Clock States Research Articles

Clock-Line-Mediated Sisyphus Cooling.

We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

Prospective Optical Lattice Clocks in Neutral Atoms with Hyperfine Structure

Optical lattice clocks combine the accuracy and stability required for next-generation frequency standards. At the heart of these clocks are carefully engineered optical lattices tuned to a wavelength where the differential AC Stark shift between ground and excited states vanishes—the so called ‘magic’ wavelength. To date, only alkaline-earth-like atoms utilizing clock transitions with total electronic angular momentum J=0 have successfully realized these magic wavelength optical lattices at the level necessary for state-of-the-art clock operation. In this article, we discuss two additional types of clock transitions utilizing states with J≠0, leveraging hyperfine structure to satisfy the necessary requirements for controlling lattice-induced light shifts. We propose realizing (i) clock transitions between same-parity clock states with total angular momentum F=0 and (ii) M1/E2 clock transitions between a state with F=0 and a second state with J=1/2, mF=0. We present atomic species which fulfill these requirements before giving a detailed discussion of both manganese and copper, demonstrating how these transitions provide the necessary suppression of fine structure-induced vector and tensor lattice light shifts for clock operations. Such realization of alternative optical lattice clocks promises to provide a rich variety of new atomic species for neutral atom clock operation, with applications from many-body physics to searches for new physics.

Theoretical calculation of “tune-out” wavelengths for clock states of Al<sup>+</sup>

In quantum optical experiments, the polarizabilities of atomic systems play a very important role, which can be used to describe the interactions of atomic systems with external electromagnetic fields. When subjected to a specific electric field such as a laser field with a particular frequency, the frequency-dependent electric-dipole (E1) dynamic polarizability of an atomic state can reach zero. The wavelength corresponding to such a frequency is referred to as the “turn-out” wavelength. In this work, the “turn-out” wavelengths for the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> clock states of Al<sup>+</sup> are calculated by using the configuration interaction plus many-body perturbation theory (CI+MBPT) method. The values of energy and E1 reduced matrix elements of low-lying states of Al<sup>+</sup> are calculated. By combining these E1 reduced matrix elements with the experimental energy values, the E1 dynamic polarizabilities of the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> clock states are determined in the angular frequency range of (0, 0.42 a.u.). The “turn-out” wavelengths are found at the zero-crossing points of the frequency-dependent dynamic polarizability curves for both the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> states. For the ground state 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub>, a single “turn-out” wavelength at 266.994(1) nm is observed. On the other hand, the excited state 3s3p <sup>3</sup>P<sub>0</sub> exhibits four distinct “turn-out” wavelengths, namely 184.56(1) nm, 174.433(1) nm, 121.52(2) nm, and 119.71(2) nm. The contributions of individual resonant transitions to the dynamic polarizabilities at the “turn-out” wavelengths are examined. It is observed that the resonant lines situated near a certain “turn-out” wavelength can provide dominant contributions to the polarizability, while the remaining resonant lines generally contribute minimally. When analyzing these data, we recommend accurately measuring these “turn-out” wavelengths to accurately determine the oscillator strengths or reduced matrix elements of the relevant transitions. This is crucial for minimizing the uncertainty of the blackbody radiation (BBR) frequency shift in Al<sup>+</sup> optical clock and suppressing the systematic uncertainty. Meanwhile, precisely measuring these “turn-out” wavelengths is also helpful for further exploring the atomic structure of Al<sup>+</sup>.

The time-freezing reformulation for numerical optimal control of complementarity Lagrangian systems with state jumps

This paper introduces a novel time-freezing reformulation and numerical methods for optimal control of complementarity Lagrangian systems (CLS) with state jumps. We cover the difficult case when the system evolves on the boundary of the dynamic’s feasible set after the state jump. In nonsmooth mechanics, this corresponds to inelastic impacts. The main idea of the time-freezing reformulation is to introduce a clock state and an auxiliary dynamical system whose trajectory endpoints satisfy the state jump law. When the auxiliary system is active, the clock state is not evolving, hence by taking only the parts of the trajectory when the clock state was active, we can recover the original solution. The resulting time-freezing system is a Filippov system that has jump discontinuities only in the first time derivative instead of the trajectory itself. This enables one to use the recently proposed Finite Elements with Switch Detection (Nurkanović et al., 2022), which makes high accuracy numerical optimal control of CLS with impacts and friction possible. We detail how to recover the solution of the original system and show how to select appropriate auxiliary dynamics. The theoretical findings are illustrated on a nontrivial numerical optimal control example of a hopping one-legged robot.

Optimizing population accumulation in a designated single Zeeman state using microwave spectroscopy

We present an all-optical method for the highly efficient preparation of cold atoms in a specific Zeeman state, such as the magnetically insensitive clock state (m F = 0) or a particular state suitable for quantum information processing and storage. This technique employs a single microwave spectrum, enabling precise determination of the population distribution, microwave polarization ratio, and microwave Rabi frequency individually. By analyzing the microwave spectrum, we can track the population distribution while systematically varying the power or period of the optical pumping field(s). In steady-state conditions, our simplified model, which incorporates resonant and off-resonant transitions, reveals an upper limit to the population purity. Through the optimization of the intensity and polarization of the optical pumping field, we have achieved exceptional population purities of up to 96(2)% or 98(1)% for the desired quantum state. These remarkable results indicate a significant advancement in state preparation accuracy. Our all-optical method introduces an approach to achieving high-purity atomic states while employing novel microwave spectroscopy to accurately detect all unknown parameters, offering valuable insights and potential applications in precision measurement and quantum computation research.

Dihedral lattice gauge theories on a quantum annealer

We study lattice gauge theory with discrete, non-Abelian gauge groups. We extend the formalism of previous studies on D-Wave’s quantum annealer as a computing platform to finite, simply reducible gauge groups. As an example, we use the dihedral group D_{n} with n=3,4 on a two plaquette ladder for which we provide proof-of-principle calculations of the ground-state and employ the known time evolution formalism with Feynman clock states.

Measuring the environment of a Cs qubit with dynamical decoupling sequences

We report the experimental implementation of dynamical decoupling on a small, non-interacting ensemble of up to 25 optically trapped, neutral Cs atoms. The qubit consists of the two magnetic-insensitive Cs clock states and , which are coupled by microwave radiation. We observe a significant enhancement of the coherence time when employing Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. A CPMG sequence with ten refocusing pulses increases the coherence time of 16.2(9) ms by more than one order of magnitude to 178(2) ms. In addition, we make use of the filter function formalism and utilise the CPMG sequence to measure the background noise floor affecting the qubit coherence, finding a power-law noise spectrum with . This finding is in very good agreement with an independent measurement of the noise in the intensity of the trapping laser. Moreover, the measured coherence evolutions also exhibit signatures of low-frequency noise originating at distinct frequencies. Our findings point toward noise spectroscopy of engineered atomic baths through single-atom dynamical decoupling in a system of individual Cs impurities immersed in an ultracold 87Rb bath.

IARMTS: Design of an Interference-Aware Routing Model with Time Synchronization Capabilities for Dense Wireless Sensor Network Deployments

Performance of dense wireless sensor networks is often degraded due to communication interference and time synchronization issues. Existing machine learning & deep learning models that propose bioinspired & pre-emptive packet-analysis solutions for these tasks either have high complexity, or high deployment costs. Moreover, these models cannot be scaled for heterogeneous node & traffic types, which limits their applicability when applied to real-time scenarios. To overcome these issues, this text proposes design of an interference-aware routing model with time synchronization capabilities for dense wireless sensor network deployments. The network initially collects temporal clock states & packet delivery performance of different nodes on heterogeneous traffic scenarios. These traffic patterns are converted into frequency, entropy, Gabor, and Wavelet components. The converted components are used to train an ensemble set of Naïve Bayes (NB), k Nearest Neighbour (kNN), Multilayer Perceptron (MLP), and Support Vector Machine (SVM) classifiers. These classifiers assist in identification of optimal clock deviations and set of routing paths. These routing paths are further fine-tuned via use of a Bacterial Foraging Optimization (BFO) Model, which assists in identification of interference-aware paths. The BFO Model uses a temporal fitness function that fuses throughput, communication delay, energy levels, and packet delivery performance for different set of contextual communications. Due to which, the model is able to showcase lower end-to-end delay, higher throughput, lower energy consumption, and higher packet delivery performance when compared with existing routing methods under high density nodes & heterogeneous network scenarios. The model showcases 99% PDR, 18.3% lower delay, 19.5% higher energy efficiency and 10.4% lower delay levels when compared with existing methods.

Parkinson's Disease: A Narrative Review on Potential Molecular Mechanisms of Sleep Disturbances, REM Behavior Disorder, and Melatonin.

Parkinson's disease (PD) is one of the most common neurodegenerative diseases. There is a wide range of sleep disturbances in patients with PD, such as insomnia and rapid eye movement (REM) sleep behavior disorder (or REM behavior disorder (RBD)). RBD is a sleep disorder in which a patient acts out his/her dreams and includes abnormal behaviors during the REM phase of sleep. On the other hand, melatonin is the principal hormone that is secreted by the pineal gland and significantly modulates the circadian clock and mood state. Furthermore, melatonin has a wide range of regulatory effects and is a safe treatment for sleep disturbances such as RBD in PD. However, the molecular mechanisms of melatonin involved in the treatment or control of RBD are unknown. In this study, we reviewed the pathophysiology of PD and sleep disturbances, including RBD. We also discussed the potential molecular mechanisms of melatonin involved in its therapeutic effect. It was concluded that disruption of crucial neurotransmitter systems that mediate sleep, including norepinephrine, serotonin, dopamine, and GABA, and important neurotransmitter systems that mediate the REM phase, including acetylcholine, serotonin, and norepinephrine, are significantly involved in the induction of sleep disturbances, including RBD in PD. It was also concluded that accumulation of α-synuclein in sleep-related brain regions can disrupt sleep processes and the circadian rhythm. We suggested that new treatment strategies for sleep disturbances in PD may focus on the modulation of α-synuclein aggregation or expression.

Ab Initio Derivation of Lattice-Gauge-Theory Dynamics for Cold Gases in Optical Lattices

We introduce a method for quantum simulation of U$(1)$ lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the study of both gauge and fermionic-matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an $ab\,initio$ modelling of the experimental setting, we systematically carry out a derivation of the target U$(1)$ gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that - while pivotal for a successful implementation - have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions, and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope $^{173}$Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.

Observing Spin-Squeezed States under Spin-Exchange Collisions for a Second

Using the platform of a trapped-atom clock on a chip, we observe the time evolution of spin-squeezed hyperfine clock states in ultracold rubidium atoms on previously inaccessible timescales up to 1 s. The spin degree-of-freedom remains squeezed after 0.6 s, which is consistent with the limit imposed by particle loss and is compatible with typical Ramsey times in state-of-the-art microwave clocks. The results also reveal a surprising spin-exchange interaction effect that amplifies the cavity-based spin measurement via a correlation between spin and external degrees of freedom. These results open up perspectives for squeezing-enhanced atomic clocks in a metrologically relevant regime and highlight the importance of spin interactions in real-life applications of spin squeezing.

MPC-based time synchronization method for V2V (vehicle-to-vehicle) communication

PurposeAs the strategy of 5G new infrastructure is deployed and advanced, 5G-R becomes the primary technical system for future mobile communication of China’s railway. V2V communication is also an important application scenario of 5G communication systems on high-speed railways, so time synchronization between vehicles is critical for train control systems to be real-time and safe. How to improve the time synchronization performance in V2V communication is crucial to ensure the operational safety and efficiency of high-speed railways.Design/methodology/approachThis paper proposed a time synchronization method based on model predictive control (MPC) for V2V communication. Firstly, a synchronous clock for V2V communication was modeled based on the fifth generation mobile communication-railway (5G-R) system. Secondly, an observation equation was introduced according to the phase and frequency offsets between synchronous clocks of two adjacent vehicles to construct an MPC-based space model of clock states of the adjacent vehicles. Finally, the optimal clock offset was solved through multistep prediction, rolling optimization and other control methods, and time synchronization in different V2V communication scenarios based on the 5G-R system was realized through negative feedback correction.FindingsThe results of simulation tests conducted with and without a repeater, respectively, show that the proposed method can realize time synchronization of V2V communication in both scenarios. Compared with other methods, the proposed method has faster convergence speed and higher synchronization precision regardless of whether there is a repeater or not.Originality/valueThis paper proposed an MPC-based time synchronization method for V2V communication under 5G-R. Through the construction of MPC controllers for clocks of adjacent vehicles, time synchronization was realized for V2V communication under 5G-R by using control means such as multistep prediction, rolling optimization, and feedback correction. In view of the problems of low synchronization precision and slow convergence speed caused by packet loss with existing synchronization methods, the observer equation was introduced to estimate the clock state of the adjacent vehicles in case of packet loss, which reduces the impact of clock error caused by packet loss in the synchronization process and improves the synchronization precision of V2V communication. The research results provide some theoretical references for V2V synchronous wireless communication under 5G-R technology.

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.

Design of Low Probability Detection Signal with Application to Physical Layer Security

In this work, we mainly focus on low probability detection (LPD) and low probability interception (LPI) wireless communication in cyber-physical systems. An LPD signal waveform based on multi-carrier modulation and an under-sampling method for signal detection is introduced. The application of the proposed LPD signal for physical layer security is discussed in a typical wireless-tap channel model, which consists of a transmitter (Alice), an intended receiver (Bob), and an eavesdropper (Eve). Since the under-sampling method at Bob’s end depends very sensitively on accurate sampling clock and channel state information (CSI), which can hardly be obtained by Eve, the security transmission is initialized as Bob transmits a pilot for Alice to perform channel sounding and clock synchronization by invoking the channel reciprocal principle. Then, Alice sends a multi-carrier information-bearing signal constructed according to Bob’s actual sampling clock and the CSI between the two. Consequently, Bob can coherently combine the sub-band signals after sampling, while Eve can only obtain a destructive combination. Finally, we derived the closed-form expressions of detection probability at Bob’s and Eve’s ends when the energy detector is employed. Simulation results show that the bit error rate (BER) at Alice’s end is gradually decreased with the increase in the signal-to-noise ratio (SNR) in both the AWGN and fading channels. Meanwhile, the BER at Eve’s end is always unacceptably high no matter how the SNR changes.

Magnetic Feshbach resonances between atoms in S2 and P03 states: Mechanisms and dependence on atomic properties

Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in $^{2}\mathrm{S}$ and ${}^{3}{\mathrm{P}}_{0}$ states, such as an alkali-metal atom colliding with Yb or Sr in a clock state. We investigate the mechanisms of these resonances and identify the terms in the collision Hamiltonian responsible for them. They involve indirect coupling between the open and closed channels, via intermediate channels involving atoms in ${}^{3}{\mathrm{P}}_{1}$ states. The resonance widths are generally proportional to the square of the magnetic field and are strongly enhanced when the magnitude of the background scattering length is large. For any given pair of atoms, the scattering length can be tuned discretely by choosing different isotopes of the ${}^{3}{\mathrm{P}}_{0}$ atom. For each combination of an alkali-metal atom and either Yb or Sr, we consider the prospects of finding an isotopic combination that has both a large background scattering length and resonances at a high but experimentally accessible field. We conclude that $^{87}\mathrm{Rb}+\mathrm{Yb}$, $\mathrm{Cs}+\mathrm{Yb}$, and $^{85}\mathrm{Rb}+\mathrm{Sr}$ are particularly promising combinations.

Coherence-preserving cooling of nuclear-spin qubits in a weak magnetic field

Nuclear-spin memories of divalent neutral atoms can allow spin-preserving resolved-sideband cooling in a strong magnetic field [I. Reichenbach and I. H. Deutsch, Phys. Rev. Lett. 99, 123001 (2007)]. We present a theory for cooling $^{87}\mathrm{Sr}$ nuclear-spin qubits in a weak magnetic field. The theory depends on laser excitation of $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ to a nearby state which results in ${m}_{J}$-dependent AC Stark shifts large compared to the hyperfine interaction. This effectively suppresses the nuclear-spin mixing due to the hyperfine interaction. Sideband cooling via the clock state quenched by the AC Stark-shifted $^{3}P_{1}$ state leads to nuclear-spin-preserving spontaneous emission back to the ground state. More than being compatible with low magnetic fields, the theory is applicable when the nuclear-spin qubits are defined by the two lowest Zeeman substates.

Robust Time Synchronization for Industrial Internet of Things by H ∞ Output Feedback Control

Precise timing over timestamped packet-exchange communication is an enabling technology in the mission-critical industrial Internet of Things (IIoT), particularly when satellite-based timing is unavailable. The main challenge is to ensure timing accuracy when the clock synchronization system is subject to disturbances caused by the drifting frequency, time-varying delay, jitter, and timestamping uncertainty. In this work, a robust packet-coupled oscillators (R-PkCOs) protocol is proposed to reduce the effects of perturbations manifested in the drifting clock, timestamping uncertainty, and delays. First, in the spanning-tree clock topology, time synchronization between an arbitrary pair of clocks is modeled as a state-space model, where clock states are coupled with each other by one-way timestamped packet exchange (referred to as packet coupling), and the impacts of both drifting frequency and delays are modeled as disturbances. A static output controller is adopted to adjust the drifting clock. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> robust control design solution is proposed to guarantee that the ratio between the modulus of synchronization precision and the magnitude of the disturbances are always less than a given value. Therefore, the proposed time synchronization protocol is robust against the disturbances, which means that the impacts of drifting frequency and delays on the synchronization accuracy are limited. The one-hour experimental results demonstrate that the proposed R-PkCO’s protocol can realize time synchronization with the precision of 6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> in a 21-node IEEE 802.15.4 network. This work has widespread impacts in the process automation of automotive, mining, oil, and gas industries.

Basic elements for simulations of standard-model physics with quantum annealers: Multigrid and clock states

We explore the potential of D-Wave's quantum annealers for computing some of the basic components required for quantum simulations of Standard Model physics. By implementing a basic multigrid (including "zooming") and specializing Feynman-clock algorithms, D-Wave's Advantage is used to study harmonic and anharmonic oscillators relevant for lattice scalar field theories and effective field theories, the time evolution of a single plaquette of SU(3) Yang-Mills lattice gauge field theory, and the dynamics of flavor entanglement in four neutrino systems.

Atomic clocks highly sensitive to the variation of the fine-structure constant based on Hf ii, Hf iv, and W vi ions

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. The cooling electric dipole ($E1$) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using ${\mathrm{Ca}}^{+}$ or ${\mathrm{Sr}}^{+}$ ions. Energy levels; Land\'e $g$ 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 (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory ($\mathrm{CI}+\mathrm{SD}$), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{\ensuremath{-}16}$ and ${10}^{\ensuremath{-}18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{\ensuremath{-}}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\ensuremath{\alpha}$ and may be used to search for dark matter producing this variation of $\ensuremath{\alpha}$. The enhancement coefficient for the $\ensuremath{\alpha}$ variation reaches $K=8.3$. Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.

Coherent and Dephasing Spectroscopy for Single-Impurity Probing of an Ultracold Bath.

We report Ramsey spectroscopy on the clock states of individual Cs impurities immersed in an ultracold Rb bath. We record both the interaction-driven phase evolution and the decay of fringe contrast of the Ramsey interference signal to obtain information about bath density or temperature nondestructively. The Ramsey fringe is modified by a differential shift of the collisional energy when the two Cs states superposed interact with the Rb bath. This differential shift is directly affected by the mean gas density and the details of the Rb-Cs interspecies scattering length, affecting the phase evolution and the contrast of the Ramsey signal. Additionally, we enhance the temperature dependence of the phase shift preparing the system close to a low-magnetic-field Feshbach resonance where the s-wave scattering length is significantly affected by the collisional (kinetic) energy. Analyzing coherent phase evolution and decay of the Ramsey fringe contrast, we probe the Rb cloud's density and temperature. Our results point at using individual impurity atoms as nondestructive quantum probes in complex quantum systems.