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We describe quantum limits to field sensing that relate noise, geometry and measurement duration to fundamental constants, with no reference to particle number. We cast the Tesche and Clarke (TC) bound on dc-SQUID sensitivity as such a limit, and find analogous limits for volumetric spin-precession magnetometers. We describe how randomly-arrayed spins, coupled to an external magnetic field of interest and to each other by the magnetic dipole-dipole interaction, execute a spin dynamics that depolarizes the spin ensemble even in the absence of coupling to an external reservoir. We show the resulting spin dynamics are scale invariant, with a depolarization rate proportional to spin number density and thus a number-independent quantum limit on the energy resolution per bandwidth ER. Numerically, we find ER ⩾ αℏ, α ∼ 1, in agreement with the TC limit, for paradigmatic spin-based measurements of static and oscillating magnetic fields.

Quantum technologies use entanglement to outperform classical technologies, and often employ strong cooling and isolation to protect entangled entities from decoherence by random interactions. Here we show that the opposite strategy—promoting random interactions—can help generate and preserve entanglement. We use optical quantum non-demolition measurement to produce entanglement in a hot alkali vapor, in a regime dominated by random spin-exchange collisions. We use Bayesian statistics and spin-squeezing inequalities to show that at least 1.52(4) × 10 13 of the 5.32(12) × 10 13 participating atoms enter into singlet-type entangled states, which persist for tens of spin-thermalization times and span thousands of times the nearest-neighbor distance. The results show that high temperatures and strong random interactions need not destroy many-body quantum coherence, that collective measurement can produce very complex entangled states, and that the hot, strongly-interacting media now in use for extreme atomic sensing are well suited for sensing beyond the standard quantum limit. It’s still unclear whether entanglement can be generated, survive, and be observed in hot environments dominated by random collisions. Here, the authors use quantum non-demolition measurement on a hot alkali vapor to put more than ten trillion atoms in a long-lived and spatially extended entangled state.

We present a magnetic sensor with energy resolution per bandwidth ER < ħ. 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 V = 1,091(30) μm³ for 3.5 s, and thus, ER = 0.075(16)ħ. 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 metrology 1 uses entanglement 2 , 3 , 4 , 5 and other quantum effects 6 to improve the sensitivity of demanding measurements 7 , 8 , 9 . Probing of delicate systems demands high sensitivity from limited probe energy and has motivated the field's key benchmark—the standard quantum limit 10 . Here we report the first entanglement-enhanced measurement of a delicate material system. We non-destructively probe an atomic spin ensemble by means of near-resonant Faraday rotation, a measurement that is limited by probe-induced scattering in quantum-memory and spin-squeezing applications 6 , 11 , 12 , 13 . We use narrowband, atom-resonant NOON states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and per-damage basis. This demonstrates quantum enhancement with fully realistic loss and noise, including variable-loss effects 14 , 15 , 16 . The experiment opens the way to ultra-gentle probing of single atoms 17 , single molecules 18 , quantum gases 19 and living cells 20 . Researchers report the entanglement-enhanced measurement of a delicate material system, in which they non-destructively probe an 85 Rb atomic spin ensemble by near-resonant Faraday rotation. They use narrowband, atom-resonant ‘NOON’ states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and a per-damage basis.

Optically pumped magnetometers (OPMs) based on alkali-atom vapors are ultra-sensitive devices for dc and low-frequency ac magnetic measurements. Here, in combination with fast-field-cycling hardware and high-resolution spectroscopic detection, we demonstrate applicability of OPMs in quantifying nuclear magnetic relaxation phenomena. Relaxation rate dispersion across the nT to mT field range enables quantitative investigation of extremely slow molecular motion correlations in the liquid state, with time constants > 1 ms, and insight into the corresponding relaxation mechanisms. The 10-20 fT/ H z sensitivity of an OPM between 10 Hz and 5.5 kHz 1 H Larmor frequency suffices to detect magnetic resonance signals from ~ 0.1 mL liquid volumes imbibed in simple mesoporous materials, or inside metal tubing, following nuclear spin prepolarization adjacent to the OPM. High-resolution spectroscopic detection can resolve inter-nucleus spin-spin couplings, further widening the scope of application to chemical systems. Expected limits of the technique regarding measurement of relaxation rates above 100 s −1 are discussed. Nuclear spin polarization and relaxation can be studied using nuclear magnetic resonance (NMR). Here the authors demonstrate a combination of fast-field cycling and optical magnetometry techniques, to realize a NMR sensor that operates in the region of very low frequency and high relaxation rate.

We describe a compact, robust and versatile system for studying the macroscopic spin dynamics in a spinor Bose-Einstein condensate. Condensates of 87 Rb are produced by all-optical evaporation in a 1560 nm optical dipole trap, using a non-standard loading sequence that employs an ancillary 1529 nm beam for partial compensation of the strong differential light-shift induced by the dipole trap itself. We use near-resonant Faraday rotation probing to non-destructively track the condensate magnetization, and demonstrate few-Larmor-cycle tracking with no detectable degradation of the spin polarization. In the ferromagnetic F = 1 ground state, we observe the spin orientation between atoms in the condensate is preserved, such that they precess all together like one large spin in the presence of a magnetic field. We characterize this dynamics in terms of the single-shot magnetic coherence times  1 and  2 * , and observe them to be of several seconds, limited only by the residence time of the atoms in the trap. At the densities used, this residence is restricted only by one-body losses set by the vacuum conditions.

Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality 1 – 3 can be experimentally demonstrated in Bell tests 4 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 loopholes 5 succeeded. Such experiments have been performed with spins in nitrogen–vacancy centres 6 , optical photons 7 – 9 and neutral atoms 10 . Here we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology 11 . To evaluate a Clauser–Horne–Shimony–Holt-type Bell inequality 4 , we deterministically entangle a pair of qubits 12 and perform fast and high-fidelity measurements 13 along randomly chosen bases on the qubits connected through a cryogenic link 14 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 physics 15 . A loophole-free violation of Bell’s inequality with superconducting circuits shows that non-locality is a viable new resource in quantum information technology realized with superconducting circuits, promising many potential applications.

We apply spin-squeezing techniques to identify and quantify highly multi-partite photonic entanglement in polarization-squeezed light. We consider a practical single-mode scenario, and find that Wineland-criterion polarization squeezing implies entanglement of a macroscopic fraction of the total photons. A Glauber-theory computation of the observable N-photon density matrix, with N up to 100, finds that N-partite entanglement is observable despite losses and without post-selection. Genuine multi-partite entanglement up to at least is similarly confirmed. The preparation method can be made intrinsically permutation-invariant, allowing highly efficient state reconstruction. In this scenario, generation plus detection requires experimental resources, in stark contrast to the typical exponential scaling. We estimate existing detectors could observe 1000-partite entanglement from a few dB of polarization squeezing.

With the growing availability of experimental loophole-free Bell tests1–5, it has become possible to implement a new class of device-independent random number generators whose output can be certified6,7 to be uniformly random without requiring a detailed model of the quantum devices used8–10. However, all these experiments require many input bits to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is consumed. Here we devise a device-independent spot-checking protocol that consumes only uniform bits without requiring any additional bits with a specific bias. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237) than consumed input bits (953,301,640). The experiment ran for 91.0 h, creating randomness at an average rate of 3,606 bits s–1 with a soundness error bounded by 5.7 × 10−7 in the presence of classical side information. Our system allows for greater trust in public sources of randomness, such as randomness beacons11, and may one day enable high-quality private sources of randomness as the device footprint shrinks.Device-independent randomness expansion is demonstrated in an experiment that is secure in the presence of a classical eavesdropper who does not share any entanglement with the setup.

Simultaneous precise measurement of the non-commuting observables spin angle and spin amplitude is achieved by directing the error due to quantum measurement back-action into an unmeasured spin component. A new spin on uncertainty (COLANGELO 21434, Phys Letter, Leonie Mueck) Many quantum systems that are currently used to enhance metrological precision obey the regular Heisenberg uncertainty relations that apply to conjugate variables such as position and momentum. These systems can be 'squeezed' to reduce the uncertainty of one variable at the expense of greater uncertainty in another, and thereby to surpass the limits set by classical physics in metrology. However, spin systems and pseudo-spin systems obey different uncertainty relations because of their underlying symmetries. On the basis of these relations, the authors demonstrate simultaneous measurement of spin amplitude and spin angle beyond classical limits. This approach has potential applications in spin-based sensors and could increase the sensitivity for several applications, such as magnetic resonance measurements, in which spin relaxation rates could be correlated with precession frequency with higher precision than is currently possible. Measurement of spin precession is central to extreme sensing in physics 1 , 2 , geophysics 3 , chemistry 4 , nanotechnology 5 and neuroscience 6 , and underlies magnetic resonance spectroscopy 7 . 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 N 1/2 —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 8 that, because spins obey non-Heisenberg uncertainty relations 9 , 10 , enables simultaneous precise knowledge of spin angle and spin amplitude. We use high-dynamic-range optical quantum non-demolition measurements 11 , 12 , 13 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 14 . 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 15 , 16 , 17 , 18 and spectroscopy 19 , 20 .