We introduce a methodology to calibrate in situ a set of coils generating bi- or tri-axial magnetic fields, at frequencies where a calibration performed in static condition would be inaccurate. The coil constants are determined in a two-step procedure. Considering the presence of a static and of a time-dependent field, firstly, the static one is oriented perpendicularly to the polarization plane of a time dependent one; secondly, the polarization of the latter is made accurately circular. The methodology uses harmonic analysis of one component of the magnetization of an atomic sample whose spins adiabatically follow the time-dependent field.

Over the past 20 years, several eye tracking technologies have been developed. This article aims to present a new type of eye tracker capable of producing detailed information on eye and head movements using an array of magnetoresistive detectors fixed on the patient's head and a small magnet inserted into a contact lens, adapted to the curvature of the cornea of the subject. The software used for data analysis can combine or compare eye and head movements and can represent them as 2D or 3D images. Preliminary data involve an initial patient who was asked to perform several tasks to establish the accuracy, reliability, and tolerance of the magnetic eye tracker and software. The tasks included assessment of saccadic eye movements and pursuit, “drawing” alphabetic shapes or letters, and reading. Finally, a Head Impulse Test (HIT) was performed to estimate the VOR gain, comparing the standard deviation established via vHIT with that established via this magnetic eye tracker (mHIT). This prototypical device is minimally invasive, lightweight, relatively cheap and tolerable, with a high degree of reliability and precision. All these characteristics could lead to the future use of the magnetic eye tracker in neurological and otoneurological fields. 

The application of a periodic nonresonant drive to a system allows the Floquet engineering of effective fields described by a broad class of quantum simulated Hamiltonians. The Floquet evolution is based on two different elements. The first one is a time-independent or stroboscopic evolution with an effective Hamiltonian corresponding to the quantum simulation target. The second element is the time evolution at the frequencies of the nonresonant driving and of its harmonics, denoted as micromotion. We examine experimentally and theoretically the harmonic dual-dressing Floquet engineering of a cold atomic two-level sample. Our focus is the dressing operation with small bare energies and large Rabi frequencies, where frequencies and amplitudes of the stroboscopic/micromotion time evolutions are comparable. At the kHz range of our dressed atom oscillations, we probe directly both the stroboscopic and micromotion components of the qubit global time evolution. We develop ad-hoc monitoring tools of the Floquet space evolution. The direct record of the time evolution following a pulsed excitation demonstrates the interplay between the two components of the spin precession in the Floquet space. From the resonant pumping of the dressed system at its evolution frequencies, Floquet eigenenergy spectra up to the fifth order harmonic of the dressing frequency are precisely measured as function of dressing parameters. Dirac-points of the Floquet eigenenergies are identified and, correspondingly, a jump in the dynamical phase shift is measured. The stroboscopic Hamiltonian eigenfrequencies are measured also from the probe of the micromotion sidebands. These monitoring tools are appropriate for quantum simulation/computation investigations. Our results evidence that the stroboscopic phase shift of the qubit wavefunction contains an additional information that opens new simulation directions. 

The dynamic response of a Bell-and-Bloom magnetometer to a parallel (to the bias field) time-dependent field is studied by means of a model that goes beyond the commonly assumed quasi-static regime. The findings unveil features that are related to the parametric nature of the considered system. It is shown that for low-amplitude time-dependent field different operating conditions are possible and that, beside the commonly reported low-pass-filter behavior, a band-pass response emerges. Moreover, we show that a larger amplitude of the time-dependent field makes the parametric nature of the system appear more clearly in the output signal. A harmonic analysis of the latter is numerically performed to highlight and characterize these emerging features. 

A wireless, wearable magnetic eye tracker is described and characterized. The proposed instrumentation enables simultaneous evaluation of eye and head angular displacements. Such a system can be used to determine the absolute gaze direction as well as to analyze spontaneous eye re-orientation in response to stimuli consisting in head rotations. The latter feature has implications to analyze the vestibulo-ocular reflex and constitutes an interesting opportunity to develop medical (oto-neurological) diagnostics. Details of data analysis are reported together with some results obtained in-vivo or with simple mechanical simulators that enable measurements under controlled  conditions. 

We analyze the information that can be retrieved from the tracking parameters produced by an innovative wearable eye tracker. The latter is based on a permanent-magnet marked corneal lens and by an array of magnetoresistive detectors that measure the magnetostatic field in several positions in the eye proximity. We demonstrate that, despite missing information due to the axial symmetry of the measured field, physiological constraints or measurement conditions make possible to infer complete eye-pose data. Angular precision and accuracy achieved with the current prototypical device are also assessed and briefly discussed.  

The results show that the instrumentation considered is suitable as a new,  moderately invasive medical diagnostics for the characterization of ocular movements and associated disorders.

We present a set of results obtained with an innovative eye-tracker based on magnetic dipole localization by means of an array of magnetoresistive sensors. The system tracks both head and eye movements with a high rate (100–200 Sa/s) and in real time. A simple setup is arranged to simulate head and eye motions and to test the tracker performance under realistic conditions. Multimedia material is provided to substantiate and exemplify the results. A comparison with other available technologies for eye-tracking is drawn, discussing advantages (e.g., precision) and disadvantages (e.g., invasivity) of the diverse approaches, with the presented method standing out for low cost, robustness, and relatively low invasivity. 

We investigated the Autler-Townes (AT) splitting produced by microwave (mw) transitions between atomic Rydberg states explored by optical spectroscopy from the ground electronic state. The laser-atom Hamiltonian describing the double irradiation of such a multilevel system is analysed on the basis of the Morris-Shore transformation. The application of this transformation to the mw-dressed atomic system allows the identification of bright, dark, and spectator states associated with different configurations of atomic states and mw polarisations. We derived synthetic spectra that show the main features of Rydberg spectroscopy. Complex AT spectra are obtained in a regime of strong mw dressing, where a hybridisation of the Rydberg fine structure states is produced by the driving. 

Based on the Landauer–Büttiker theory, we explore the thermal regimes of two-terminal nanoscale systems with an energy-peaked transmission function. The device is in contact with two reservoirs held at different temperatures and chemical potentials. We identify the operation regions where the system acts as energy pump (thermal machine) or heat pump (refrigerator machine), or where it is working in dissipative modes. The corresponding thermoelectric parameters are obtained without numerical calculations. The recent literature, by focusing on systems with box-like or step-like shapes of the transmission functions, demonstrated that bounds of quantum origin exist for output power and heat currents of thermal machines and refrigerators. The simple model we adopt in this paper allows us to grasp easily and without numerical calculations the presence of quantum bounds for the above thermoelectric quantities, as function of the position of the transmission peak with respect to the chemical potentials of the left and right reservoirs. In spite of the simple model and treatment, our results are in qualitative agreement with analytic findings in previous researches obtained with more realistic description of the electronic transmission function. 

Controlled modifications of the magnetic response of a two-level system are produced in dressed systems by one high-frequency, strong, and nonresonant electromagnetic field. This quantum control is greatly enhanced and enriched by a harmonic, commensurable, and orthogonally oriented dual dressing, as discussed here. The secondary field enables a fine tuning of the qubit response, with control parameter amplitude, harmonic content, spatial orientation, and phase relation. Our analysis, mainly based on a perturbative approach with respect to the driving strength, includes also nonperturbative numerical solutions. The Zeeman response becomes anisotropic in a triaxial geometry and includes a nonlinear quadratic contribution. The long-time dynamics is described by an anisotropic effective magnetic field representing the handle for the system full engineering. Through the low-order harmonic mixing, the bichromatic driving generates a synthetic static field modifying the system dynamics. The spin temporal evolution includes a micromotion at harmonics of the driving frequency whose role in the spin detection is examined. Our dressing increases the two-level energy splitting, improving the spin detection sensitivity. In the weak-field direction it compensates the static fields applied in different geometries. The results presented here lay a foundation for additional applications to be harnessed in quantum simulations. 

A recently introduced tuning-dressed scheme makes a Bell and Bloom magnetometer suited to detect weak variations of a radio-frequency (RF) magnetic field. We envisage the application of such innovative detection scheme as an alternative (or rather as a complement) to RF atomic magnetometers in electromagnetic-induction-imaging apparatuses.  

The dynamic response of a parametric system constituted by a spin precessing in a time dependent magnetic field is studied by means of a perturbative approach that unveils unexpected features, and is then experimentally validated. The first-order analysis puts in evidence different regimes: beside a tailorable low-pass-filter behaviour, a band-pass response with interesting potential applications emerges. Extending the analysis to the second perturbation order permits to study the response to generically oriented fields and to characterize several non-linear features in the behaviour of such kind of systems. 

The magnetic dressing phenomenon occurs when spins precessing in a static field (holding field) are subjected to an additional strong alternating field. It is usually studied when such extra field is homogeneous and oscillates in one direction. We study the dynamics of spins under dressing condition in two unusual configurations. In the first instance, an inhomogeneous dressing field produces a space-dependent dressing phenomenon, which helps to operate the magnetometer in a strongly inhomogeneous static field. In the second instance, besides the usual configuration with a static and a strong orthogonal oscillating magnetic fields, we add a secondary oscillating field, which is perpendicular to both. The system shows novel and interesting features that are accurately explained and modelled theoretically. Possible applications of these novel features are briefly discussed. 

We characterize the performance of a system based on a magnetoresistor array. This instrument is developed to map the magnetic field, and to track a dipolar magnetic source in the presence of a static homogeneous field. The position and orientation of the magnetic source with respect to the sensor frame is retrieved together with the orientation of the frame with respect to the environmental field. A nonlinear best-fit procedure is used, and its precision, time performance, and reliability are analyzed. This analysis is performed in view of the practical application for which the system is designed that is an eye-tracking diagnostics and rehabilitative tool for medical purposes, which require high speed (≥100 Sa/s) and sub-millimetric spatial resolution. A throughout investigation on the results makes it possible to list several observations, suggestions, and hints, which will be useful in the design of similar setups. 

We present the hardware of a cheap multi-sensor magnetometric setup, where a relatively large set of magnetic field components is measured in several positions by calibrated magnetoresistive detectors. The setup is developed to map the (inhomogeneous) field generated by a known magnetic source, which is measured and then discerned from the background (homogeneous) geomagnetic field. The data output from this hardware can be successfully and reliably used to retrieve the position and orientation of the magnetic source with respect to the sensor frame, together with the orientation of the frame with respect to the environmental field. Possible applications of the setup are briefly discussed, and a synthetic description of the methods of data elaboration and analysis is provided. 

Spin-noise spectroscopy is emerging as a powerful technique for studying the dynamics of various spin systems also beyond their thermal equilibrium and linear response. In this context, we demonstrate a nonstandard mode of the spin-noise analysis applied to an out-of-equilibrium nonlinear atomic system realized by a Bell-Bloom atomic magnetometer. Driven by an external pump and undergoing a parametric excitation, this system is known to produce noise squeezing. Our measurements not only reveal a strong asymmetry in the noise distribution of the atomic signal quadratures at the magnetic resonance, but also provide insight into the mechanism behind its generation and evolution. In particular, a structure in the spectrum is identified which allows to investigate the main dependencies and the characteristic timescales of the noise process. The results obtained are compatible with parametrically induced noise squeezing. Notably, the noise spectrum provides information on the spin dynamics even in regimes where the macroscopic atomic coherence is lost, effectively enhancing the sensitivity of the measurements. Our Letter promotes spin-noise spectroscopy as a versatile technique for the study of noise squeezing in a wide range of spin-based magnetic sensors. 

The addition of a weak oscillating field modifying strongly dressed spins enhances and enriches the system quantum dynamics. Through low-order harmonic mixing, the bichromatic driving generates additional rectified static field acting on the spin system. The secondary field allows for a fine tuning of the atomic response and produces effects not accessible with a single dressing field, such as a spatial triaxial anisotropy of the spin coupling constants and acceleration of the spin dynamics. This tuning-dressed configuration introduces an extra handle for the system full engineering in quantum control applications. Tuning amplitude, harmonic content, spatial orientation, and phase relation are control parameters. A theoretical analysis, based on perturbative approach, is experimentally tested by applying a bichromatic radiofrequency field to an optically pumped Cs atomic vapour. The theoretical predictions are precisely confirmed by measurements performed with tuning frequencies up to the third harmonic. 

The presence of a weak remanence in Ultra-Low-Field (ULF) NMR sample containers is investigated on the basis of proton precession. The high-sensitivity magnetometer used for the NMR detection, enables simultaneously the measurement of the static field produced in the sample proximity by ferromagnetic contaminants. The presence of the latter is studied by high resolution chemical analyses of the surface, based on X-ray fluorescence spectroscopy and secondary ions mass spectroscopy. Methodologies to reduce the contamination are explored and characterized. This study is of relevance in any ULF-NMR experiment, as in the ULF regime spurious ferromagnetism becomes easily a dominant cause of artefacts. 

We present a system developed to premagnetize liquid samples in an ultra-low-field nuclear magnetic resonance experiment. Liquid samples of a few milliliters are exposed to a magnetic field of about 70 mT, which is abruptly switched off, to leave a transverse microtesla field, where nuclei start precessing. An accurate characterization of the transients and intermediate field level enables a reliable operation of the detection system, which is based on an optical magnetometer. 

Magnetic resonance imaging (MRI) is universally acknowledged as an excellent tool to extract detailed spatial information with minimally invasive measurements. Efforts toward ultra-low-field (ULF) MRI are made to simplify the scanners and to reduce artifacts and incompatibilities. Optical atomic magnetometers (OAMs) are among the sensitive magnetic detectors eligible for ULF operation; however, they are not compatible with the strong field gradients used in MRI. We show that a magnetic-dressing technique restores the OAM operability despite the gradient, and we demonstrate submillimetric resolution MRI with a compact experimental setup based on an in situ detection. The proof-of-concept experiment produces unidimensional imaging of remotely magnetized samples with a dual sensor, but the approach is suited to be adapted for 3-D imaging of samples magnetized in loco. An extension to multisensor architectures is also possible. 

Magnetic hydrogels are interesting nanomaterials able to change their shape and temperature if exposed to external magnetic fields. Thanks to these features, which originate from the microstructure of magnetic hydrogels (magnetic nanoparticles tied together through polymeric chains), these substances have several applications in technological fields and biomedicine. Hydrogels are able to absorb and release large amounts of water, which makes them eligible materials for drug delivery. This feature is made even more attractive in cases where the delivery/release can be externally controlled. Controlling the system using external magnetic fields requires keystone processes like modeling and simulation. In this paper, the properties of the system have been analyzed using a 2D microscopical simulation of a suitable physical model. Experimentally, the behavior of the system with and without the application of external magnetic fields and its dissipative effects have been characterized. Specifically, we analyze the change of size and temperature of an hydrogel system as a function of the external magnetic field frequency, thus providing a fundamental tool for developing magnetic substances suitable for specific applications. 

Nuclear magnetic resonance detection in ultra-low-field regime enables the measurement of different components of a spurious remanence in the polymeric material constituting the sample container. A differential atomic magnetometer detects simultaneously the static field generated by the container and the time-dependent signal from the precessing nuclei. The nuclear precession responds with frequency shifts and decay rate variations to the container magnetization. Two components of the latter act independently on the atomic sensor and on the nuclear sample. A model of the measured signal allows a detailed interpretation on the basis of the interaction geometry. 

We report on the use of parametric excitation to coherently manipulate the collective spin state of an atomic vapor at room temperature. Signatures of the parametric excitation are detected in the ground-state spin evolution. These include the excitation spectrum of the atomic coherences, which contains resonances at frequencies characteristic of the parametric process. The amplitudes of the signal quadratures show amplification and attenuation, and their noise distribution is characterized by a strong asymmetry, similar to those observed in mechanical oscillators. The parametric excitation is produced by periodic modulation of the pumping beam, exploiting a Bell-Bloom-like technique widely used in atomic magnetometry. Notably, we find that the noise squeezing obtained by this technique enhances the signal-to-noise ratio of the measurements up to a factor of 10, and improves the performance of a Bell-Bloom magnetometer by a factor of 3. 

We study the possibility of counteracting the line broadening of atomic magnetic resonances due to inhomogeneities of the static magnetic field by means of spatially dependent magnetic dressing, driven by an alternating field that oscillates much faster than the Larmor precession frequency. We demonstrate that an intrinsic resonance linewidth of 25 Hz that has been broadened up to hundreds of hertz by a magnetic field gradient can be recovered by the application of an appropriate inhomogeneous dressing field. The findings of our experiments may have immediate and important implications, because they enable the use of atomic magnetometers as robust, high-sensitivity sensors to detect in situ the signal from ultralow-field NMR-imaging setups. 

We present a method developed to actively compensate common-mode magnetic disturbances on a multisensor device devoted to differential measurements. The system uses a field-programmable-gated-array card, and operates in conjunction with a high-sensitivity magnetometer: compensating the common mode of magnetic disturbances results in a relevant reduction of the difference-mode noise. The digital nature of the compensation system allows for the use of a numerical approach aimed at automatically adapting the feedback-loop filter response. A common-mode-disturbance attenuation exceeding 50 dB is achieved, resulting in a final improvement of the differential noise floor by a factor  of 10 over the whole spectral interval of interest. 

Spin-exchange collisions in hot vapors are generally regarded as a decoherence mechanism. In contrast, we show that linear and nonlinear spin-exchange coupling can lead to the generation of atomic coherence in a Bell-Bloom magnetometer. In particular, we theoretically and experimentally demonstrate that nonlinear spin-exchange coupling, acting in an analogous way to a wave-mixing mechanism, can create additional modes of coherent excitation which inherit the magnetic properties of the natural Larmor coherence. The generated coherences further couple via linear spin-exchange interaction, leading to an increase of the natural coherence lifetime of the system. Notably, the measurements are performed in a low-density caesium vapor and for nonzero magnetic field, outside the standard conditions for collisional coherence transfer. The strategies discussed are important for the development of spin-exchange coupling into a resource for an improved measurement platform based on room-temperature alkali-metal vapors. 

We present NMR spectra of remote-magnetized deuterated water, detected in an unshielded environment by means of a differential atomic magnetometer. The measurements are performed in a μT field, while pulsed techniques are applied—following the sample displacement—in a 100 μT field, to tip both D and H nuclei by controllable amounts. The broad-band nature of the detection system enables simultaneous detection of the two signals and accurate evaluation of their decay times. The outcomes of the experiment demonstrate the potential of ultra-low-field NMR spectroscopy in important applications where the correlation between proton and deuteron spin–spin relaxation rates as a function of external parameters contains significant information.  

A low cost, stable, programmable, unipolar current source is described. The circuit is designed in view of a modular arrangement, suitable for applications where several DC sources must be controlled at once. A hybrid switching/linear design helps in improving the stability and in reducing the power dissipation and cross-talking. Multiple units can be supplied by a single DC power supply, while allowing for a variety of maximal current values and compliance voltages at the outputs. The circuit is analogically controlled by a unipolar voltage, enabling current programmability and control through commercial digital-to-analogue conversion cards.  

We investigate magnetic resonances driven in thermal vapor of alkali-metal atoms by laser radiation broadly modulated at a frequency resonant with the Zeeman splitting. A model accounting for both hyperfine and Zeeman pumping is developed, and its results are compared with experimental measurements performed at relatively weak pump irradiance. The interplay between the two pumping processes generates intriguing interaction conditions, often overlooked by simplified models. 

We present experimental data and theoretical interpretation of NMR spectra of remotely magnetized samples, detected in an unshielded environment by means of a differential atomic magnetometer. The measurements are performed in an ultra-low-field at an intermediate regime, where the J-coupling and the Zeeman energies have comparable values and produce rather complex line sets, which are satisfactorily interpreted.  

A multichannel atomic magnetometer operating in an unshielded environment is described and characterised. The magnetometer is based on D1 optical pumping and D2 polarimetry of Cs vapour contained in gas-buffered cells. Several technical implementations are described and discussed in detail. The demonstrated sensitivity of the set-up is 100fT/sqrtHz when operating in the difference mode.  

The electron tunneling current through nanostructures is considered in the presence ofthe electron-phonon interactions. In the Keldysh nonequilibrium formalism, the lesser,greater, advanced and retarded self-energies components are expressed by means ofappropriate Langreth rules. We discuss the key role played by the entailed Hilberttransforms, and provide an analytic way for their evaluation. Particular attention isgiven to the current-conserving lowest-order-expansion for the treament of theelectron-phonon interaction; by means of an appropriate elaboration of the analyticproperties and pole structure of the Green’s functions and of the Fermi functions, wearrive at a surprising simple, elegant, fully analytic and easy-to-use expression of theHilbert transforms and involved integrals in the energy domain. 

We study quantum transport through two-terminal nanoscale devices in contact with two particle reservoirs at different temperatures and chemical potentials. We discuss the general expressions controlling the electric charge current, heat currents, and the efficiency of energy transmutation in steady conditions in the linear regime. With focus in the parameter domain where the electron system acts as a power generator, we elaborate workable expressions for optimal efficiency and thermoelectric parameters of nanoscale devices. The general concepts are set at work in the paradigmatic cases of Lorentzian resonances and antiresonances, and the encompassing Fano transmission function: the treatments are fully analytic, in terms of the trigamma functions and Bernoulli numbers. From the general curves here reported describing transport through the above model transmission functions, useful guidelines for optimal efficiency and thermopower can be inferred for engineering nanoscale devices in energy regions where they show similar transmission functions.