A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2–12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10–12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16. Boson sampling using ultracold atoms in a two-dimensional, tunnel-coupled optical lattice is enabled by high-fidelity programmable control with optical tweezers of a large number of atoms trapped in an optical lattice.

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor. Optical atomic clocks, the current state-of-the-art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology. Augmenting tweezer-based clocks featuring microscopic control and detection with the high-fidelity entangling gates developed for atom-array information processing offers a promising route towards leveraging highly entangled quantum states for improved optical clocks. Here we develop and employ a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 9 optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit using GHZ states of up to 4 qubits. However, due to their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared to unentangled atoms. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.

Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions. For example, these capabilities have been leveraged for state-of-the-art frequency metrology as well as microscopic studies of entangled many-particle states. In this work, we combine these applications to realize spin squeezing - a widely studied operation for producing metrologically useful entanglement - in an optical atomic clock based on a programmable array of interacting optical qubits. In this first demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost 4 dB of metrological gain. Additionally, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional frequency stability of $1.087(1)\times 10^{-15}$ at one-second averaging time, which is 1.94(1) dB below the standard quantum limit, and reaches a fractional precision at the $10^{-17}$ level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts in order to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock opens the door to a wide range of quantum-information inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks.

Quantum walks provide a framework for designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. We do this by combining the fast, programmable control provided by optical tweezers with the scalable, homogeneous environment of an optical lattice. With these tools we study continuous-time quantum walks of single atoms on a square lattice and perform proof-of-principle demonstrations of spatial search with these walks. When scaled to more particles, the capabilities demonstrated can be extended to study a variety of problems in quantum information science, including performing more effective versions of spatial search using a larger graph with increased connectivity.

Dataset for main figures in "Long-lived Bell states in an array of optical clock qubits".

We present a continuous-wave, 810 nm laser with watt-level powers. Our system is based on difference-frequency generation of 532 nm and 1550 nm fiber lasers in a single pass through periodically poled lithium niobate (PPLN). We measure the broadband spectral noise and residual intensity noise to be compatible with off-resonant dipole trapping of ultracold atoms. Given the large bandwidth of the fiber amplifiers, the output can be optimized for a range of wavelengths, including the strontium clock-magic wavelength of 813 nm. Furthermore, with the exploration of more appropriate nonlinear crystals, we believe there is a path toward scaling this proof-of-principle design to many watts of power, and that this approach could provide a robust, rack-mountable trapping-laser for future use in strontium-based optical clocks.

We have experimentally investigated the influence of repeated laser pulses on laser-induced breakdown (LIB) in water following a focused 1064 nm laser pulse, for repetition rates between 0.5 and 20 Hz and up to 100 pulses. LIB plasma image data are collected as a function of repetition rate and laser pulse number, using an intensified CCD camera with sub-nanosecond camera-laser timing. Each pulse induces multiple breakdowns, shockwaves, and macroscopic cavitation bubbles. These effects disappear by the time the next pulse arrives. Even so, we find that the water target retains effects from previous pulses that persist up to roughly a second and that modify subsequent LIB properties including plasma location, spatial extension, and total emission intensity. We quantify the effects by tracking the first moment of the plasma emission intensity, which we call the “center of intensity” (CoI). Three distinct reproducible repetition-rate-dependent phases are identified with repeated pulses. In particular, (1) with initial pulses, emission intensity decreases and the CoI broadens and propagates downstream from the laser focus reaching a maximum axial distance away from the focal point, (2) with additional pulses, the CoI narrows and travels back upstream toward the laser, and (3) with continued pulses, the plasma gains back a portion of the lost intensity and the CoI reaches a steady state position, not at the focal point. Two possible causal effects are highlighted; particle inclusion concentration changes and microbubbles in the laser path.

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 ensembles of approximately $ 150 $ atoms. This leads to half-minute-scale atomic coherence on an optical clock transition, corresponding to quality factors well in excess of $10^{16}$. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is on par with leading atomic systems, yielding a relative fractional frequency stability of $5.2(3)\times10^{-17}~(\tau/s)^{-1/2}$ for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout available in this system, these results pave the way towards long-lived engineered entanglement on an optical clock transition in tailored atom arrays.

Submitted for the DAMOP19 Meeting of The American Physical Society An optical clock platform with strontium atoms in tweezers MATTHEW NORCIA, AARON YOUNG, WILLIAM ECKNER, BENJAMIN JOHNSTON, ADAM KAUFMAN, JILA, NIST, University of Colorado at Boulder — Arrays of strontium atoms trapped within optical tweezers provide an intriguing new platform for optical frequency metrology, with a unique combination of appealing features including relatively large particle numbers, absence of interatomic collisions, long coherence times, and low dead times through repeated lossless imaging. Further, if Rydberg interactions were introduced between the tweezer-trapped atoms, the microscopic control afforded by this system may enable entanglementenhanced performance. Here, we demonstrate highly coherent excitation of the ultra narrow S0 to P0 clock transition in arrays of tweezer-trapped 88Sr atoms, as well as repeated interrogation of the same ensemble of atoms using high-fidelity, low loss measurements. These results provide the key ingredients for a new form of highly capable optical clocks. Matthew Norcia University of Colorado, Boulder Date submitted: 26 Jan 2019 Electronic form version 1.4

Building up an optical clock Arrays of optical tweezers can be used to trap atoms, which can then be manipulated individually. Such arrays have shown promise in quantum simulation of many-body systems. Norcia et al. now demonstrate that they can also be used as a platform for optical clocks. The researchers lined up 10 optical tweezers in a one-dimensional array, where each tweezer held either one or zero atoms of strontium. The atoms were subjected to laser light whose frequency was tuned to a clock transition in strontium. By monitoring the number of atoms in each tweezer, the researchers measured a long coherence time of a few seconds. Increasing the number of tweezers should improve the figures of merit of this platform. Science , this issue p. 93

We demonstrate a set of tools for microscopic control of neutral strontium atoms. We report single-atom loading into an array of sub-wavelength scale optical tweezers, light-shift free control of a narrow-linewidth optical transition, three-dimensional ground-state cooling, and high-fidelity nondestructive imaging of single atoms on sub-wavelength spatial scales. Extending the microscopic control currently achievable in single-valence-electron atoms to species with more complex internal structure, like strontium, unlocks a wealth of opportunities in quantum information science, including tweezer-based metrology, new quantum computing architectures, and new paths to low-entropy many-body physics.