Loophole-free Bell inequality violation with superconducting circuits.

Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1-3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen-vacancy centres6, optical photons7-9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell's inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser-Horne-Shimony-Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell's inequality with a P value smaller than 10-108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.

Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below ℏ.

We present a magnetic sensor with energy resolution per bandwidth [Formula: see text] We show how a 87Rb single-domain spinor Bose-Einstein condensate, detected by nondestructive Faraday rotation probing, achieves single-shot low-frequency magnetic sensitivity of 72(8) fT measuring a volume [Formula: see text] for 3.5 s, and thus, [Formula: see text] We measure experimentally the condensate volume, spin coherence time, and readout noise and use phase space methods, backed by three-dimensional mean-field simulations, to compute the spin noise. Contributions to the spin noise include one-body and three-body losses and shearing of the projection noise distribution, due to competition of ferromagnetic contact interactions and quadratic Zeeman shifts. Nonetheless, the fully coherent nature of the single-domain, ultracold two-body interactions allows the system to escape the coherence vs. density trade-off that imposes an energy resolution limit on traditional spin precession sensors. We predict that other Bose-condensed alkalis, especially the antiferromagnetic 23Na, can further improve the energy resolution of this method.

Quantum-Enhanced Magnetometry at Optimal Number Density.

We study the use of squeezed probe light and evasion of measurement backaction to enhance the sensitivity and measurement bandwidth of an optically pumped magnetometer (OPM) at sensitivity-optimal atom number density. By experimental observation, and in agreement with quantum noise modeling, a spin-exchange-limited OPM probed with off-resonance laser light is shown to have an optimal sensitivity determined by density-dependent quantum noise contributions. Application of squeezed probe light boosts the OPM sensitivity beyond this laser-light optimum, allowing the OPM to achieve sensitivities that it cannot reach with coherent-state probing at any density. The observed quantum sensitivity enhancement at optimal number density is enabled by measurement backaction evasion.

Simultaneous tracking of spin angle and amplitude beyond classical limits.

Measurement of spin precession is central to extreme sensing in physics, geophysics, chemistry, nanotechnology and neuroscience, and underlies magnetic resonance spectroscopy. Because there is no spin-angle operator, any measurement of spin precession is necessarily indirect, for example, it may be inferred from spin projectors at different times. Such projectors do not commute, and so quantum measurement back-action-the random change in a quantum state due to measurement-necessarily enters the spin measurement record, introducing errors and limiting sensitivity. Here we show that this disturbance in the spin projector can be reduced below N1/2-the classical limit for N spins-by directing the quantum measurement back-action almost entirely into an unmeasured spin component. This generates a planar squeezed state that, because spins obey non-Heisenberg uncertainty relations, enables simultaneous precise knowledge of spin angle and spin amplitude. We use high-dynamic-range optical quantum non-demolition measurements applied to a precessing magnetic spin ensemble to demonstrate spin tracking with steady-state angular sensitivity 2.9 decibels below the standard quantum limit, simultaneously with amplitude sensitivity 7.0 decibels below the Poissonian variance. The standard quantum limit and Poissonian variance indicate the best possible sensitivity with independent particles. Our method surpasses these limits in non-commuting observables, enabling orders-of-magnitude improvements in sensitivity for state-of-the-art sensing and spectroscopy.

Laser-written vapor cells for chip-scale atomic sensing and spectroscopy.

We report the fabrication of alkali-metal vapor cells using femtosecond laser machining. This laser-written vapor-cell (LWVC) technology allows arbitrarily-shaped 3D interior volumes and has potential for integration with photonic structures and optical components. We use non-evaporable getters both to dispense rubidium and to absorb buffer gas. This enables us to produce cells with sub-atmospheric buffer gas pressures without vacuum apparatus. We demonstrate sub-Doppler saturated absorption spectroscopy and single beam optical magnetometry with a single LWVC. The LWVC technology may find application in miniaturized atomic quantum sensors and frequency references.

Improving Short-Term Stability in Optical Lattice Clocks by Quantum Nondemolition Measurement.

We propose a multimeasurement estimation protocol for quantum nondemolition (QND) measurements in a Rabi clock interferometer. The method is well suited for current state-of-the-art optical lattice clocks with QND measurement capabilities. The protocol exploits the correlations between multiple nondestructive measurements of the initially prepared coherent spin state. A suitable Gaussian estimator for the clock laser detuning is presented, and an analytic expression for the sensitivity of the protocol is derived. We use this analytic expression to optimize the protocol using available experimental parameters, achieving an improvement of 7.9 dB with respect to the standard quantum limit in terms of clock stability. We also discuss the measurement back-action effects of our protocol into the atomic state.

SU(2)-in-SU(1,1) Nested Interferometer for High Sensitivity, Loss-Tolerant Quantum Metrology.

We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.

Autoheterodyne Characterization of Narrow-Band Photon Pairs.

We describe a technique to measure photon pair joint spectra by detecting the time-correlation beat note when nondegenerate photon pairs interfere at a beam splitter. The technique implements a temporal analog of the Ghosh-Mandel effect with one photon counter and a time-resolved Hong-Ou-Mandel interference with two. It is well suited to characterize pairs of photons, each of which can interact with a single atomic species, as required to study recently predicted photon-photon interaction in subwavelength atomic arrays. With this technique, we characterize photon pairs from cavity-enhanced parametric down-conversion with a bandwidth ≈ 5 MHz and frequency separation of ∼200 MHz near the D_{1} line of atomic Rb.

Bose-Einstein Condensate Comagnetometer.

We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1 s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.

Experimental Low-Latency Device-Independent Quantum Randomness.

Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 random bits with an average experiment time of less than 5 min per block and with a certified error bounded by 2^{-64}≈5.42×10^{-20}.

Narrowband photon pairs with independent frequency tuning for quantum light-matter interactions.

We describe a cavity-enhanced spontaneous parametric down-conversion (CE-SPDC) source for narrowband photon pairs with filters designed such that 97.7% of the correlated photons are in a single mode of 4.3(4) MHz bandwidth. Type-II phase matching, a tuneable-birefringence resonator, MHz-resolution pump tuning, and tuneable Fabry-Perot filters are used to achieve independent signal and idler tuning. We map the CE-SPDC spectrum using difference frequency generation to precisely locate the emission clusters, demonstrate CE-SPDC driven atomic spectroscopy, and measure a contribution from unwanted modes of 7.7%. The generated photon pairs efficiently interact with neutral rubidium, a well-developed system for quantum networking and quantum simulation. The techniques are readily extensible to other material systems.

Maltese cross coupling to individual cold atoms in free space.

We report on the simultaneous observation from four directions of the fluorescence of single 87Rb atoms trapped at the common focus of four high numerical aperture (NA=0.5) aspheric lenses. We use an interferometrically-guided pick-and-place technique to precisely and stably position the lenses along the four cardinal directions with their foci at a single central point. The geometry gives right angle access to a single quantum emitter, and will enable new trapping, excitation, and collection methods. The fluorescence signals indicate both sub-Poissonian atom number statistics and photon anti-bunching, showing suitability for cold atom quantum optics.

Interferometric photodetection in silicon photonics for phase diffusion quantum entropy sources.

We report the interferometric photodetection of a phase-diffusion quantum entropy source in a silicon photonics chip. The device uses efficient and robust single-laser accelerated phase diffusion methods, and implements the unbalanced Mach-Zehnder interferometer with optimized splitting ratio and photodetection, in a 0.5 mm×1 mm footprint. We demonstrate Gbps raw entropy-generation rates in a technology compatible with conventional CMOS fabrication techniques.

Atom-resonant squeezed light from a tunable monolithic ppRKTP parametric amplifier.

We demonstrate vacuum squeezing at the D1 line of atomic rubidium (795 nm) with a tunable, doubly-resonant, monolithic subthreshold optical parametric oscillator in periodically-poled Rb-doped potassium titanyl phosphate (ppRKTP). The squeezing appears to be undiminished by a strong dispersive optical nonlinearity recently observed in this material.

Signal Tracking Beyond the Time Resolution of an Atomic Sensor by Kalman Filtering.

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic processes, to estimate stochastic input signals that we generate by optical pumping. Comparing the known input to the estimates, we confirm the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor's intrinsic time resolution. With proper filter choice, we obtain similar benefits when tracking partially known and non-Gaussian signal processes, as are found in most practical sensing applications. The method evades the trade-off between sensitivity and time resolution in coherent sensing.

Randomness in quantum mechanics: philosophy, physics and technology.

This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology. For this reason the article contains three parts that will be essentially devoted to different aspects of quantum randomness, and even directed, although not restricted, to various audiences: a philosophical part, a physical part, and a technological part. For these reasons the article is written on an elementary level, combining simple and non-technical descriptions with a concise review of more advanced results. In this way readers of various provenances will be able to gain while reading the article.

Fully-resonant, tunable, monolithic frequency conversion as a coherent UVA source.

We demonstrate a monolithic frequency converter incorporating up to four tuning degrees of freedom, three temperature and one strain, allowing resonance of pump and generated wavelengths simultaneous with optimal phase-matching. With a Rb-doped periodically-poled potassium titanyl phosphate (KTP) implementation, we demonstrate efficient continuous-wave second harmonic generation from 795 to 397, with low-power efficiency of 72% and high-power slope efficiency of 4.5%. The measured performance shows good agreement with theoretical modeling of the device. We measure optical bistability effects, and show how they can be used to improve the stability of the output against pump frequency and amplitude variations.

Self-tuning optical resonator.

We demonstrate a nonlinear optical resonator that tunes itself onto resonance with an input beam. In a monolithic Fabry-Perot cavity implemented in rubidium-doped periodically poled potassium titanyl phosphate, an intensity-dependent refractive index produces line pulling by multiple free-spectral ranges (FSRs). In this condition, the cavity passively maintains optical resonance in the face of FSR-scale excursions of the drive laser frequency: when one resonant operating point becomes unstable, the resonator rapidly transitions to another resonant operating point. We demonstrate stable second-harmonic generation with no active feedback to the laser or cavity. The self-tuning effect appears to be supported by a very strong, previously unreported optical nonlinearity.

Real-time shot-noise-limited differential photodetection for atomic quantum control.

We demonstrate high-efficiency, shot-noise-limited differential photodetection with real-time signal conditioning, suitable for feedback-based quantum control of atomic systems. The detector system has quantum efficiency of 0.92, is shot-noise-limited from 7.4×105 to 3.7×108 photons per pulse, and provides real-time voltage-encoded output at up to 2.3 M pulses per second.

Absolute frequency references at 1529 and 1560 nm using modulation transfer spectroscopy.

We demonstrate a double optical frequency reference (1529 and 1560 nm) for the telecom C-band using 87Rb modulation transfer spectroscopy. The two reference frequencies are defined by the 5S(1/2)F=2→5P(3/2)F'=3 two-level and 5S(1/2)F=2→5P(3/2)F'=3→4D(5/2)F''=4 ladder transitions. We examine the sensitivity of the frequency stabilization to probe power and magnetic field fluctuations, calculate its frequency shift due to residual amplitude modulation, and estimate its shift due to gas collisions. The short-term Allan deviation was estimated from the error signal slope for the two transitions. Our scheme provides a simple and high performing system for references at these important wavelengths. We estimate that an absolute accuracy of ∼1 kHz is realistic.