Clock Transition Research Articles

Near-Surface ^{125}Te^{+} Spins with Millisecond Coherence Lifetime.

Impurity spins in crystal matrices are promising components in quantum technologies, particularly if they can maintain their spin properties when close to surfaces and material interfaces. Here, we investigate an attractive candidate for microwave-domain applications, the spins of group-VI ^{125}Te^{+} donors implanted into natural Si at depths as shallow as 20nm. We show that surface band bending can be used to ionize such near-surface Te to spin-active Te^{+} state, and that optical illumination can be used further to control the Te donor charge state. We examine spin activation yield, spin linewidth, and relaxation (T_{1}) and coherence times (T_{2}) and show how a zero-field 3.5GHz "clock transition" extends spin coherence times to over 1ms, which is about an order of magnitude longer than other near-surface spin systems.

Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce. In this work, the hyperfine-induced Landé g-factors and quadratic Zeeman shift coefficients of the nsnp clock states for 111,113Cd and 25Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory. To obtain accurate values of these parameters, the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the Landé g-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy. Our calculations provide important data for estimating the first- and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.

Figure data sets for the paper "Coherent optical-microwave interface for manipulation of low-field electronic clock transitions in 171Yb3+:Y2SiO5"

Figure data sets for the paper "Coherent optical-microwave interface for manipulation of low-field electronic clock transitions in 171Yb3+:Y2SiO5"

Subrecoil Clock-Transition Laser Cooling Enabling Shallow Optical Lattice Clocks.

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the μK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow ^{1}S_{0}-^{3}P_{0} clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10^{-19} level.

Enhancing Spin Coherence in Optically Addressable Molecular Qubits through Host-Matrix Control

Optically addressable spins are a promising platform for quantum information science due to their combination of a long-lived qubit with a spin-optical interface for external qubit control and readout. The ability to chemically synthesize such systems—to generate optically addressable molecular spins—offers a modular qubit architecture which can be transported across different environments and atomistically tailored for targeted applications through bottom-up design and synthesis. Here, we demonstrate how the spin coherence in such optically addressable molecular qubits can be controlled through engineering their host environment. By inserting chromium (IV)-based molecular qubits into a nonisostructural host matrix, we generate noise-insensitive clock transitions, through a transverse zero-field splitting, that are not present when using an isostructural host. This host-matrix engineering leads to spin-coherence times of more than 10 μs for optically addressable molecular spin qubits in a nuclear and electron-spin-rich environment. We model the dependence of spin coherence on transverse zero-field splitting from first principles and experimentally verify the theoretical predictions with four distinct molecular systems. Finally, we explore how to further enhance optical-spin interfaces in molecular qubits by investigating the key parameters of optical linewidth and spin-lattice relaxation time. Our results demonstrate the ability to test qubit structure-function relationships through a tunable molecular platform and highlight opportunities for using molecular qubits for nanoscale quantum sensing in noisy environments.Received 18 March 2022Revised 16 June 2022Accepted 1 July 2022DOI:https://doi.org/10.1103/PhysRevX.12.031028Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChemical Physics & Physical ChemistryQuantum engineeringQuantum information processingSpintronicsQuantum InformationCondensed Matter, Materials & Applied Physics

Active optical clock lasing on the Cs 7S1/2-6P3/2 transition under a weak magnetic field

In the bad-cavity limit, the collective atomic dipole is highly coherent, resulting in the phase information of an active optical clock (AOC) laser primarily stored in the atomic gain medium. Therefore, compared with the good-cavity laser, the sensitivity of an AOC laser to cavity fluctuations is greatly reduced, as characterized by the suppressed cavity-pulling effect. In this work, the AOC lasing on the cesium 7S1/2-6P3/2 clock transition with a natural linewidth of 1.81 MHz under a weak magnetic field is achieved. We calculate the Zeeman spectra of upper and lower states of clock transition, and measure the beat-note spectrum between different Zeeman-sublevel transitions of 7S1/2-6P3/2. Moreover, the cavity-pulling, temperature, power, and linewidth characteristics of the AOC laser are demonstrated under a weak magnetic field. Such an emerging laser can be applied as a narrow-linewidth local oscillator, as well as an active optical frequency standard, which is promising for the field of precision measurement.

Long-lived Bell states in an array of optical clock qubits

The generation of long-lived entanglement in optical atomic clocks is one of the main goals of quantum metrology. Arrays of neutral atoms, where Rydberg-based interactions may generate entanglement between individually controlled and resolved atoms, constitute a promising quantum platform to achieve this. Here we leverage the programmable state preparation afforded by optical tweezers and the efficient strong confinement of a three-dimensional optical lattice to prepare an ensemble of strontium-atom pairs in their motional ground state. We engineer global single-qubit gates on the optical clock transition and two-qubit entangling gates via adiabatic Rydberg dressing, enabling the generation of Bell states with a state-preparation-and-measurement-corrected fidelity of 92.8(2.0)% (87.1(1.6)% without state-preparation-and-measurement correction). For use in quantum metrology, it is furthermore critical that the resulting entanglement be long lived; we find that the coherence of the Bell state has a lifetime of 4.2(6) s via parity correlations and simultaneous comparisons between entangled and unentangled ensembles. Such long-lived Bell states can be useful for enhancing metrological stability and bandwidth. In the future, atomic rearrangement will enable the implementation of many-qubit gates and cluster state generation, as well as explorations of the transverse field Ising model.

Determination of hyperfine splittings and Landé gJ factors of 5s2S1/2 and 5p2P1/2,3/2 states of Cd+111,113 for microwave frequency standards

Regarding microwave frequency standards based on trapped ions, we report on the determination of the hyperfine splittings and the Land\'e ${g}_{J}$ factors of $^{111,113}\mathrm{Cd}^{+}$. The hyperfine splittings and Land\'e ${g}_{J}$ factors of the $5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2,3/2}$ states of $^{111,113}\mathrm{Cd}^{+}$ are calculated using the multiconfiguration Dirac-Hartree-Fock scheme. Furthermore, the hyperfine splittings of the $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state of $^{111,113}\mathrm{Cd}^{+}$ are derived based on the laser-induced fluorescence spectroscopy. The ${\mathrm{Cd}}^{+}$ ions are confined in a linear Paul trap and sympathetically cooled by laser-cooled ${\mathrm{Ca}}^{+}$ ions. The calculated values and the derived values are cross-checked, thereby guaranteeing the reliability of our results. The results provided in this paper can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, thus further improving the stability and accuracy of the microwave frequency standards based on trapped $^{111,113}\mathrm{Cd}^{+}$ ions.

Proposed clock transition in atomic chromium and the possible detection schemes

In this article radiative parameters for atomic chromium were determined by a semi-empirical method. The eigenvector amplitudes, determined in our previously published work concerning the hyperfine structure parametrization for even-parity atomic chromium levels, were used. The calculated values of oscillator strengths and lifetimes for low-lying metastable Cr I levels are presented. On the basis of the calculations performed, a possible clock transition in neutral chromium is proposed. Possible detection schemes for the clock transition were investigated experimentally and are presented in this work.

Magneto-optical trapping of a group-III atom

The authors demonstrate the first magneto-optical trap of indium atoms, which belong to group III of the periodic table. These atoms offer a unique combination of features, such as the simultaneous presence of Feshbach resonances and optical clock transitions. The techniques introduced in this work can be applied to other elements in group III.

Effect of optical lattice field on characteristics of a clock transition in thulium atoms

This paper presents a detailed analysis of the effect of the optical lattice field on clock transition spectroscopy, as exemplified by thulium atoms. We consider the applicability of the sifting of atoms in an optical lattice by ramping down the power of the laser light that produces it. This method allows the number of filled vibrational sublevels to be reduced down to a single vibrational state, without changing the inner state of the atoms. The effectiveness of the method is illustrated by the example of the spectroscopy of a clock transition in thulium atoms in the resolved sideband regime.

Photoionization cross sections of ultracold 88Sr in 1P1 and 3S1 states at 390 nm and the resulting blue-detuned magic wavelength optical lattice clock constraints.

We present the measurements of the photoionization cross sections of the excited 1P1 and 3S1 states of ultracold 88Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the 1S0-3P0 clock transition. The photoionization cross section of the 1P1 state is determined from the measured ionization rates of 88Sr in the magneto-optical trap in the 1P1 state to be 2.20(50)×10-20 m2, while the photoionization cross section of 88Sr in the 3S1 state is inferred from the photoionization-induced reduction in the number of atoms transferred through the 3S1 state in an operating optical lattice clock to be 1.38(66) ×10-18 m2. Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the 3S1 state would make the use of the 3S1 state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used 3D1,2 states during the detection part of the optical clock cycle.

Analyzing the Rydberg-based optical-metastable-ground architecture for Yb171 nuclear spins

Neutral alkaline earth(-like) atoms have recently been employed in atomic arrays with individual readout, control, and high-fidelity Rydberg-mediated entanglement. This emerging platform offers a wide range of new quantum science applications that leverage the unique properties of such atoms: ultra-narrow optical "clock" transitions and isolated nuclear spins. Specifically, these properties offer an optical qubit ("o") as well as ground ("g") and metastable ("m") nuclear spin qubits, all within a single atom. We consider experimentally realistic control of this "omg" architecture and its coupling to Rydberg states for entanglement generation, focusing specifically on ytterbium-171 ($^{171}\text{Yb}$) with nuclear spin $I = 1/2$. We analyze the $S$-series Rydberg states of $^{171}\text{Yb}$, described by the three spin-$1/2$ constituents (two electrons and the nucleus). We confirm that the $F = 3/2$ manifold -- a unique spin configuration -- is well suited for entangling nuclear spin qubits. Further, we analyze the $F = 1/2$ series -- described by two overlapping spin configurations -- using a multichannel quantum defect theory. We study the multilevel dynamics of the nuclear spin states when driving the clock or Rydberg transition with Rabi frequency $\Omega_\text{c} = 2 \pi \times 200$ kHz or $\Omega_\text{R} = 2 \pi \times 6$ MHz, respectively, finding that a modest magnetic field ($\approx200\,\text{G}$) and feasible laser polarization intensity purity ($\lesssim0.99$) are sufficient for gate fidelities exceeding 0.99.

Effects of variation of the fine structure constant α and quark mass mq in Mössbauer nuclear transitions

High accuracy measurements in M\"ossbauer transitions open up the possibility to use them in the search for temporal and spatial variations of the fine structure constant $\ensuremath{\alpha}$, quark mass ${m}_{q}$, and dark matter field which may lead to the variations of $\ensuremath{\alpha}$ and ${m}_{q}$. We calculate the sensitivity of nuclear transitions to variations of $\ensuremath{\alpha}$ and ${m}_{q}$. M\"ossbauer transitions have high sensitivity to variation of quark mass ${m}_{q}$ and the strong interaction scale ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ to which atomic optical clocks are not sensitive. The enhancement factors $K$, defined by $\frac{\ensuremath{\delta}f}{f}={K}_{\ensuremath{\alpha}}\frac{\ensuremath{\delta}\ensuremath{\alpha}}{\ensuremath{\alpha}}$ and $\frac{\ensuremath{\delta}f}{f}={K}_{q}\frac{\ensuremath{\delta}{m}_{q}}{{m}_{q}}$ where $f$ is the transition energy, may be large in some transitions. The 8-eV nuclear clock transition in $^{229}\mathrm{Th}$ $({K}_{q}\ensuremath{\approx}{10}^{4})$ and 76-eV transition in $^{235}\mathrm{U}$ $({K}_{\ensuremath{\alpha}}\ensuremath{\approx}{K}_{q}\ensuremath{\approx}{10}^{3})$ may be investigated using laser spectroscopy methods.

Observation of Nonlinearity of Generalized King Plot in the Search for New Boson

We measure isotope shifts for neutral Yb isotopes on an ultranarrow optical clock transition S10−P03 with an accuracy of a few hertz. Combined with one of the recently reported isotope-shift measurements of Yb+ on two optical transitions, the result allows us to construct the King plots—a set of scaled isotope shifts data on two different optical transitions plotted in two-dimensional plane. When only the leading-order terms of isotope shifts are taken into account, a King plot should exhibit a linear relation as a result of elimination of the leading nuclear-size dependence. Extremely large nonlinearity unexplainable by a quadratic field shift is revealed, which was proposed previously as a source of the observed nonlinearity of the King plot. We further construct the generalized King plot with three optical transitions so that we can eliminate the contribution arising from a higher-order effect within the standard model. Our analysis of the generalized King plot shows a deviation from linearity at the 3σ level, indicating that there exist at least two higher-order contributions in the measured isotope shifts. Under reasonable assumptions, we obtain the upper bound of the product of the couplings for a new boson, mediating a force between electrons and neutrons—|yeyn|/(ℏc)<1×10−10 for the mass less than 1 keV—with the 95% confidence level, providing an important step toward probing new physics via isotope-shift spectroscopy.2 MoreReceived 18 October 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevX.12.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structure of atoms & moleculesElectronic transitionsHypothetical particle physics modelsNuclear charge distributionPhysical SystemsAtomsHypothetical particlesTechniquesPrecision measurementsSpectroscopyAtomic, Molecular & OpticalParticles & Fields

New designed helical resonator to improve measurement accuracy of magic radio frequency

Based upon the new designed helical resonator, the resonant radio frequency (RF) for trapping ions can be consecutively adjusted in a large range (about 12 MHz to 29 MHz) with high Q-factors (above 300). We analyze the helical resonator with a lumped element circuit model and find that the theoretical results fit well with the experimental data. With our resonator system, the resonant frequency near magic RF frequency (where the scalar Stark shift and the second-order Doppler shift due to excess micromotion cancel each other) can be continuously changed at kHz level. For 88Sr+ ion, compared to earlier results, the measurement accuracy of magic RF frequency can be improved by an order of magnitude upon rough calculation, and therefore the net micromotion frequency shifts can be further reduced. Also, the differential static scalar polarizability Δα 0 of clock transition can be experimentally measured more accurately.

Development and tuning of the microwave resonant cavity of a cryogenic cesium atomic fountain clock.

A cryogenic cesium atomic fountain clock is a novel clock with the microwave cavity and atomic free flight region placed in liquid nitrogen. On the one hand, the blackbody radiation shift is reduced at cryogenic temperature. On the other hand, the vacuum in the atomic free flight region is optimized, and the background gas collision shift reduced. The microwave resonant cavity is the most important unit in a cryogenic cesium atomic fountain clock. Through theoretical and simulative investigation, this study designs the configuration and dimensions for an optimized microwave cavity. Concurrently, experiments reveal the effects of temperature, pressure, humidity, and other factors on the resonant frequency of the microwave cavity. Combining the theoretical and experimental study, we obtain the resonant frequency difference between the microwave cavity in a cryogenic vacuum and at room temperature and ambient pressure. By subtracting this frequency difference, we adjust the microwave cavity for room temperature and ambient pressure, then vacuumize and immerse it in liquid nitrogen for verification and fine tuning. Finally, we determine that the microwave cavity resonant frequency deviation from the clock transition frequency is 10 kHz with an unloaded quality factor of 25 000, which meets the application requirements of the cryogenic cesium atomic fountain clock.

A 9.2-GHz clock transition in a Lu(II) molecular spin qubit arising from a 3,467-MHz hyperfine interaction.

Spins in molecules are particularly attractive targets for next-generation quantum technologies, enabling chemically programmable qubits and potential for scale-up via self-assembly. Here we report the observation of one of the largest hyperfine interactions for a molecular system, Aiso = 3,467 ± 50 MHz, as well as a very large associated clock transition. This is achieved through chemical control of the degree of s-orbital mixing into the spin-bearing d orbital associated with a series of spin-½ La(II) and Lu(II) complexes. Increased s-orbital character reduces spin-orbit coupling and enhances the electron-nuclear Fermi contact interaction. Both outcomes are advantageous for quantum applications. The former reduces spin-lattice relaxation, and the latter maximizes the hyperfine interaction, which, in turn, generates a 9-GHz clock transition, leading to an increase in phase memory time from 1.0 ± 0.4 to 12 ± 1 μs for one of the Lu(II) complexes. These findings suggest strategies for the development of molecular quantum technologies, akin to trapped ion systems.

Measurement of Optical Rubidium Clock Frequency Spanning 65 Days.

Optical clocks are emerging as next-generation timekeeping devices with technological and scientific use cases. Simplified atomic sources such as vapor cells may offer a straightforward path to field use, but suffer from long-term frequency drifts and environmental sensitivities. Here, we measure a laboratory optical clock based on warm rubidium atoms and find low levels of drift on the month-long timescale. We observe and quantify helium contamination inside the glass vapor cell by gradually removing the helium via a vacuum apparatus. We quantify a drift rate of /day, a 10 day Allan deviation less than , and an absolute frequency of the Rb-87 two-photon clock transition of 385,284,566,371,190(1970) Hz. These results support the premise that optical vapor cell clocks will be able to meet future technology needs in navigation and communications as sensors of time and frequency.

Dynamic polarizabilities of the clock states of Al+

The dynamic polarizabilities of and states of Al+ are calculated using the hybrid configuration interaction and many-body perturbation theory method, and multiconfiguration Dirac–Hartree–Fock method in this work. Five ultraviolet magic wavelengths for the Al+ clock transition – are predicted. Although the suitable lasers are not available presently, the potential precision measurement on these magic wavelengths for the Al+ clock transition would be used to extract the ratios of several certain transition matrix elements with high accuracy, and then help to improve the precision and reliability of the estimate of the BBR shift of the Al+ clock transition. The differential dynamic polarizabilities at certain wavelengths are evaluated, which are useful to assess the ac Stark shift of the Al+ clock transition frequency and helpful in the clock experiments to suppress the ac Stark shift of the clock transition as possible as it can.