Microchip-Based Trapped-Atom Clocks

超越十小时的相干性在去相干自由的囚禁离子钟量子比特中

Beyond-Ten-Hour Coherence in a Decoherence-Free Trapped-Ion Clock Qubit

本文通过结合钟态量子比特与去相干自由子空间编码，实现了超过十小时的相干性，突破了传统技术限制，为可扩展的量子信息处理奠定了基础。

Ensemble master equation for a trapped-atom clock with one- and two-body losses

An ensemble density matrix model that includes one- and two-body losses is derived for a trapped-atom clock. A trapped-atom clock is mainly affected by one- and two-body losses, generally giving nonexponential decays of populations; nevertheless, three-body recombination is also quantitatively analyzed to demonstrate the boundaries of its practical relevance. The importance of one-body losses is highlighted without which population trapping behavior would be observed. The model is written with decay constants expressed through experimental parameters. It can complement, e.g., the ISRE (identic…

Magic wavelengths for lattice trapped Rubidium four-level active optical clock

After pumped from $5s_{1/2}$ ground state to $6p_{1/2}$ state, the population inversion between $6s_{1/2}$ and $5p_{1/2,3/2}$ will be established for Rubidium four-level active optical clock. In this paper, we calculate AC Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in lattice trapped Rubidium four-level active optical clock. Several magic wavelengths are found that can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of trapping laser, the fractional frequency uncertainty of clock transition due…

"Magic" radio-frequency dressing for trapped atomic microwave clocks

It has been proposed to use magnetically trapped atomic ensembles to enhance the interrogation time in microwave clocks. To mitigate the perturbing effects of the magnetic trap, near-magic-field configurations are employed, where the involved clock transition becomes independent of the atom's potential energy to first order. Still, higher order effects are a dominating source for dephasing, limiting the performance of this approach. Here we propose a simple method to cancel the energy dependence to both first and second order, using weak radio-frequency dressing. We give values for dressing fr…

原位差分光移消除用于囚禁原子钟

In-Situ Differential-Light-Shift Cancellation for Trapped-Atom Clocks

本文提出一种原位方法消除由光学囚禁场引起的差分光移，通过同时探测不同囚禁强度的原子团，利用Ramsey光谱测量并外推至零强度极限，实现无光移频率的确定，适用于铷原子在时间平均势中的验证。

囚禁离子光钟中质量亏损和时间膨胀的从头算量子理论

Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks

本文从头推导了电磁束缚两粒子系统的相对论哈密顿量，应用于Paul阱冷离子，系统量子力学地处理了离子钟中的相对论频移，澄清了时间膨胀与质量亏损的作用。

Stability of a trapped atom clock on a chip

We present a compact atomic clock interrogating ultracold 87Rb magnetically trapped on an atom chip. Very long coherence times sustained by spin self-rephasing allow us to interrogate the atomic transition with 85% contrast at 5 s Ramsey time. The clock exhibits a fractional frequency stability of $5.8\times 10^{-13}$ at 1 s and is likely to integrate into the $1\times10^{-15}$ range in less than a day. A detailed analysis of 7 noise sources explains the measured frequency stability. Fluctuations in the atom temperature (0.4 nK shot-to-shot) and in the offset magnetic field ($5\times10^{-6}$ r…

自主多离子光学钟与芯片集成光子光交付

Autonomous multi-ion optical clock with on-chip integrated photonic light delivery

本研究展示了一种自主多离子光学钟，通过芯片集成光子技术实现高稳定性的频率控制，为便携式量子传感器和计算机提供新架构。

Extended coherence time on the clock transition of optically trapped Rubidium

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of Rb-87 by applying the recently discovered spin self-rephasing. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a s…

Improved estimate of the collisional frequency shift in Al$^+$ optical clocks

Collisions between background gas particles and the trapped ion in an atomic clock can subtly shift the frequency of the clock transition. The uncertainty in the correction for this effect makes a significant contribution to the total systematic uncertainty budget of trapped-ion clocks. Using a non-perturbative analytic framework that was developed for this problem, we estimate the frequency shift in Al$^+$ ion clocks due to collisions with helium and hydrogen. Our calculations significantly improve the uncertainties in the collisional shift coefficients, and show that the collisional frequenc…

Robust optical clock transitions in trapped ions

We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions,…

Quantum Algorithmic Readout in Multi-Ion Clocks

Optical clocks based on ensembles of trapped ions offer the perspective of record frequency uncertainty with good short-term stability. Most suitable atomic species lack closed transitions for fast detection such that the clock signal has to be read out indirectly through transferring the quantum state of clock ions to co-trapped logic ions by means of quantum logic operations. For ensembles of clock ions existing methods for quantum logic readout require a linear overhead in either time or the number of logic ions. Here we report a quantum algorithmic readout whose overhead scales logarithmic…

Analysis of a Cesium lattice optical clock

We propose and analyze a Cesium lattice optical clock (CLOC) which has the potential for high performance and simple operation in a compact form factor using a forbidden optical transition in Cs atoms at 685 nm. Cs atoms are trapped in a 3D optical lattice using a magic trap wavelength of $λ_{\textrm m}=803~\textrm nm$. To reduce sensitivity to magnetic fields the atoms are probed on two cycling transitions with equal magnitude, but opposite magnetic shifts. Operation of the clock requires only three diode lasers at 685, 803, 852 nm and is simplified compared to other higher-performance optica…

Precise determination of micromotion for trapped-ion optical clocks

As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low $10^{-18}$ range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in th…

Mass-energy equivalence in harmonically trapped particles

Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators. Here we present a framework to systematically include quantum effects arising from the mass-energy equivalence in harmonically trapped systems. We find that the mass-energy equivalence leads to squeezing, displacement and frequency changes of harmonic modes associated with different internal energies. The framework predicts new phenomena, notably, the existence of a lower bound to the fractional frequency shift in atomic clocks arising from the…

Non-Destructive Probing of Rabi Oscillations on the Cesium Clock Transition near the Standard Quantum Limit

We report on non-destructive observation of Rabi oscillations on the Cs clock transition. The internal atomic state evolution of a dipole-trapped ensemble of cold atoms is inferred from the phase shift of a probe laser beam as measured using a Mach-Zehnder interferometer. We describe a single color as well as a two-color probing scheme. Using the latter, measurements of the collective pseudo-spin projection of atoms in a superposition of the clock states are performed and the observed spin fluctuations are shown to be close to the standard quantum limit.

Optically trapped atom interferometry using the clock transition of large Rb-87 Bose-Einstein condensates

We present a Ramsey-type atom interferometer operating with an optically trapped sample of 10^6 Bose-condensed Rb-87 atoms. The optical trap allows us to couple the |F =1, mF =0>\rightarrow |F =2, mF =0> clock states using a single photon 6.8GHz microwave transition, while state selective readout is achieved with absorption imaging. Interference fringes with contrast approaching 100% are observed for short evolution times. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the at…

一种基于量子逻辑的利用移动光晶格进行囚禁离子极化率测量精度转移的方案

A scheme for quantum-logic based transfer of accuracy in polarizability measurement for trapped ions using a moving optical lattice

针对囚禁离子光原子钟受黑体辐射影响产生钟跃迁频移、现有极化率测量受激光功率校准精度限制的问题，提出基于量子逻辑的极化率测量精度转移方案，无需高精度激光功率校准，还可参照类氢离子实现高精度极化率转移。

Colloquium: Physics of optical lattice clocks

Recently invented and demonstrated, optical lattice clocks hold great promise for improving the precision of modern timekeeping. These clocks aim at the 10^-18 fractional accuracy, which translates into a clock that would neither lose or gain a fraction of a second over an estimated age of the Universe. In these clocks, millions of atoms are trapped and interrogated simultaneously, dramatically improving clock stability. Here we discuss the principles of operation of these clocks and, in particular, a novel concept of "magic" trapping of atoms in optical lattices. We also highlight recently pr…

Controlling systematic frequency uncertainties at the $10^{-19}$ level in linear Coulomb crystals

Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertain…

量子时间的光学离子钟特征

Quantum signatures of proper time in optical ion clocks

本文研究了光学离子钟中量子时间效应，通过哈密顿形式推导了谐振子中时间膨胀效应，并展示了真空能量、压缩和量子修正对二次多普勒移位的影响，证明了量子时间干涉测量的可能性。

Quantum Lock-in Force Sensing using Optical Clock Doppler Velocimetry

Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing \cite{RMPforce2003, Rugar2004, YazdiIEEE}. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. Examples for such mechanical oscillators include micro-fabricated cantilevers \cite{YazdiIEEE}, carbon nanotubes \cite{NanotubeForce} as well as single trapped ions \cite{Bollinger, Udem} . The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator thus inc…

Controlling dipole-dipole frequency shifts in a lattice-based optical atomic clock

Motivated by the ideas of using cold alkaline earth atoms trapped in an optical lattice for realization of optical atomic clocks, we investigate theoretically the perturbative effects of atom-atom interactions on a clock transition frequency. These interactions are mediated by the dipole fields associated with the optically excited atoms. We predict resonance-like features in the frequency shifts when constructive interference among atomic dipoles occur. We theoretically demonstrate that by fine-tuning the coherent dipole-dipole couplings in appropriately designed lattice geometries, the undes…

Ultra-cold mechanical resonators coupled to atoms in an optical lattice

We propose an experiment utilizing an array of cooled micro-cantilevers coupled to a sample of ultra-cold atoms trapped near a micro-fabricated surface. The cantilevers allow individual lattice site addressing for atomic state control and readout, and potentially may be useful in optical lattice quantum computation schemes. Assuming resonators can be cooled to their vibrational ground state, the implementation of a two-qubit controlled-NOT gate with atomic internal states and the motional states of the resonator is described. We also consider a protocol for entangling two or more cantilevers o…

Precision measurements with cold atoms and trapped ions

Recent progresses on quantum control of cold atoms and trapped ions in both the scientific and technological aspects greatly advance the applications in precision measurement. Thanks to the exceptional controllability and versatility of these massive quantum systems, unprecedented sensitivity has been achieved in clocks, magnetometers and interferometers based on cold atoms and ions. Besides, these systems also feature many characteristics that can be employed to facilitate the applications in different scenarios. In this review, we briefly introduce the principles of optical clocks, cold atom…

观测自旋交换碰撞下的自旋压缩态长达一秒

Observing spin-squeezed states under spin-exchange collisions for a second

利用芯片上的囚禁原子钟平台，观测到超冷铷原子自旋压缩态在长达1秒时间尺度上的演化，并发现自旋交换相互作用增强腔自旋测量的效应，为压缩增强原子钟开辟前景。

Active Frequency Measurement on Superradiant Strontium Clock Transitions

We develop a stochastic mean-field theory to describe active frequency measurements of pulsed superradiant emission, studied in recent experiments with strontium-87 atoms trapped in an optical lattice inside an optical cavity [M. Norcia, et al., Phys. Rev. X 8, 21036 (2018)]. Our theory reveals the intriguing dynamics of atomic ensembles with multiple transition frequencies, and it reproduces the superradiant beats signal, noisy power spectra, and frequency uncertainty in remarkable agreement with the experiments. Moreover, by reducing the number of atoms, elongating the superradiant pulses an…

Exponential scaling of clock stability with atom number

In trapped-atom clocks, the primary source of decoherence is often the phase noise of the oscillator. For this case, we derive theoretical performance gains by combining several atomic ensembles. For example, M ensembles of N atoms can be combined with a variety of probe periods, to reduce the frequency variance to M 2^-M times that of standard Ramsey clocks. A similar exponential improvement is possible if the atomic phases of some of the ensembles evolve at reduced frequencies. These ensembles may be constructed from atoms or molecules with lower-frequency transitions, or generated by dynami…

Quantum noise limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition

We investigate theoretically and experimentally a nondestructive interferometric measurement of the state population of an ensemble of laser cooled and trapped atoms. This study is a step towards generation of (pseudo-) spin squeezing of cold atoms targeted at the improvement of the Caesium clock performance beyond the limit set by the quantum projection noise of atoms. We calculate the phase shift and the quantum noise of a near resonant optical probe pulse propagating through a cloud of cold 133Cs atoms. We analyze the figure of merit for a quantum non-demolition (QND) measurement of the col…

Superradiant Cooling, Trapping, and Lasing of Dipole-Interacting Clock Atoms

A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such …

Superradiance on the milliHertz linewidth strontium clock transition

Today's best atomic clocks are limited by frequency noise on the lasers used to interrogate the atoms. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock, and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. Here, we demonstrate and characterize superradiant emission from the mHz linewidth clock transition in an ensemble of laser-cooled $^{87}$Sr atoms trapped within a high-finesse optical cavity. We measure a collective en…

采用可扩展光子调制器的高保真囚禁离子量子比特操作

High-fidelity trapped-ion qubit operations with scalable photonic modulators

针对囚禁离子实验传统光调制器难规模化的问题，研究团队设计制备了可与表面电极离子阱单片集成的压电光机光子多级Mach-Zehnder调制器，经量子层析表征实现了超99.7%的单量子比特门保真度。

使用共陷俘超冷原子在百万分之几水平测量基态87Sr的g因子

Measurement of the g factor of ground-state 87Sr at the parts-per-million level using co-trapped ultracold atoms

利用共陷俘超冷87Rb原子的方案，将基态超冷87Sr核g因子的测量精度提升至百万分之几水平，确立了其作为优异真空内磁强计的地位，并适用于量子模拟、计算和光原子钟等领域。

Coherence properties of nanofiber-trapped cesium atoms

We experimentally study the ground state coherence properties of cesium atoms in a nanofiber-based two-color dipole trap, localized 200 nm away from the fiber surface. Using microwave radiation to coherently drive the clock transition, we record Ramsey fringes as well as spin echo signals and infer a reversible dephasing time $T_2^\ast=0.6$ ms and an irreversible dephasing time $T_2^\prime=3.7$ ms. By theoretically modelling the signals, we find that, for our experimental parameters, $T_2^\ast$ and $T_2^\prime$ are limited by the finite initial temperature of the atomic ensemble and the heatin…

用囚禁原子干涉仪观测质能等价

Witnessing mass-energy equivalence with trapped atom interferometers

提出在原子干涉仪中增加激光脉冲以建立高度叠加态时钟，通过观测可见度调制和原子共振频率偏移来检验质能等价引发的引力时间膨胀与量子叠加的相互作用。

Gravitational Redshift Tests with Atomic Clocks and Atom Interferometers

Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i.) Contributions beyond linear order to …

An atomic array optical clock with single-atom readout

Currently, the most accurate and stable clocks use optical interrogation of either a single ion or an ensemble of neutral atoms confined in an optical lattice. Here, we demonstrate a new optical clock system based on an array of individually trapped neutral atoms with single-atom readout, merging many of the benefits of ion and lattice clocks as well as creating a bridge to recently developed techniques in quantum simulation and computing with neutral atoms. We evaluate single-site resolved frequency shifts and short-term stability via self-comparison. Atom-by-atom feedback control enables dir…

圆形里德堡原子内部的离子时钟量子比特

An ionic clock qubit inside a circular Rydberg atom

该研究构建了双离子-里德堡系统，利用同一碱土原子的两个电子编码两个量子比特，实现了相干耦合与类莫尔默-瑟伦森门操作，为量子模拟和计量学提供了新途径。

Optimized geometries for future generation optical lattice clocks

Atoms deeply trapped in magic wavelength optical lattices provide a Doppler- and collision-free dense ensemble of quantum emitters ideal for high precision spectroscopy. Thus, they are the basis of some of the best optical clock setups to date. However, despite their minute optical dipole moments the inherent long range dipole-dipole interactions in such lattices generate line shifts, dephasing and modified decay. We show that in a perfectly filled lattice these effects are resonantly enhanced depending on lattice constant, lattice geometry and excitation scheme inducing clock shifts of many a…

Inelastic collisions and density-dependent excitation suppression in a ${}^{87}$Sr optical lattice clock

We observe two-body loss of ${}^3P_0$ ${}^{87}$Sr atoms trapped in a one-dimensional optical lattice. We measure loss rate coefficients for atomic samples between 1 and 6 $μ$K that are prepared either in a single nuclear-spin-sublevel or with equal populations in two sublevels. The measured temperature and nuclear spin preparation dependence of rate coefficients agree well with calculations and reveal that rate coefficients for distinguishable atoms are only slightly enhanced over those of indistinguishable atoms. We further observe a suppression of excitation and losses during interrogation o…

High precision differential clock comparisons with a multiplexed optical lattice clock

Rapid progress in the precision and accuracy of optical atomic clocks over the last decade has advanced the frontiers of timekeeping, metrology, and quantum science. However, the stabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves, leaving room for further progress. Here we implement a "multiplexed" one-dimensional optical lattice clock, in which spatially-resolved, movable ensembles of ultra-cold strontium atoms are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser, and read-out in parallel. By perfo…

A tweezer clock with half-minute atomic coherence at optical frequencies and high relative stability

The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is foundational for many studies in quantum metrology, simulation, and information. Here, we realize these features by leveraging the favorable properties of tweezer-trapped alkaline-earth atoms while introducing a new, hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout, and preservation of atomic coherence. With this approach, we achieve trapping and optical clock excited-state lifetimes exceeding $ 40 $ seconds in ensembl…

扩展原子钟稳定性的基本极限

Extending the fundamental limit of atomic clock stability

本文提出多能级原子模型，改进了原子钟稳定性计算，通过考虑量子投影噪声和自发辐射，提升了频率稳定性达4.5dB，并在奇宇称贝尔态原子间频率比较中进一步提升至5.4dB。

A trapped single ion inside a Bose-Einstein condensate

Improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms and coherent light-matter interfaces have been built. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms and to detect variations of fundamental constants in precision atomic clocks. Until now, atomic quantum gases and single trapped ions have been treated sepa…