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 direct experimental estimation of laser noise contributions. Results agree well with an ab initio Monte Carlo simulation that incorporates finite temperature, projective readout, laser noise, and feedback dynamics. Our approach, based on a tweezer array, also suppresses interaction shifts while retaining a short dead time, all in a comparatively simple experimental setup suited for transportable operation. These results establish the foundations for a third optical clock platform and provide a novel starting point for entanglement-enhanced metrology, quantum clock networks, and applications in quantum computing and communication with individual neutral atoms that require optical-clock-state control.

Popular Summary

Optical clocks have surpassed traditional microwave clocks in both stability and accuracy. They enable new experiments in geodesy, fundamental physics, and quantum many-body physics, in addition to a prospective redefinition of the second. Current optical clocks either interrogate a single ion or an ensemble of lattice-trapped atoms. Ideally, one could merge the benefits of these platforms by developing a clock based on a large array of isolated atoms that can be read out and controlled individually. As a major advance in this direction, we present an atomic-array optical clock with a single-atom-resolved readout of 40 individually trapped neutral atoms.

This new platform benefits from both a large and scalable number of atoms as well as the ability to prepare and read out individual isolated atoms. The latter capability avoids interaction shifts that degrade clock performance and enables the characterization of clock performance on the single-atom level. Specifically, we can measure inhomogeneous systematic errors across the array, and we propose a scheme leveraging single-atom readout to correct for them. We further study how varying the number of atoms contributes to clock stability.

Further, our work enables a myriad of new applications. Specifically, it provides atom-by-atom error evaluation, feedback, and thermometry; facilitates quantum metrology applications, such as quantum-enhanced clocks and clock networks; and enables novel quantum computation, simulation, and communication architectures that require optical-clock-state control combined with single-atom trapping.

Figure 1

Atomic array optical clock. (a) We interrogate about 40 ${}^{88}\mathrm{Sr}$ atoms, trapped in an 81-site tweezer array, on the ultranarrow clock transition at 698 nm and use high-resolution fluorescence imaging at 461 nm to detect population changes in the clock states (labeled $|g⟩$ and $|e⟩$) with single-atom resolution. This information is processed by a central processing unit (CPU), and a feedback signal is applied to the clock laser frequency using an acousto-optic modulator (AOM). (b) Tweezer-averaged probability to remain in $|g⟩$ as a function of frequency offset measured with an in-loop probe sequence (circles). Dashed horizontal lines indicate state-resolved detection fidelities (Appendix pp2-s5). To generate an error signal, we interrogate twice: once below ($A$) and once above ($B$) resonance. (c) Tweezer-averaged error signal as a function of frequency offset (circles). The shaded areas in (b) and (c) show results from MC simulations. (d) Simplified experimental sequence, consisting of tweezer loading and $N$-times-repeated $AB$ feedback blocks followed by an optional probe block, with $N=10$ throughout. (e) To detect the clock state population in block $A$, we take a first image before interrogation to identify which tweezers are occupied and a second image after interrogation to detect which atoms remain in $|g⟩$ (images 1 and 2). The same procedure is repeated for block $B$ (images 3 and 4). We show fluorescence images with identified atoms (circles) (Appendix pp2-s4) and examples of single tweezer error signals $e_j$.

Figure 2

Site-resolved error signal. (a) Repetition-averaged single-tweezer error signal $⟨e_j⟩$ as a function of frequency offset measured with an in-loop sequence. (b) Fitted zero crossings as a function of tweezer index for our usual interrogation trap depth of $U_1=245(31)E_r$, where $E_r=h\times 3.43\mathrm{kHz}$ (circles). Solid lines correspond to theory predictions, with the shaded area resulting from systematic uncertainty in trap depth (Appendix pp5). (c) Ternary probability distribution for $e_j$ for a selected tweezer. The vertical dashed line shows the mean. (d) Variance of the error signal as a function of atom number, calculated through postselection. The solid line is a fit with a $1/N_A$ function plus an offset. The purple region is a MC simulation. (e) Plot of correlations between the error signals of even and odd sites.

Figure 3

Systematic evaluation of clock shifts with tweezer depth and wavelength. (a) Illustration of interleaved self-comparison, where two independent AOM frequencies ($f_1$ and $f_2$) are updated in an alternating fashion. Respective interrogation blocks are set to two independent tweezer depths $U_1$ and $U_2$. (b) Average frequency difference $f_2-f_1$ as a function of $U_2/U_1$, with $U_1$ fixed to our usual interrogation depth, for multiple frequency offsets of the trapping laser (see legend for color coding). We fit the data with a model for light shifts in optical tweezers (colored lines) with only a single free parameter (for all data simultaneously), accounting for an unknown frequency offset (Appendix pp5). Operational magic intensities are found at the minima of these curves (gray squares and connecting line), which minimize the sensitivity to trap-depth fluctuations. The trap laser frequency is tuned such that the minimum coincides with our nominal depth. (c) Combining this technique with the single-tweezer-resolved error $⟨e_j⟩$, we can extract a frequency dependence with trap depth for each tweezer (colored squares). Solid lines show the expected dependence for the outermost and central tweezers. The data correspond to the $-7\mathrm{MHz}$ set in (b). Inset: Local frequency shifts for $U_2/U_1=10$. The color coding of the inset defines the color coding of its subfigure.

Figure 4

Stability results. (a) Fractional Allan deviation ${\sigma }_y$ obtained via self-comparison as a function of integration time $\tau$ (circles). Fitting a $1/\sqrt{\tau }$ behavior past an initial lock onset time (red solid line), we find $2.5\times {10}^{-15}/\sqrt{\tau }$. The shaded area denotes MC results. The purple solid line shows the quantum projection noise limit obtained from MC by switching off all other noise sources. (b) Based on atom-by-atom feedback control, we perform a series of self-comparisons with fixed atom number $N_A$. Shown is the Allan variance ${\sigma }_y^2$ at 1 second (from a $1/\sqrt{\tau }$ fit) as a function of $N_A$. Inset: Allan variance ${\sigma }_y^2$ as a function of $1/N_A$. Solid lines show a fit with a functional form ${\sigma }_y^2={\sigma }_{\infty }^2+{\sigma }_{N_A}^2$, where ${\sigma }_{N_A}$ scales as $1/\sqrt{N_A}$.

Figure 5

Frequency noise spectrum of the clock laser. Power spectral density of the frequency noise of our clock laser measured from a beat signal with a reference laser over a 42-hour period (red trace). Our theoretical estimate of the thermal noise contribution is plotted in yellow. We also plot our best-case (purple) and worst-case (blue) models for total frequency noise, as used in Monte Carlo simulations.

Figure 6

Rabi oscillations on the clock transition with $\pi$-pulse length of 110 ms. Each point is probed directly after stabilizing the clock laser with a feedback sequence as described in the main text. The shaded area denotes Monte Carlo results.

Figure 7

Clock sideband thermometry. Array-averaged radial sideband spectrum of the optical clock transition, taken with a carrier Rabi frequency of approximately 360 Hz. A narrow carrier stands in between two broader sidebands on the red and blue detuned sides. Sideband broadening is due mainly to small inhomogeneities in the array. A suppressed red sideband indicates significant motional ground-state population. The solid line is a simultaneous fit to two skewed Gaussians. From the ratio of the area under the red sideband to that under the blue sideband, we obtain $\overline{n}\approx 0.66$. The carrier is probed for an interrogation time of 1.4 ms, while the sidebands are probed for 3.3 ms.

Figure 8

Spatially resolved clock comparison. The fractional Allan deviation from an asynchronous clock comparison between the left and right halves of our array. Fitting a $1/\sqrt{\tau }$ behavior past an initial lock onset time, we find $3.1\times {10}^{-15}/\sqrt{\tau }$, slightly higher than the result measured for a self-comparison of the full array (Fig. 4). Importantly, we see no upturn for times approaching $10^4\mathrm{s}$ and below the ${10}^{-16}$ level, indicating that slowly varying drifts of gradients across the array do not contribute to instability up to our sensitivity.