Field Metrology Research Articles

Enhanced Quantum Metrology with Non-Phase-Covariant Noise.

The detrimental impact of noise on sensing performance in quantum metrology has been widely recognized by researchers in the field. However, there are no explicit fundamental laws of physics stating that noise invariably weakens quantum metrology. We reveal that phase-covariant noise either degrades or remains neutral to sensing precision, whereas non-phase-covariant noise can potentially enhance parameter estimation, surpassing even the ultimate precision limit achievable in the absence of noise. This implies that a non-Hermitian quantum sensor may outperform its Hermitian counterpart in terms of sensing performance. To illustrate and validate our theory, we present several paradigmatic examples of magnetic field metrology.

Design and measurement of three-dimensional uniform-field coils based on swarm intelligence algorithms under ferromagnetic boundaries

Combination systems of high permeability magnetic shields and coils are widely used in fields such as the magnetic field standard metrology and the zero magnetic room construction. To solve the problem that the magnetic field of uniform-field coils under the ferromagnetic boundary of magnetic shields is difficult to design precisely and the uniformity is difficult to improve, three-dimensional uniform field coils are designed based on the magnetic field model of coils under the ferromagnetic boundary using the target-field method (TFM), and the weight coefficient vectors determining the coils’ structure are optimized using intelligent optimization algorithms, which improves the uniformity of the magnetic field in the target region by 2 orders of magnitude through whale optimization algorithm (WOA). Then, the radial WOA-TFMUFY coil and the axial WOA-TFMUFZ coil are designed considering sidewall optical holes, and their magnetic field distribution is analyzed and verified under different permeabilities and axial opening sizes of the shield. Compared to the traditional saddle coil and Lee-whiting coil, the maximum magnetic field non-uniformity in the target uniform field region is reduced by 82.2 % and 92.8 % for the WOA-TFMUFY coil and WOA-TFMUFZ coil. The maximum relative errors between the measured magnetic field generated by the designed coils and the finite element method (FEM) simulation results are no higher than 2.2%. This novel method can provide more precise and uniform magnetic field metrology standard elements.

RF spectra induced by different polarized microwave

Electric field measurement techniques based on Rydberg atoms have proven to have unique advantages in high sensitivity and have drawn wide attention in microwave electric field metrology and communication. The Rydberg states employed for microwave sensing are usually excited by two- or three-step laser irradiation. It leads to the Rydberg atoms being populated by some specific magnetic quantum number states determined by the laser polarization configurations, whose further coupling to another Rydberg state is also constrained by the microwave polarization. Based on a three-laser optical excitation, we demonstrate this effect on the microwave spectra of the 85Rb transitions 41F7/2 → 42D5/2 and 41F7/2 → 41G7/2 at various combining polarization configurations. It shows a strong polarization dependence on the microwave spectrum and then affects the sensitivity of Rydberg atom-based microwave field sensing. Advisable polarization schemes for higher sensitivity are suggested by the two types of transitions.

Experimental Recognition of Plastic Domain in Contact Problem Based on Full Field Metrology and Neural Network

Contact usually results in stress concentration which can easily cause the yield of materials and structures. The classic elastic–plastic yield criterion needs to utilize stress or strain field for calculation. However, most advanced full-field measurement methods output the displacement as the original data, and the fitting from displacement to strain will induce error accumulation in applications. In this paper, a plastic domain characterization method is developed that can directly judge the elastic–plastic state of materials based on the full-field displacement and neural network. By establishing and training a three-layer-based neural network, the relationship between the displacement and the elastic/plastic stage of the sampling points is modeled. A physical model is formulated based on the yield criterion and embedded in the layer of the network, which can increase the convergence rate and accuracy. Only the displacements of the contact member are required in this method, which can be easily measured by the optical metrologies. The performances of the developed method are carefully discussed through simulated data and real-world tests. Results show that the method can accurately identify the plastic domain during the tests.

Microwave Field Metrology Based on Rydberg States of Alkali-Metal Atoms

The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.

Petahertz-scale nonlinear photoconductive sampling in air

The electric field waveform of a light field can be used to unlock a detailed recording of its interaction with matter, but accessing it requires a measurement with subfemtosecond temporal resolution. We demonstrate nonlinear photoconductive sampling of light fields at optical frequencies in ambient air. The resulting detection method provides broadband electric field measurement in an inexpensive setup using a self-healing medium. A direct comparison is made between detection in air and in quartz, validating the technique up to 0.7 PHz. This provides both a simple route toward field metrology and a new platform for future studies in attosecond physics without the need for complex vacuum setups or sophisticated sample preparation.

Deceleration of optical pulses based on electromagnetically induced transparency of Rydberg atoms

Based on the Electromagnetically-Induced-Transparency (EIT) effect of cesium Rydberg atoms, the dispersion of the probe light will experience a drastically change while the absorption is diminished, as the frequency of it is resonated with that of the corresponding atomic transition. In this case, as the light pulse propagates in the atomic medium, the group velocity of the pulse will be slowed. In the cesium atoms 3-ladder-level system (<inline-formula><tex-math id="M2">\begin{document}$ 6{\rm S}_{1/2}\rightarrow6{\rm P}_{3/2}\rightarrow49{\rm D}_{5/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M2.png"/></alternatives></inline-formula>),the frequency of the probe light is locked at the resonance transition of <inline-formula><tex-math id="M3">\begin{document}$ 6{\rm S}_{1/2}\rightarrow6{\rm P}_{3/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M3.png"/></alternatives></inline-formula>, while the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency near the transition of <inline-formula><tex-math id="M4">\begin{document}$ 6{\rm P}_{3/2}\rightarrow49{\rm D}_{5/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M4.png"/></alternatives></inline-formula>, We observed the EIT phenomenon and explored the relationship between the power of coupling laser and linewidth of the EIT signal. The experimental results show that the linewidth of the EIT signal is proportional to the power of the coupling laser. Then under the two-photon resonance condition, the deceleration of the probe light pulse caused by the steep change of the dispersion curve is observed. We also systematically investigate the influences of coupling optical power and temperature of vapor cell on the slowing down of light pulse. The experimental results show that the weaker the coupled light was, the longer the delay time; and the higher the temperature of the atomic gas chamber was, the more obvious the deceleration effect would be observed, those of which are consistent with the theoretical calculations. The investigation of the deceleration of optical pulses based on the Rydberg Electromagnetically-Induced-Transparency is important for understanding the coherence mechanism of 3-ladder-level system and some potential applications, such as in Rydberg-atom-based electric field metrology. This research provides a new tool for the measurement of pulsed microwave electric field through the optical pulse deceleration effect.

Phase-Sensitive Vector Terahertz Electrometry from Precision Spectroscopy of Molecular Ions

This article proposes a new method for sensing THz waves that can allow electric field measurements traceable to the International System of Units and to the fundamental physical constants by using the comparison between precision measurements with cold trapped HD+ ions and accurate predictions of molecular ion theory. The approach exploits the lightshifts induced on the two-photon rovibrational transition at 55.9 THz by a THz wave around 1.3 THz, which is off-resonantly coupled to the HD+ fundamental rotational transition. First, the direction and the magnitude of the static magnetic field applied to the ion trap is calibrated using Zeeman spectroscopy of HD+. Then, a set of lightshifts are converted into the amplitudes and the phases of the THz electric field components in an orthogonal laboratory frame by exploiting the sensitivity of the lightshifts to the intensity, the polarization and the detuning of the THz wave to the HD+ energy levels. The THz electric field measurement uncertainties are estimated for quantum projection noise-limited molecular ion frequency measurements with the current accuracy of molecular ion theory. The method has the potential to improve the sensitivity and accuracy of electric field metrology and may be extended to THz magnetic fields and to optical fields.

A Multiple-Band Rydberg Atom-Based Receiver: AM/FM Stereo Reception

With the re-definition of the International System of Units (SI) that occurred in October of 2018, there has recently been a great deal of attention on the development of atom-based sensors for metrology applications. In particular, great progress has been made in using Rydberg-atom based techniques for electric (E) field metrology. These Rydberg-atom based E-field sensors have made it possible to develop atom-based receivers and antennas, which potentially have many benefits over conventional technologies in detecting and receiving modulated signals. In this paper, we demonstrate the ``first'' multi-channel atom-based reception of both amplitude (AM) and frequency (FM) modulation signals. We demonstrate this by using two different atomic species in order to detect and receive AM and FM modulated signals in stereo. Also, in this paper we investigate the effect of Gaussian noise on the ability to receive AM/FM signals. These results illustrate the multi-band (or multi-channel) receiving capability of a atom-based receiver/antenna to produce high fidelity stereo reception from both AM and FM signals. This paper shows an interesting way of applying the relatively newer (and something esoteric) field of quantum-optics and atomic-physics to the century old topic of radio reception.

Attosecond optoelectronic field measurement in solids

The sub-cycle interaction of light and matter is one of the key frontiers of inquiry made accessible by attosecond science. Here, we show that when light excites a pair of charge carriers inside of a solid, the transition probability is strongly localized to instants slightly after the extrema of the electric field. The extreme temporal localization is utilized in a simple electronic circuit to record the waveforms of infrared to ultraviolet light fields. This form of petahertz-bandwidth field metrology gives access to both the modulated transition probability and its temporal offset from the laser field, providing sub-fs temporal precision in reconstructing the sub-cycle electronic response of a solid state structure.

Improving the calibration of phase measuring deflectometry by a polynomial representation of the display shape

BackgroundPhase measuring deflectometry is a highly precise and full field metrology technique for specular surfaces based on the distortion of known reference patterns observed as a reflection at the surface under test. Typically, liquid crystal displays are employed to provide the required patterns. Due to a lack of research, these displays are used without sufficient calibration.MethodsIn this work, we present an enhanced calibration for phase measuring deflectometry, taking flatness deviations of the display surface into account. The display shape is modelled as a polynomial surface whose coefficients are determined by minimizing the retrace error in a global optimization procedure during calibration. This approach does not require any additional measurements or hardware. Improvements due to the enhanced calibration model are qualified experimentally using a flat and a spherical concave mirror.Results and conclusionThe model-based parameterization of the display surface yields significant improvement on both samples. The peak to valley (PV) of measured deviations on the plane mirror are reduced by 67% to 0.55 μm. Measuring the spherical sample without the display parameterization leads to a rather large shape deviation of 33.40 μm PV which is reduced by 94% to 1.98 μm. The viability of our approach confirms the dominant role of flatness deviations of the display surface as an error source in absolute shape measurement using phase measuring deflectometry.

Halbach Effect at the Nanoscale from Chiral Spin Textures

Mallinson's idea that some spin textures in planar magnetic structures could produce an enhancement of the magnetic flux on one side of the plane at the expense of the other gave rise to permanent magnet configurations known as Halbach magnet arrays. Applications range from wiggler magnets in particle accelerators and free electron lasers to motors and magnetic levitation trains, but exploiting Halbach arrays in micro- or nanoscale spintronics devices requires solving the problem of fabrication and field metrology below a 100 μm size. In this work, we show that a Halbach configuration of moments can be obtained over areas as small as 1 μm × 1 μm in sputtered thin films with Néel-type domain walls of unique domain wall chirality, and we measure their stray field at a controlled probe-sample distance of 12.0 ± 0.5 nm. Because here chirality is determined by the interfacial Dyzaloshinkii-Moriya interaction, the field attenuation and amplification is an intrinsic property of this film, allowing for flexibility of design based on an appropriate definition of magnetic domains. Skyrmions (<100 nm wide) illustrate the smallest kind of such structures, for which our measurement of stray magnetic fields and mapping of the spin structure shows they funnel the field toward one specific side of the film given by the sign of the Dyzaloshinkii-Moriya interaction parameter D.

Noise transfer characteristics of Rydberg electromagnetically induced transparency

The transfer mechanism from the amplitude noise of the coupling light to the phase noise of the probe light in a Rydberg electromagnetic induced transparency effect derived from a ladder-type system including 6S1/2↔6P3/2↔62D5/2 of Cs atoms is demonstrated by using Mach-Zehnder interferometer and balanced homodyne detection technology. In our experiments, the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency nearby the transition from 6P3/2 to 62D5/2 Rydberg state, while the frequency of the probe light is locked at the resonance transition of the 6S1/2↔6P3/2. The relative phase stability of two arms of Mach-Zehnder interferometer, which is constructed with the first order diffraction light of probe light through an acoustic-optic modulator, is accomplished by the controlled piezoelectric ceramic with the PID feedback loop. The interferences between the probe light and the reference light of Mach-Zehnder interferometer under the different relative phases are observed. The interference spectrum of probe light is in good agreement with the theoretical simulation result of the ladder-type three-level system. Therefore, we study the transfer characteristics from the frequency noise of coupling light to the phase noise of probe light when coupling light frequency resonance happens at the transition 6P3/2↔62D5/2. We find the significant suppression of the phase noise of probe light at the higher frequency noise. Moreover, we observe the characteristics of the phase noise of the probe light varying with the power of the coupling light under the different detuning degrees of coupling light. In the red detuning side, the transferred phase noise of probe light decreases with the increase of coupling light power, which is different significantly from the scenario under the blue detuning condition. The ions produced in the ionization process of Rydberg atoms will form the local electric field that would cause the energy level of Rydberg states to shift. The investigation of the noise transfer between the coupling light and probe light in the Rydberg electromagnetically induced transparency effect is important for understanding the coherence mechanism of ladder-type system and the some potential applications, such as in Rydberg-atom-based electric field metrology.

Electric field metrology for SI traceability: Systematic measurement uncertainties in electromagnetically induced transparency in atomic vapor

We investigate the relationship between the Rabi frequency (ΩRF, related to the applied electric field) and Autler-Townes (AT) splitting, when performing atom-based radio-frequency (RF) electric (E) field strength measurements using Rydberg states and electromagnetically induced transparency (EIT) in an atomic vapor. The AT splitting satisfies, under certain conditions, a well-defined linear relationship with the applied RF field amplitude. The EIT/AT-based E-field measurement approach derived from these principles is currently being investigated by several groups around the world as a means to develop a new SI-traceable RF E-field measurement technique. We establish conditions under which the measured AT-splitting is an approximately linear function of the RF electric field. A quantitative description of systematic deviations from the linear relationship is key to exploiting EIT/AT-based atomic-vapor spectroscopy for SI-traceable field measurement. We show that the linear relationship is valid and can be used to determine the E-field strength, with minimal error, as long as the EIT linewidth is small compared to the AT-splitting. We also discuss interesting aspects of the thermal dependence (i.e., hot- versus cold-atom) of this EIT-AT technique. An analysis of the transition from cold- to hot-atom EIT in a Doppler-mismatched cascade system reveals a significant change of the dependence of the EIT linewidth on the optical Rabi frequencies and of the AT-splitting on ΩRF.

Atom-Based RF Electric Field Metrology: From Self-Calibrated Measurements to Subwavelength and Near-Field Imaging

We discuss a fundamentally new method for electric (E) field strength (V/m) metrology applicable to the near-field. This new approach is significantly different from currently used field measurement techniques in that it is based on the interaction of radio-frequency (RF) E-fields with Rydberg atoms (alkali atoms placed in a glass vapor cell that are excited optically to Rydberg states). The applied RF E-field alters the state of the atoms. The Rydberg atoms act like an RF-to-optical transducer, converting an RF E-field strength to an optical-frequency response. In this new approach, we employ the phenomena of electromagnetically induced transparency (EIT) and Autler-Townes splitting. The RF transition in the four-level atomic system causes a split of the EIT transmission spectrum of a probe laser into two peaks. This splitting is easily measured and is directly proportional to the applied RF E-field amplitude. The significant dipole response of Rydberg atoms enables this technique to make self-calibrating measurements over a large frequency band including 500 MHz to 500 GHz (and possibly up to 1 THz and down to 10s of megahertz). In this paper, we report on our results in the development of this metrology approach, including the first fiber-coupled vapor-cell for E-field measurements. We also discuss key applications, including self-calibrated measurements, millimeter-wave and sub-THz measurements, field mapping, and sub-wavelength and near-field imaging. We show results for mapping the fields inside vapor cells, for measuring the E-field distribution along the surface of a circuit board, and for measuring the near-field at the aperture in a cavity. We also discuss the uncertainties of this measurement technique.

Electrical Characterization of PV Modules employing Supercapacitors – A Scalable Method for Field Metrology

Electrical Characterization of PV Modules employing Supercapacitors – A Scalable Method for Field Metrology

Atom-interferometric measurement of Stark level splittings

Multiple adiabatic/diabatic passages through avoided crossings in the Stark map of cesium Rydberg atoms are employed as beam splitters and recombiners in an atom-interferometric measurement of energy-level splittings. We subject cold cesium atoms to laser-excitation, electric-field and detection sequences that constitute an (internal-state) atom interferometer. For the read-out of the interferometer we utilize state-dependent collisions, which selectively remove atoms of one kind from the detected signal. We investigate the dependence of the interferometric signal on timing and field parameters, and find good agreement with time-dependent quantum simulations of the interferometer. Fourier analysis of the interferometric signals yield coherence frequencies that agree with corresponding energy-level differences in calculated Stark maps. The method enables spectroscopy of states that are inaccessible to direct laser-spectroscopic observation, due to selection rules, and has applications in field metrology.

Metrology Information System for Management and Field Scene Detection

In order to deal with the field metrology, this paper proposed an information management system which contains daily work management section, human resource section, data management section, auto-reminding section and portable device. It combines the human resource management, equipment management, data processing and filed detection and embodies them in one system located in office and the other one in field. As an information system, it ensures the security and reliability of detection data.

Direct measurement of the field from a magnetic recording head using an InAs Hall sensor on a contact write/read tester

At 1Tbit/in2 areal density magnetic recording dimensions, reliable magnetic field metrology does not exist. One technique to map the spatial profile of the magnetic field of a write head is to use a contact read/write tester. A magnetic recording head is brought into contact with a Hall sensor, and is subsequently scanned with nm resolution. For a 300nm track width longitudinal recording head, the magnetic field of the head was mapped. Measurements include the down track field gradient and cross-track field profile and the current-field transfer curve. These results suggest this technique offers a viable write field metrology.

High-accuracy displacement interferometry refin air

The absolute accuracy of laser interferometers employed in displacement metrology is limited by two dominant factors: uncertainties in the source vacuum wavelength and the refractive index of the ambient air. In this paper we describe an interferometer system designed to minimize these uncertainties. Based on a commercial interferometer, the new system features direct measurement of the vacuum wavelength by frequency comparison with a portable iodine-stabilized He–Ne laser. The refractive index of air is computed from accurately measured values of pressure, temperature, and relative humidity. Combined with a desktop computer, the interferometer system permits the automated field measurement of displacement errors (such as those associated with precision machine tools) with an absolute accuracy of 8.5 parts in 108. Performance of the interferometer in field metrology is illustrated by the results of recent validation testing of the large optics diamond turning machine (LODTM) at Lawrence Livermore National Laboratory. These results highlight the need for new measurements of the absolute refractive index of standard air in order to reduce a limiting uncertainty on such measurements of ±5 parts in 108.