Ho3+ ion actually increases. These findings suggest that negative pressure, achieved using chemical means or elongational strain, could further open the transparency window in this rare earth-containing spin qubit system, thus paving the way for the use of device surfaces and interface elongational/compressive strains to better manage decoherence pathways.

Experimental determination of the E2−M1 polarizability of the strontium clock transition

State-of-the-art optical lattice clocks require careful characterization of systematic frequency shifts, which often needs to include contributions to the coupling of atoms to the trapping light field that are beyond the electric-dipole approximation. An experimental determination of the light-shift coefficient that accounts for electric-quadrupole and magnetic-dipole transitions for the clock transition in neutral strontium is reported on, addressing the substantial discrepancy between values detailed in previous works from theory and experiment.

High-dynamic-range microwave sensing using atomic Rabi resonances.

Detection of the microwave (MW) field with high accuracy is very important in the physical science and engineering fields. Herein, an atomic Rabi resonance-based MW magnetic field sensor with a high-dynamic-range is reported, where α and β Rabi resonances are used to measure MW fields. In MW measurement experiments, the sensor successfully measured a magnetic field of about 10 nT at 9.2GHz using the α Rabi resonance line on the cesium clock transition and continuously detected the MW magnetic field in the X-band over a high dynamic power range of >60 dB from the β Rabi resonance. Finally, the MW power frequency shift and power broadening are investigated to support more sensitive field measurements. The proposed MW detection method can be extended to cover a higher dynamic range and a wider frequency band by applying stronger excitations and exploring non-clock atomic transitions, respectively. In addition to MW magnetic field sensing, other potential application of the proposed method can be explored, including SI-traceable MW calibration and atomic communication.

Cavity sub- and superradiance for transversely driven atomic ensembles

Large atomic ensembles coupled to a single optical resonator mode can be steered to strongly enhanced or suppressed collective emission via phase controlled excitation. Employing the Tavis-Cummings model we find so far unreported phenomena. Using a second order cumulant expansion we predict that a homogeneously excited ensemble equally distributed between odd and even sites along the cavity mode is extremely subradiant as long as the average excitation remains below 50%, but shows pulsed emission for inversion. The combination of these two properties enables the implementation of an efficient cavity-enhanced Ramsey probing featuring a fast readout and minimal heating with particular advantages for atomic clock transitions. For continuous illumination the nonlinear atom-field interaction induces regular superradiant self-pulsing. Additionally, we observe an increased pulse delay time in comparison to an excitation through the cavity.

Coherent spin dynamics of rare-earth doped crystals in the high-cooperativity regime

Rare-earth doped crystals have long coherence times and the potential to provide quantum interfaces between microwave and optical photons. Such applications benefit from a high cooperativity between the spin ensemble and a microwave cavity---this motivates an increase in the rare-earth ion concentration which in turn impacts the spin coherence lifetime. We measure spin dynamics of two rare-earth spin species, $^{145}\mathrm{Nd}$ and Yb, doped into ${\mathrm{Y}}_{\text{2}}{\mathrm{SiO}}_{\text{5}}$, coupled to a planar microwave resonator in the high-cooperativity regime, in the temperature range $1.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ to $14\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. We identify relevant decoherence mechanisms, including instantaneous diffusion arising from resonant spins and temperature-dependent spectral diffusion from impurity electron and nuclear spins in the environment. We explore two methods to mitigate the effects of spectral diffusion in the Yb system in the low-temperature limit, first, using magnetic fields of up to 1 T to suppress impurity spin dynamics and, second, using transitions with low effective $g$ factors to reduce sensitivity to such dynamics. Finally, we demonstrate how the ``clock transition'' present in the $^{171}\mathrm{Yb}$ system at zero field can be used to increase coherence times up to ${T}_{2}=6(1)\phantom{\rule{0.16em}{0ex}}\mathrm{ms}$.

Search for Ultralight Dark Matter from Long-Term Frequency Comparisons of Optical and Microwave Atomic Clocks.

We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between a ^{171}Yb optical lattice clock and a ^{133}Cs fountain microwave clock that span 298days with an uptime of 15.4%. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from 10^{-22} to 10^{-20} eV/c^{2} are set, assuming that each of these couplings is the dominant source of the modulation in the frequency ratio. The absolute frequency of the ^{171}Yb clock transition is also determined as 518 295 836 590 863.69(28)Hz, which is one of the important contributions toward a redefinition of the second in the International System of Units.

Phase-stabilized UV light at 267 nm through twofold second harmonic generation.

Providing phase stable laser light is important to extend the interrogation time of optical clocks towards many seconds and thus achieve small statistical uncertainties. We report a laser system providing more than 50 µW phase-stabilized UV light at 267.4 nm for an aluminium ion optical clock. The light is generated by frequency-quadrupling a fibre laser at 1069.6 nm in two cascaded non-linear crystals, both in single-pass configuration. In the first stage, a 10 mm long PPLN waveguide crystal converts 1 W fundamental light to more than 0.2 W at 534.8 nm. In the following 50 mm long DKDP crystal, more than 50 µW of light at 267.4 nm are generated. An upper limit for the passive short-term phase stability has been measured by a beat-node measurement with an existing phase-stabilized quadrupling system employing the same source laser. The resulting fractional frequency instability of less than 5×10-17 after 1 s supports lifetime-limited probing of the 27Al+ clock transition, given a sufficiently stable laser source. A further improved stability of the fourth harmonic light is expected through interferometric path length stabilisation of the pump light by back-reflecting it through the entire setup and correcting for frequency deviations. The in-loop error signal indicates an electronically limited instability of 1 × 10-18 at 1 s.

Electrical two-qubit gates within a pair of clock-qubit magnetic molecules

Enhanced coherence in HoW10 molecular spin qubits has been demonstrated by use of clock-transitions (CTs). More recently it was shown that, while operating at the CTs, it was possible to use an electrical field to selectively address HoW10 molecules pointing in a given direction, within a crystal that contains two kinds of identical but inversion-related molecules. Herein we theoretically explore the possibility of employing the electric field to effect entangling two-qubit quantum gates within a 2-qubit Hilbert space resulting from dipolar coupling of two CT-protected HoW10 molecules in a diluted crystal. We estimate the thermal evolution of T1, T2, find that CTs are also optimal operating points from the point of view of phonons, and lay out how to combine a sequence of microwave and electric field pulses to achieve coherent control within a switchable two-qubit operating space between symmetric and asymmetric qubit states that are protected both from spin-bath and from phonon-bath decoherence. This two-qubit gate approach presents an elegant correspondence between physical stimuli and logical operations, meanwhile avoiding any spontaneous unitary evolution of the qubit states. Finally, we found a highly protected 1-qubit subspace resulting from the interaction between two clock molecules.

μ POP Clock: A Microcell Atomic Clock Based on a Double-Resonance Ramsey Scheme

We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the \ensuremath{\mu}POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4--5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the \ensuremath{\mu}POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ \ensuremath{\tau}${}^{\ensuremath{-}1/2}$ and reaching the \ensuremath{\le}2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ level at timescales of 1000 s to one day. The short-term instability budget established for the \ensuremath{\mu}POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the \ensuremath{\mu}POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.

Precise measurement of 171Yb magnetic constants for 1 S 0–3 P 0 clock transition

We present a precise measurement of 171Yb magnetic constants for 1 S 0–3 P 0 clock transition. The background magnetic field is firstly compensated to < 1 mGs (1 Gs = 10−4 T) through measuring the splitting of two π transitins of 171Yb clock transition at different compensation coils currents. Then, the splitting ratios of the π and σ components of 171Yb clock transition at different bias magnetic fields are measured, and the first-order Zeeman coefficient is determined to be α = 199.49(5) Hz/Gs. The second-order Zeeman shifts at various bias magnetic fields are also measured through interleaved self-comparison in which the bias magnetic fields are modulated between high and low values. The second-order Zeeman coefficient is fitted to be β = –6.09(3) Hz/mT2, which is consistent with the result of NIST group.

Tunable VUV frequency comb for 229mTh nuclear spectroscopy.

Laser spectroscopy of the 229mTh 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 229mTh nuclear clock transition.

Toward a New Generation of Compact Transportable Yb+ Optical Clocks

Optical atomic clocks are currently one of the most sensitive tools making it possible to precisely test the fundamental symmetry properties of spacetime and Einstein’s theory of relativity. At the same time, the extremely high stability and accuracy of compact transportable optical clocks open new perspectives in important fields, such as satellite navigation, relativistic geodesy, and the global time and frequency network. Our project aimed to develop a compact transportable optical clock based on a single ytterbium ion. We present the first prototype of the Yb+ clock (298 kg in 1 m3) and present several solutions aimed to improve the clock’s robustness to approach the demands of a space-qualified system. We present spectroscopic studies of a 435.5 nm quadrupole clock transition with Fourier-limited spectra of 25 Hz. The estimated instability of the output frequency at 1 GHz, which was down-converted with an optical frequency comb (OFC), is at the level of 9×10−15/τ, and the long-term instability and inaccuracy are at the level of 5×10−16. As the next steps, we present a new design for the clock laser and the OFC.

Femtosecond-comb based 10 MHz-to-optical frequency link with uncertainty at the 10−18 level

The International System of Units (SI) definition of the ‘second’ is likely to be redefined in the optical frequency region in the near future. Therefore, uncertainty reduction in the frequency link between 10 MHz, which is used in the frequency link with an artificial satellite, and the ultrastable laser for observing clock transitions in optical clocks, is an important issue for numerical determination in the new definition and for International Atomic Time operation after the redefinition. We have evaluated all the possible uncertainty factors in the frequency link with a femtosecond comb between 10 MHz and an optical frequency and obtained the lowest uncertainty yet reported of 3.9 × 10−18 by temperature-stabilizing RF multipliers and by using temperature insensitive coaxial cables. Furthermore, we have validated the uncertainty of the frequency link by simultaneously measuring an optical frequency of an identical laser using two femtosecond combs referenced to a common 10 MHz source and confirmed to be consistent with the evaluated uncertainty.

Two-Photon Polarizability of Ba+ Ion: Control of Spin-Mixing Processes in an Ultracold 137Ba+ − 87Rb Mixture

In this work, we present a scheme of a two-photon interaction to calculate magic wavelengths for the 62S12 − 52D32,52 clock transitions of Ba+ ion employing the relativistic coupled-cluster method. These magic wavelengths can be essential inputs to achieve better accuracy in the future ionic clock experiments. In this paper, we further show an application of a two-photon interaction to the spin-mixing processes, |0,0⟩↔|+1,−1⟩ and |0,0⟩↔|−1,+1⟩, of an ultra-cold spin-1 mixture of 137Ba+ ions and 87Rb atoms. We determine the protocols for selecting these spin-mixing oscillations by changing the strength and frequencies of the externally applied magnetic field and laser beams, respectively.

Recent progress on quantum frequency standards at BIRMM

Quantum frequency standards are crucial for time measurement, satellite navigation, telecommunication, and other essential applications. Beijing Institute of Radio Metrology and Measurement (BIRMM) has been working on quantum frequency standards and their applications for tens of years. This paper introduces the latest progress on quantum frequency standards at BIRMM, including a calcium optical clock, an active hydrogen maser, and a mercury ion microwave clock. Based on the 1S0-3P1 transition of calcium atoms, a transportable optical clock prototype is built with a stability of 8 × 10–15 at 1 s. A compact active hydrogen maser has been developed for the Chinese space station. It will be used for scientific research such as examining Einstein’s theory of general relativity and has just been lunched. The preliminary frequency stability of the maser is 1.27 × 10–15 at 10000 s. Additionally, a prototype mercury ion microwave clock is developed using the hyperfine transition between 62S1/2, F = 0 and 62S1/2, F = 1. The trapped Hg+ ions are pumped by mercury discharge lamps and cooled by Helium gas. The measured clock transition linewidth is about 1 Hz, and frequency stability of 4 × 10–13 at 1 s and 4 × 10–14 at 1000 s is achieved.