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Optical atomic clocks have demonstrated revolutionary advances in precision timekeeping, but their applicability to the real world is critically dependent on whether such clocks can operate outside a laboratory setting. The challenge to clock portability stems from the many obstacles not only in miniaturizing the underlying components of the clock $-$ namely the ultrastable laser, the frequency comb, and the atomic reference itself $-$ but also in making the clock resilient to environmental fluctuations. Photonic integration offers one compelling solution to simultaneously address the problems of miniaturization and ruggedization, but brings with it a new set of challenges in recreating the functionality of an optical clock using chip-scale building blocks. The clock laser used for atom interrogation is one particular point of uncertainty, as the performance of the meticulously-engineered bulk-cavity stabilized lasers would be exceptionally difficult to transfer to chip. Here we demonstrate that a chip-integrated ultrahigh quality factor (Q) spiral cavity, when interfaced with a 1348 nm seed laser, reaches a fractional frequency instability of $7.5 \times 10^{-14}$, meeting the stability requirements for interrogating the narrow-linewidth transition of $^{88}$Sr$^+$ upon frequency doubling to 674 nm. In addition to achieving the record for laser stability on chip, we use this laser to showcase the operation of a Sr-ion clock with short-term instability averaging down as $3.9 \times 10^{-14} / \sqrt{\tau}$, where $\tau$ is the averaging time. Our demonstration of an optical atomic clock interrogated by an integrated spiral cavity laser opens the door for future advanced clock systems to be entirely constructed using lightweight, portable, and mass-manufacturable integrated optics and electronics.

We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped $^{40}\text{Ca}^{+}$ ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the 6-dimensional $\text{D}_{5/2}$ state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding $99\%$ in each case, limited entirely by known experimental imperfections., Comment: Main text: 6 pages, 4 figures. Supplementary Material: 7 pages, 5 figures, 2 tables Fixed a reference and updated publication information

When comparing the performance of multi-armed bandit algorithms, the potential impact of missing data is often overlooked. In practice, it also affects their implementation where the simplest approach to overcome this is to continue to sample according to the original bandit algorithm, ignoring missing outcomes. We investigate the impact on performance of this approach to deal with missing data for several bandit algorithms through an extensive simulation study assuming the rewards are missing at random. We focus on two-armed bandit algorithms with binary outcomes in the context of patient allocation for clinical trials with relatively small sample sizes. However, our results apply to other applications of bandit algorithms where missing data is expected to occur. We assess the resulting operating characteristics, including the expected reward. Different probabilities of missingness in both arms are considered. The key finding of our work is that when using the simplest strategy of ignoring missing data, the impact on the expected performance of multi-armed bandit strategies varies according to the way these strategies balance the exploration-exploitation trade-off. Algorithms that are geared towards exploration continue to assign samples to the arm with more missing responses (which being perceived as the arm with less observed information is deemed more appealing by the algorithm than it would otherwise be). In contrast, algorithms that are geared towards exploitation would rapidly assign a high value to samples from the arms with a current high mean irrespective of the level observations per arm. Furthermore, for algorithms focusing more on exploration, we illustrate that the problem of missing responses can be alleviated using a simple mean imputation approach., Comment: 30 pages, 6 figures

Comparisons of high-accuracy optical atomic clocks \cite{Ludlow2015} are essential for precision tests of fundamental physics \cite{Safronova2018}, relativistic geodesy \cite{McGrew2018, Grotti2018, Delva2019}, and the anticipated redefinition of the SI second \cite{Riehle2018}. The scientific reach of these applications is restricted by the statistical precision of interspecies comparison measurements. The instability of individual clocks is limited by the finite coherence time of the optical local oscillator (OLO), which bounds the maximum atomic interrogation time. In this letter, we experimentally demonstrate differential spectroscopy \cite{Hume2016}, a comparison protocol that enables interrogating beyond the OLO coherence time. By phase-coherently linking a zero-dead-time (ZDT) \cite{Schioppo2017} Yb optical lattice clock with an Al$^+$ single-ion clock via an optical frequency comb and performing synchronised Ramsey spectroscopy, we show an improvement in comparison instability relative to our previous result \cite{network2020frequency} of nearly an order of magnitude. To our knowledge, this result represents the most stable interspecies clock comparison to date.

Sample size derivation is a crucial element of the planning phase of any confirmatory trial. A sample size is typically derived based on constraints on the maximal acceptable type I error rate and a minimal desired power. Here, power depends on the unknown true effect size. In practice, power is typically calculated either for the smallest relevant effect size or a likely point alternative. The former might be problematic if the minimal relevant effect is close to the null, thus requiring an excessively large sample size. The latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect size. A Bayesian perspective on the sample size derivation for a frequentist trial naturally emerges as a way of reconciling arguments about the relative a priori plausibility of alternative effect sizes with ideas based on the relevance of effect sizes. Many suggestions as to how such `hybrid' approaches could be implemented in practice have been put forward in the literature. However, key quantities such as assurance, probability of success, or expected power are often defined in subtly different ways in the literature. Starting from the traditional and entirely frequentist approach to sample size derivation, we derive consistent definitions for the most commonly used `hybrid' quantities and highlight connections, before discussing and demonstrating their use in the context of sample size derivation for clinical trials.

Response-Adaptive Randomization (RAR) is part of a wider class of data-dependent sampling algorithms, for which clinical trials are typically used as a motivating application. In that context, patient allocation to treatments is determined by randomization probabilities that change based on the accrued response data in order to achieve experimental goals. RAR has received abundant theoretical attention from the biostatistical literature since the 1930's and has been the subject of numerous debates. In the last decade, it has received renewed consideration from the applied and methodological communities, driven by well-known practical examples and its widespread use in machine learning. Papers on the subject present different views on its usefulness, and these are not easy to reconcile. This work aims to address this gap by providing a unified, broad and fresh review of methodological and practical issues to consider when debating the use of RAR in clinical trials., Comment: Update in response to editor comments

We describe the design and fabrication of a scalable atom-light photonic interface based on a silicon nitride microring resonator on a transparent silicon dioxide-nitride multi-layer membrane. This new photonic platform is fully compatible with freespace cold atom laser cooling, stable trapping, and sorting at around $100~$nm from the microring surface, permitting the formation of an organized, strongly interacting atom-photonic hybrid lattice. We demonstrate small radius ($R\sim$16$\mu$m) microring and racetrack resonators with a high quality factor $Q=3.2\times 10^5$, projecting a single atom cooperativity parameter of $C=25$ and a vacuum Rabi frequency of $2g= 2\pi\times 340~$MHz for trapped cesium atoms interacting with a microring resonator mode. We show that the quality factor is currently limited by the surface roughness of the multi-layer membrane, grown using low pressure chemical vapor deposition (LPCVD) processes. We discuss possible further improvements to a quality factor above $Q>5\times10^6$, potentially achieving single atom cooperativity parameter of $C > 500$ for strong single atom-photon coupling., Comment: 15 pages, 12 figures

Trapped atoms near nanophotonics form an exciting platform for bottom-up synthesis of strongly interacting quantum matter. The ability to induce tunable long-range atom-atom interactions with photons presents an opportunity to explore many-body physics and quantum optics. Here we implement a configurable optical tweezer array over a planar photonic circuit tailored for cold atom integration and control for trapping and high-fidelity imaging of one or more atoms in an array directly on a photonic structure. Using an optical conveyor belt formed by a moving optical lattice within a tweezer potential, we show that single atoms can be transported from a reservoir into close proximity of a photonic interface, potentially allowing for the synthesis of a defect-free atom-nanophotonic hybrid lattice. Our experimental platform can be integrated with generic planar photonic waveguides and resonators, promising a pathway towards on-chip many-body quantum optics and applications in quantum technology., Comment: 10 pages, 8 figures

Photoassociation (PA) is a powerful technique to synthesize molecules directly and continuously from cold and ultracold atoms into deeply bound molecular states. In freespace, however, PA efficiency is constrained by the number of spontaneous decay channels linking the initial excited molecular state to a sea of final (meta)stable rovibronic levels. Here, we propose a novel scheme based on molecules strongly coupled to a guided photonic mode in a photonic crystal waveguide that turns PA into a powerful tool for near deterministic formation of ultracold molecules in their ground rovibrational level. Our example shows a potential ground state molecule production efficiency $> 90\%$, and a saturation rate $>10^6$ molecules per second. By combining state-of-the-art cold atomic and molecular physics with nanophotonic engineering, our scheme presents a novel experimental package for trapping, cooling, and optical manipulation of ultracold molecules, opening up new possibilities in the direction of ultracold chemistry and quantum information.

We describe a collective state atomic interferometer (COSAIN) with the signal fringe as a function of phase-difference or rotation narrowed by $\sqrt{N}$ compared to a conventional interferometer - $N$ being the number of atoms - without entanglement. This effect arises from the interferences among collective states, and is a manifestation of interference at a Compton frequency of ten nonillion Hz, or a de Broglie wavelength of ten attometer, for $N=10^6$ and $v = 300 m/s$. The population of the collective state of interest is detected by a null measurement scheme, in which an event corresponding to detection of zero photons corresponds to the system being in that particular collective state. The signal is detected by collecting fluorescence through stimulated Raman scattering of Stokes photons, which are emitted predominantly against the direction of the probe beam, for a high enough resonant optical density. The sensitivity of the ideal COSAIN is found to be given by the standard quantum limit. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAIN increases the quantum efficiency of detection significantly in comparison to a typical conventional Raman atomic interferometer employing fluorescence detection, yielding a net improvement in stability by as much as a factor of $10$. We discuss how the inhomogeneities arising from the non-uniformity in experimental parameters affect the COSAIN signal. We also describe an alternate experimental scheme to enhance resonant optical density in a COSAIN by using cross-linearly polarized counter-propagating Raman beams., Comment: As will appear in Physical Review A

We describe a collective state atomic clock with Ramsey fringes narrowed by a factor of $\sqrt{N}$ compared to a conventional clock, N being the number of non-interacting atoms, without violating the uncertainty relation. This narrowing is explained as being due to interferences among the collective states, representing an effective $\sqrt{N}$ fold increase in the clock frequency, without entanglement. The detection process, which measures a collective state, can be used to increase the quantum efficiency of detection significantly, yielding a net improvement in stability by as much as a factor of 10.

Previously, we had proposed the technique of light shift imbalance induced blockade which leads to a condition where a collection of non-interacting atoms under laser excitation remains combined to a superposition of the ground and the first excited states, thus realizing a collective state quantum bit which in turn can be used to realize a quantum computer. In this paper, we show first that the light shift imbalance by itself is actually not enough to produce such a blockade, and explain the reason why the limitation of our previous analysis had reached this constraint. We then show that by introducing Rydberg interaction, it is possible to achieve such a blockade for a wide range of parameters. Analytic arguments used to establish these results are confirmed by numerical simulations. The fidelity of coupled quantum gates based on such collective state qubits is highly insensitive to the exact number of atoms in the ensemble. As such, this approach may prove to be viable for scalable quantum computing based on neutral atoms., Comment: 12 pages with 12 figures

We investigate the behavior of an ensemble of $N$ non-interacting, identical atoms, excited by a laser. In general, the $i$-th atom sees a Rabi frequency $\Omega_i$, an initial position dependent laser phase $\phi_i$, and a motion induced Doppler shift of $\delta_i$. When $\Omega_i$ or $\delta_i$ is distinct for each atom, the system evolves into a superposition of $2^N$ intercoupled states, of which there are $N+1$ symmetric and $(2^N-(N+1))$ asymmetric collective states. For a collective state atomic interferometer (COSAIN) we recently proposed, it is important to understand the behavior of all the collective states under various conditions. In this paper, we show how to formulate the properties of these states under various non-idealities, and use this formulation to understand the dynamics thereof. We also consider the effect of treating the center of mass degree of freedom of the atoms quantum mechanically on the description of the collective states, illustrating that it is indeed possible to construct a generalized collective state, as needed for the COSAIN, when each atom is assumed to be in a localized wave packet. The analysis presented in this paper is important for understanding the dynamics of the COSAIN, and will help advance the analysis and optimization of spin squeezing in the presence of practically unavoidable non-idealities as well as in the domain where the center of mass motion of the atoms is quantized., Comment: Title, abstract and text edited

Previously, we proposed a data buffering system that makes use of a pair of white light cavities. For application to telecommunication systems, it would be convenient to realize such a device using fiber optic resonators. In this paper, we present the design of such a system, where the white light cavity effect is produced by using stimulated Brillouin scattering. The system consists of a pair of fiber optic white light cavities placed in series. As in the original proposal, the delay time can be controlled independently of the bandwidth of the data pulses. Furthermore, we show how the bandwidth of the system can be made as large as several times the Brillouin frequency shift. We also show that the net delay achievable in such a buffer can be significantly larger than what can be achieved using a conventional recirculating loop buffer., Comment: 13 pages, 8 figures