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Quantum sensors represent a new generation of sensors with improved precision, accuracy, stability, and robustness to environmental effects compared to their classical predecessors. After decades of laboratory development, several types of quantum sensors are now commercially available or are part-way through the commercialization process. This article provides a brief description of the operation of a selection of quantum sensors that employ the principles of atom-light interactions and discusses progress toward packaging those sensors into products. This article covers quantum inertial and gravitational sensors, including gyroscopes, accelerometers, gravimeters, and gravity gradiometers that employ atom interferometry, nuclear magnetic resonance gyroscopes, atomic and spin-defect magnetometers, and Rydberg electric field sensors., Comment: 96 pages

We present a novel four-channel OPM sensor for magnetoencephalography that utilizes a two-color pump/probe scheme on a single optical axis. We characterize its performance across 18 built sensor modules. The new sensor implements several improvements over our previously developed sensor including lower vapor-cell operating temperature, improved probe-light detection optics, and reduced optical power requirements. The sensor also has new electromagnetic field coils on the sensor head which are designed using stream-function-based current optimization. We detail the coil design methodology and present experimental characterization of the coil performance. The magnetic sensitivity of the sensor is on average 12.3 fT/rt-Hz across the 18 modules while the average gradiometrically inferred sensitivity is about 6.0 fT/rt-Hz. The sensor 3-dB bandwidth is 100 Hz on average. The on-sensor coil performance is in good agreement with the simulations.

In magnetoencephalography, linear minimum norm inverse methods are commonly employed when a solution with minimal a priori assumptions is desirable. These methods typically produce spatially extended inverse solutions, even when the generating source is focal. Various reasons have been proposed for this effect, including intrisic properties of the minimum norm solution, effects of regularization, noise, and limitations of the sensor array. In this work, we express the lead field in terms of the magnetostatic multipole expansion and develop the minimum-norm inverse in the multipole domain. We demonstrate the close relationship between numerical regularization and explicit suppression of spatial frequencies of the magnetic field. We show that the spatial sampling capabilities of the sensor array and regularization together determine the resolution of the inverse solution. For the purposes of stabilizing the inverse estimate, we propose the multipole transformation of the lead field as an alternative or complementary means to purely numerical regularization.

The most complicated and challenging system within a light-pulse atom interferometer (LPAI) is the laser system, which controls the frequencies and intensities of multiple laser beams over time to configure quantum gravity and inertial sensors. The main function of an LPAI laser system is to perform cold-atom generation, state-preparation, state-selective detection and to generate coherent two-photon process for the light-pulse sequence. Substantial miniaturization and ruggedization of the laser system can be achieved by bringing most key functions of the laser system onto photonic integrated circuit (PIC). We demonstrate a high-performance silicon photonic suppressed-carrier single-sideband (SC-SSB) modulator at 1560 nm, which can dynamically frequency shift within the LPAI. With independent RF-channel control, we study the imbalances in both the optical and RF phases/amplitudes to reach 30 dB carrier-suppression, unprecedented 47.8 dB sideband-suppression at peak conversion-efficiency: -6.846 dB (20.7 %). Using a silicon photonic SSB-modulator, we demonstrate cold-atom generation, state-selective detection, and atom interferometer fringes to estimate gravitational acceleration, $g \approx 9.77 \pm 0.01 \,\rm{m/s^2}$, in a Rubidium ($^{87}$Rb) atom system., Comment: 25 pages, 14 figures

In this paper, we propose a method to estimate the position, orientation and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer and model these discreetly sampled fields using vector-spherical harmonics (VSH) functions. We then localize and calibrate a sensor by minimizing the sum of squared errors between the model signals and the sensor responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. By determining the coil currents based on the VSH models, the coil fields can approximate these low-order field components, yielding computationally simple initial estimates of the sensor parameters. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2{\deg} and 0.8%, respectively. Last, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG., Comment: 21 pages, 6 figures

The extreme miniaturization of a cold-atom interferometer accelerometer requires the development of novel technologies and architectures for the interferometer subsystems. Here we describe several component technologies and a laser system architecture to enable a path to such miniaturization. We developed a custom, compact titanium vacuum package containing a microfabricated grating chip for a tetrahedral grating magneto-optical trap (GMOT) using a single cooling beam. In addition, we designed a multi-channel photonic-integrated-circuit-compatible laser system implemented with a single seed laser and single sideband modulators in a time-multiplexed manner, reducing the number of optical channels connected to the sensor head. In a compact sensor head containing the vacuum package, sub-Doppler cooling in the GMOT produces 15 uK temperatures, and the GMOT can operate at a 20 Hz data rate. We validated the atomic coherence with Ramsey interferometry using microwave spectroscopy, then demonstrated a light-pulse atom interferometer in a gravimeter configuration for a 10 Hz measurement data rate and T = 0 - 4.5 ms interrogation time, resulting in $\Delta$ g / g = 2.0e-6. This work represents a significant step towards deployable cold-atom inertial sensors under large amplitude motional dynamics., Comment: 21 pages, 10 figures

Compact cold-atom sensors depend on vacuum technology. One of the major limitations to miniaturizing these sensors are the active pumps -- typically ion pumps -- required to sustain the low pressure needed for laser cooling. Although passively pumped chambers have been proposed as a solution to this problem, technical challenges have prevented successful operation at the levels needed for cold-atom experiments. We present the first demonstration of a vacuum package successfully independent of ion pumps for more than a week; our vacuum package is capable of sustaining a cloud of cold atoms in a magneto-optical trap (MOT) for greater than 200 days using only non-evaporable getters and a rubidium dispenser. Measurements of the MOT lifetime indicate the package maintains a pressure of better than $2\times10^{-7}$ Torr. This result will significantly impact the development of compact atomic sensors, including those sensitive to magnetic fields, where the absence of an ion pump will be advantageous., Comment: 6 pages, 5 figures. (This replacement corrects cross-section value.)

We present experimental studies of atom-ion collisions using buffer-gas cooled, trapped ytterbium (Yb$^+$) ions immersed in potassium (K) vapor. The range of the collisional temperature is on the order of several hundred kelvin (thermal regime). We have determined various collisional rate coefficients of the Yb$^+$ ion per K-atom number density. We find the upper bounds of charge-exchange rate coefficients $\kappa_{\rm ce}$ to be $(12.7\pm1.6)\times10^{-14}$ cm$^3$s$^{-1}$ for K-$^{171}$Yb$^+$ and $(5.3\pm0.7)\times10^{-14}$ cm$^3$s$^{-1}$ for K-$^{172}$Yb$^+$. For both isotopes, the spin-destruction rate coefficient $\kappa_{\rm sd}$ has an upper bound at $(1.46\pm0.77)\times10^{-9}$ cm$^3$s$^{-1}$. The spin-exchange rate coefficient $\kappa_{\rm se}$ is measured to be $(1.64\pm0.51)\times10^{-9}$ cm$^3$s$^{-1}$. The relatively low charge-exchange rate reported here demonstrates the advantage of using K atoms to sympathetically cool Yb$^+$ ions, and the relatively high spin-exchange rate may benefit research work in quantum metrology and quantum information processing on an atom-ion platform using K atoms and Yb$^+$ ions., Comment: 6 pages, 4 figures

A non-invasive functional-brain-imaging system based on optically-pumped-magnetometers (OPM) is presented. The OPM-based magnetoencephalography (MEG) system features 20 OPM channels conforming to the subject's scalp. Due to proximity (12 mm) of the OPM channels to the brain, it is anticipated that this MEG system offers an enhanced spatial resolution as it can capture finer spatial features compared to traditional MEG systems employing superconducting quantum interference device (SQUID). We have conducted two MEG experiments on three subjects: somatosensory evoked magnetic field (SEF) and auditory evoked magnetic field (AEF) using our OPM-based MEG system and a commercial SQUID-based MEG system. We have cross validated the robustness of our system by calculating the distance between the location of the equivalent current dipole (ECD) yielded by our OPM-based MEG system and the ECD location calculated by the commercial SQUID-based MEG system. We achieved sub-centimeter accuracy for both SEF and AEF responses in all three subjects.

We describe a multichannel magnetoencephalography (MEG) system that uses optically pumped magnetometers (OPMs) to sense the magnetic fields of the human brain. The system consists of an array of 20 OPM channels conforming to the human subject's head, a person-sized magnetic shield containing the array and the human subject, a laser system to drive the OPM array, and various control and data acquisitions systems. We conducted two MEG experiments: auditory evoked magnetic field (AEF) and somatosensory evoked magnetic field (SEF), on three healthy male subjects, using both our OPM array and a 306-channel Elekta-Neuromag superconducting quantum interference device (SQUID) MEG system. The described OPM array measures the tangential components of the magnetic field as opposed to the radial component measured by all SQUID-based MEG systems. Herein we compare the results of the OPM- and SQUID-based MEG systems on the auditory and somatosensory data recorded in the same individuals on both systems.

A laser-cooled neutral-atom beam from a low-velocity intense source is split into two beams while guided by a magnetic-field potential. We generate our multimode-beamsplitter potential with two current-carrying wires on a glass substrate combined with an external transverse bias field. The atoms bend around several curves over a $10$-cm distance. A maximum integrated flux of $1.5\cdot10^{5} \mathrm{atoms/s}$ is achieved with a current density of $5\cdot10^{4} \mathrm{Ampere/cm^{2}}$ in the 100-$\mathrm{\mu m}$ diameter wires. The initial beam can be split into two beams with a 50/50 splitting ratio.

The notion of wave-particle duality may be quantified by the inequality V^2+K^2 <=1, relating interference fringe visibility V and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially-mixed input states. A quantum eraser scheme has been realized that recovers interference fringes even when no which-way information is available to erase., Comment: 6 pages, 4 figures. To appear in Phys. Rev. A

Laser-cooled neutral atoms from a low-velocity atomic source are guided via a magnetic field generated between two parallel wires on a glass substrate. The atoms bend around three curves, each with a 15-cm radius of curvature, while traveling along a 10-cm-long track. A maximum flux of 2*10^6 atoms/sec is achieved with a current density of 3*10^4 A/cm^2 in the 100x100-micrometer-cross-section wires. The kinetic energy of the guided atoms in one transverse dimension is measured to be 42 microKelvin., Comment: 9 pages