Quantum-enhanced magnetometry at optimal number density

We study the use of squeezed probe light and evasion of measurement back-action 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 back-action evasion.Comment: 5 pages + 3 supplementary, 5 figure

Measurement-induced nonlocal entanglement in a hot, strongly-interacting atomic system

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 $1.52(4)\times 10^{13}$ of the $5.32(12) \times 10^{13}$ 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.Comment: 10 pages, 10 figure

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.Comment: 15 pages, 4 figure

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.Comment: 15 pages, 4 figure

Long-term laser frequency stabilization using fiber interferometers

We report long-term laser frequency stabilization using only the target laser and a pair of 5 m fiber interferometers, one as a frequency reference and the second as a sensitive thermometer to stabilize the frequency reference. When used to stabilize a distributed feedback laser at 795 nm, the frequency Allan deviation at 1000 s drops from 5.6*10^{-8} to 6.9*10^{-10}. The performance equals that of an offset lock employing a second, atom-stabilized laser in the temperature control

Phase estimation via quantum interferometry for noisy detectors

The sensitivity in optical interferometry is strongly affected by losses during the signal propagation or at the detection stage. The optimal quantum states of the probing signals in the presence of loss were recently found. However, in many cases of practical interest, their associated accuracy is worse than the one obtainable without employing quantum resources (e.g. entanglement and squeezing) but neglecting the detector's loss. Here we detail an experiment that can reach the latter even in the presence of imperfect detectors: it employs a phase-sensitive amplification of the signals after the phase sensing, before the detection. We experimentally demonstrated the feasibility of a phase estimation experiment able to reach its optimal working regime. Since our method uses coherent states as input signals, it is a practical technique that can be used for high-sensitivity interferometry and, in contrast to the optimal strategies, does not require one to have an exact characterization of the loss beforehand.Comment: 4 pages + supplementary information (10 pages), 3 + 4 figure

Cavity-resonated detection of spin polarization in a microfabricated atomic vapor cell

We demonstrate continuous Pound-Drever-Hall (PDH) nondestructive monitoring of the electron spin polarization of an atomic vapor in a microfabricated vapor cell within an optical resonator. The two-chamber silicon and glass cell contains $^{87}$Rb and 1.3 amagat of N$_{2}$ buffer gas, and is placed within a planar optical resonator formed by two mirrors with dichroic dielectric coatings to resonantly enhance the coupling to phase-modulated probe light near the D$_2$ line at 780 nm. We describe the theory of signal generation in this system, including the spin-dependent complex refractive index, cavity optical transfer functions, and PDH signal response to spin polarization. We observe cavity transmission and PDH signals across $\approx 200$ GHz of detuning around the atomic resonance line. By resonant optical pumping on the 795 nm D$_1$ line, we observe spin-dependent cavity line shifts, in good agreement with theory. We use the saturation of the line shift vs. optical pumping power to calibrate the number density and efficiency of the optical pumping. In the unresolved sideband regime, we observe quantum-noise-limited PDH readout of the spin polarization density, with a flat noise floor of $9 \times 10^9$ spins cm$^{-3}$ Hz$^{-1/2}$ for frequencies above 700 Hz. We note possible extensions of the technique