High-precision Phase Measurement Research Articles

Quantum Fisher information of multi-qubit WV entangled state under Lipkin-Meshkov-Glick model

As an important quantity in the field of parameter estimation theory and quantum precision measurement, quantum Fisher information (QFI) can not only be used to set the theoretical limit of measurement precision in quantum system, but also be exploited to witness metrological useful quantum entanglement. Recently, it has also been broadly used in many aspects of quantum information science, including quantum metrology, multipartite entanglement structure detection, quantum phase transition, quantum chaos, quantum computation and etc. In this work, from the perspective of quantum measurement, we study the quantum Fisher information of an <i>N</i>-qubit WV state (<inline-formula><tex-math id="M4">\begin{document}$\alpha \left\vert W_N \right\rangle +\sqrt{1-\alpha^2}\left\vert 00\cdots0\right\rangle$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231179_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231179_M4.png"/></alternatives></inline-formula>) under local operation and Lipkin-Meshkov-Glick (LMG) model. Furthermore, with the general Cramér-Rao lower bound (CRLB) we analyze its performance in high-precision phase measurement. The results show that, under the local operation, the QFI of an <i>N</i>-qubit WV state becomes larger with the increase of parameter <i>α</i>. This not only means the enhanced quantum entanglement, but also implies the powerful ability in high-precision quantum measurement. In the LMG model, as the increase of interactional strength <i>γ</i> the QFI of <inline-formula><tex-math id="M5">\begin{document}$N=3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231179_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231179_M5.png"/></alternatives></inline-formula> qubits WV state gradually tends to be stable and almost not be affected by parameter <i>α</i>, which relaxes the requirement in the preparation of target state and indicates a great potential in achieving the relatively stable measurement precision. When the number of qubits from WV state is larger than 3, the QFI of WV state increases with the increase of parameter <i>α</i>. In the case of fixed parameter <i>α</i>, we investigate the QFI of an <i>N</i>-qubit WV state with respect to interaction strength <i>γ</i>. It is found that the QFI of WV state will increase with the increasing interaction strength, which implies that the greater the interaction strength, the stronger the quantum measurement ability of the WV state. Our work will promote the development of high-precision quantum metrology and especially the interaction-enhanced quantum measurement, and further provide new insights in quantum information processing.

A high precision phase measurement system implemented in FPGA with phase interpolator.

High precision timing distribution is crucial to many large scale cosmology and particle physics experiments. Besides the space and energy information, the accurate timing provides an extra dimension for physics event reconstruction. In the timing distribution system, accurate clock phase measurement is an indispensable tool to monitor the phase drift and to achieve accurate phase adjustment. This paper introduces a novel phase measurement method implemented in the Xilinx Field Programmable Gate Array (FPGA). It uses the dedicated phase interpolator in the multi-gigabit transceiver. A design based on this method is implemented within the Kintex Ultrascale series FPGA. The preliminary test result shows that a sub-picosecond level precision is achieved. With this system, the nonlinearity of the phase adjustment in the Xilinx transceiver is measured.

High precision phase estimation with controllable sensitivity and dynamic range

High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.

Analysis and design of fringe phase control system for scanning beam interference lithography

Scanning beam interference lithography (SBIL) is an advanced technology developed for manufacturing large-area diffraction grating at a nanometer-scale phase accuracy. To withstand environmental disturbances and maintain the interference fringes still relative to the substrate, SBIL requires high-precision phase control. We proposed a fringe phase control system with homodyne detection for SBIL. First, a homodyne detector is employed to achieve high-precision phase measurement, while ensuring the simplicity of the optics and high laser utilization. The time-varying nonlinear error in the measurement results is corrected by a dynamic ellipse fitting method. To reduce the latency effect, a lead controller is designed using the root locus method based on the model identification result. The lead controller considerably increases the control bandwidth while ensuring a sufficient phase margin, which further suppresses disturbances and stabilizes the interference fringes to within ∼1 / 60 of the fringe period. Wide-range phase tracking for perpendicular scanning with high accuracy is also verified through an experiment.

Absolute phase marking technology and fiber-optic remote coherent phase transmission.

Fiber-optic time and frequency synchronization technology demonstrates ultra-high synchronization performance and has been gradually applied in various fields. Based on frequency synchronization, this study addressed the problems of period ambiguity and initial phase uncertainty of the phase signal to realize the coherent transmission of the phase. An absolute phase marking technology was developed based on high-speed digital logic with zero-crossing detection and an optimized control strategy. It can realize picosecond-level absolute phase marking and provide a picosecond-level ultra-low peak-to-peak jitter pulse marking signal to eliminate phase period ambiguity and determine initial phase and transmission delay. Thus, by combining the high-precision phase measurement capability of the synchronized frequency signal and long-distance ambiguity elimination capability of the pulse-per-second signal, a high-precision remote coherent phase transmission over an optical fiber is realized. After frequency synchronization, the peak-to-peak jitter between the local and remote phase-marking signals can be only 3.3 ps within 10,000 s measurement time. The uncertainty of the coherent phase transmission is 2.577 ps. This technology can significantly improve the phase coherence of fiber-optic time and frequency transmission and provide a new approach to achieve peak-to-peak picosecond-level reference phase marking and high-precision fiber-optic remote coherent phase transmission. This demonstrates broad application prospects in coherence fields such as radar networking.

Dynamic low-coherence interferometry using a double Fizeau cavity.

The coexistence of anti-vibration and a common optical path is difficult to realize in dynamic Fizeau interferometry. To address this problem, we propose a dynamic low-coherence interferometry (DLI) using a double Fizeau cavity. The DLI method is a new optical model that creatively renders both surfaces of the RM to interfere with the test surface, utilizing a low-coherence source and optical path matching to construct the common-path p-polarized Fizeau cavity (p-FC) and carrier-frequency s-polarized Fizeau cavity (s-FC). The relative tilt phases of the s-FC are calculated using the carrier frequency interferograms; then the final phase is retrieved with the relative tilt phases and p-FC interferograms. The experimental results demonstrate that the DLI method can provide high-precision phase measurement in a vibration environment.

Wide-view and accurate deformation measurement at microscales by phase extraction of scanning moiré pattern with a spatial phase-shifting technique.

A scanning-based second-order moiré method is proposed for high-accuracy deformation measurement in a large field of view (FOV) by analyzing the phase distribution of a single-shot scanning moiré fringe image using a spatial phase-shifting technique. In this method, the grating pitch can be as small as around one pixel in the scanning moiré image to ensure a wide FOV, while high-precision phase measurement is achievable. The strain measurement accuracy has been verified from simulations at different grating pitches, applied strains, and noise levels. The simulation results show that the closer the grating pitch is to the scanning pitch, the smaller the strain measurement error, and the recommended pitch ratio is 0.9∼1.1. Furthermore, the feasibility of this method has been verified from a tensile experiment on an aluminum specimen under a laser scanning microscope with scanning moiré images recorded. The microscale strains of aluminum measured at different tensile loads agree well with the strain gauge results. As an integration of the scanning and sampling moiré methods, this method has the advantages of a large FOV, high accuracy, strong noise immunity, and visualization of magnified deformation. Compared with the traditional phase-shifting scanning moiré method, this method only needs to record a single scanning moiré image and is suitable for dynamic deformation analysis.

GNSS attitude estimation based on adaptive Kalman filtering using phase measurement

Attitude estimation using multi-antenna Global Navigation Satellite System (GNSS) has caught broad attention in recent years. The methods of indirectly calculating attitude parameters based on baseline vectors have been widely used. However, the accuracy of such methods needs to be further improved. An algorithm of directly estimating attitude parameters based on adaptive Kalman filtering (AKF) is proposed. The high-precision phase measurements are used and the system noise covariance matrix corresponding to Euler angles and angle rates is adaptively adjusted according to the maximum a posteriori estimation principle. To decrease the linearisation errors and speed the filtering convergence, a switching strategy is implemented. Namely, when the number of fixed ambiguities is equal to or more than three, the authors deem that the attitude estimate is sufficiently accurate, hence the initial state vector is constructed to start filtering. Otherwise, the attitude parameters are indirectly obtained. The static and simulation experiments are carried out. A comparative study is implemented with the two methods of indirectly calculating attitude parameters. The static and simulation results demonstrate that the proposed method has a competent performance in both accuracy and fixing success rate. The simulation results also show that the adaptability of the AKF method is nice.

Three-dimensional entanglement on a silicon chip

Entanglement is a counterintuitive feature of quantum physics that is at the heart of quantum technology. High-dimensional quantum states offer unique advantages in various quantum information tasks. Integrated photonic chips have recently emerged as a leading platform for the generation, manipulation and detection of entangled photons. Here, we report a silicon photonic chip that uses interferometric resonance-enhanced photon-pair sources, spectral demultiplexers and high-dimensional reconfigurable circuitries to generate, manipulate and analyse path-entangled three-dimensional qutrit states. By minimizing on-chip electrical and thermal cross-talk, we obtain high-quality quantum interference with visibilities above 96.5% and a maximally entangled-qutrit state with a fidelity of 95.5%. We further explore the fundamental properties of entangled qutrits to test quantum nonlocality and contextuality, and to implement quantum simulations of graphs and high-precision optical phase measurements. Our work paves the path for the development of multiphoton high-dimensional quantum technologies.

Quantitative phase imaging based on Fresnel diffraction from a phase plate

The structural complexity and instability of many interference phase microscopy methods are the major obstacles toward high-precision phase measurement. In this vein, improving more efficient configurations as well as proposing methods are the subjects of growing interest. Here, we introduce Fresnel diffraction from a phase step to the realm of quantitative phase imaging. By employing Fresnel diffraction of a divergent (or convergent) beam of light from a plane-parallel phase plate, we provide a viable, simple, and compact platform for three-dimensional imaging of micrometer-sized specimens. The recorded diffraction pattern of the outgoing light from an imaging system in the vicinity of the plate edge can be served as a hologram, which would be analyzed via the Fourier transform method to measure the sample phase information. The period of diffraction fringes is adjustable simply by rotating the plate without the reduction of both the field of view and fringe contrast. The high stability of the presented method is affirmatively confirmed through comparison of the result with that of the conventional Mach–Zehnder based digital holographic method. Quantitative phase measurements on silica microspheres, onion skins, and red blood cells ensure the validity of the method and its ability for monitoring nanometer-scale fluctuations of living cells, particularly in real-time.

Dynamic phase-deforming interferometry: suppression of errors from vibration and air turbulence.

In this Letter, dynamic phase-deforming interferometry (PDI) is proposed to solve the impact of environmental vibration and air turbulence on the measurement accuracy. Two interference passes, namely, the measurement pass (MP) and carrier-frequency pass (CP), are constructed, utilizing one detector to acquire the fringe patterns of the two passes simultaneously. The relative deformation phases of the CP fringe patterns are calculated with the Fourier transform method; then the phase extraction of the MP is performed via the least squares method to obtain the final phase distribution. The optical layout and phase-extraction algorithm of the PDI method are investigated, and the principle simulation and measurement experiments are performed. The experimental results show that the PDI can provide not only high-precision phase measurement under the influence of environmental vibration and air turbulence, but also has low system complexity and fast measurement speed.

An Innovative High-Precision Scheme for a GPS/MEMS-SINS Ultra-Tight Integrated System.

The Doppler-assisted error provided by a low-precision microelectromechanical system (MEMS) strapdown inertial navigation system (SINS) increases rapidly. Therefore, the bandwidth of the tracking loop for a global positioning system (GPS)/MEMS-SINS ultra-tight integration system is too narrow to track Doppler shift. GPS measurement error is correlated with the MEMS-SINS velocity error when the Doppler-assisted error exists, leading to tracking loop lock loss. The estimated precision of the integrated Kalman filter (IKF) also decreases. Even the integrated system becomes unstable. To solve this problem, an innovative GPS/MEMS-SINS ultra-tight integration scheme based on using high-precision carrier phase measurements as the IKF measurements is proposed in this study. By assisting the tracking loop with time-differenced carrier phase (TDCP) velocity, the carrier loop noise bandwidth and code correlator spacing are reduced. The tracking accuracies of the carrier and code are increased. The navigation accuracy of GPS/MEMS-SINS ultra-tight integration is further improved.

Subhertz interferometry at the quantum noise limit.

Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.

Enhanced reference-plane-based dual-frequency absolute phase retrieval for depth measurement

Digital fringe projection is one of the most widely adopted optical non-contact methods used for high-precision depth measurement in industry. Nevertheless, new approaches with less measurement complexity and higher accuracy are still emerging in the research field. In this paper, we first analyze the efficiency of the reference-plane-based dual-frequency (RDF) pixel-by-pixel absolute phase retrieval method. The RDF method is able to provide a high-precision phase measurement, but the constraint of measurement depth range limits its application. We therefore propose an enhanced reference-plane-based dual-frequency (ERDF) pixel-by-pixel absolute phase retrieval method. The proposed ERDF method overcomes the constraint of measurement depth range and preserves the merits of the RDF method. In the ERDF method, the lower-frequency phase map is completely unwrapped with reference-plane-based single-frequency method, and the higher-frequency phase map is completely unwrapped using the lower-frequency unwrapped phase. The ERDF method is suitable for measuring objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the advantages of the proposed ERDF method as compared to the RDF method.

Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths.

A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8μm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120mrad for each and every individual laser shot for a 1kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.

Traceable trans-scale heterodyne interferometer with subnanometer resolution

In order to realize the traceable trans-scale displacement measurements with high resolutions in the fields of fundamental scientific research and ultra-precision machining, we demonstrate a trans-scale heterodyne interferometer with a sub-nanometer resolution, through assembling a compact iodine-stabilized laser at 532 nm. Using modulation transfer spectroscopy, the green laser is traced back to the transition line R(56)32-O(a10), which is one of the recommended spectral lines for meter redefinition. The Allan standard deviation of the laser frequency is 1.310-12 within an average time of 1 s. Compared with most He-Ne lasers, the green laser has a short wavelength and good stability, which leads to a higher resolution. We use two acoustic-optic modulators driven by a two-channel acoustic-optic driver sharing the same crystal oscillator to separate input beams spatially. The frequency of one beam is shifted by 80 MHz and the other is shifted by 82 MHz, which results in a beat frequency of 2 MHz. As a result, the nonlinearity caused by source mixing substantially is reduced. The phase noises of the fibers and two acoustic-optic modulators are well compensated. In order to minimize the difficulty in adjusting the optical path and the error of the measurement, we integrate the interferometry components and design a monolithic prism. The optical resolution of the interferometer reaches to /4. The experiment is carried out in a vacuum environment to reduce the influence of the refractive index of air. High-precision phase measurement technology is used to improve the accuracy of the interferometer. The errors of the interferometer can be classified as random and systematic errors. Random errors include the error from the frequency instability of the laser and the error due to environmental effects. Systematic errors include the phase measurement error and the nonlinearity error. To verify the performance of the interferometer, these errors must be evaluated. In a span of 100 mm, the measurement uncertainties caused by laser wavelength uncertainty, the air refractive index uncertainty, the phase measurement uncertainty and the nonlinearity error are 3 pm, 300 pm, 6.3 pm and 118 pm, respectively. Finally, the performance evaluation shows that the combined uncertainty of the interferometer reaches 322 pm in a span of 100 mm, which is mainly due to the refractive index of air. The heterodyne interferometer meets the requirements for traceable trans-scale measurement with a sub-nanometer resolution, which can be widely used in instrument calibration, length standard making, and geometric measurement.

Surface profile measurement of a highly reflective silicon wafer by phase-shifting interferometry

In phase-shifting Fizeau interferometers, the phase-shift error and multiple-beam interference are the most common sources of systematic error affecting high-precision phase measurements. The nonsinusoidal waveforms can be minimized by applying synchronous detection with more than 4-sample. However, when the phase-shift calibration is inaccurate, these algorithms cannot eliminate the effects of nonsinusoidal characteristics. Moreover, when measuring the surface profile of highly reflective samples, the calculated phase is critically determined not only by the decrease in the fringe contrast but also by the coupling error between the harmonics and phase-shift error. In this paper, the phase errors calculated by conventional phase-shifting algorithms were estimated by considering the coupling error. We show that the 4N−3 algorithm, comprising the polynomial window function and the DFT term, has the smallest phase error among the conventional phase-shifting algorithms. The surface profile of the highly reflective silicon wafer was measured using a wavelength-tuning Fizeau interferometer and the 4N−3 algorithm.

High-precision microscopic phase imaging without phase unwrapping for cancer cell identification

Experiments for cell identification are presented using a high-precision cell phase measurement system that does not require any phase unwrapping. This system is based on a Mach-Zehnder interferometer using a phase-locking technique, and it measures the change in optical path length while the sample is scanned across the optical axis. The spatial resolution is estimated to be less than 1.1μm. The sensitivity of optical path length difference is estimated to be less than 2nm. Using experiments, we investigate the potential of this approach for cancer cell identification. In our preliminary experiments, cancer cells were distinguished from normal cells through comparison of optical path length differences.

High precision phase measurement technique for cell impedance spectroscopy

This paper presents a new approach for high precision phase measurement. The new system is developed for biomedical applications such as complex cell impedance measurement and dielectric tissue analysis. In many of the named applications it is necessary to measure the complex dielectric constant of a sample as a function of frequency. Therefore the developed system is capable of measuring amplitude and especially high precision phase of the measurement signal over a wide frequency range from 10 Hz to 10 MHz. The experimental result of the new method shows a phase resolution of up to 0.01 degree at 1 MHz and 0.1 degree at 10 MHz. The excellent phase measurement resolution is achieved by a time transformation of the signal using a digital sampling circuitry. The functional principle of the digital sampling circuitry is based on Delta – Modulation and is implemented inside a cheap standard FPGA. The new system is successfully used in blood analysis applications and allows for a practical implementation of cost efficient capacitive hematocrit sensors for the first time.

Information protection based on nanosecond synchronization of time scales in meteor burst channel

The work is dedicated to metrological validation of meteor-based method of information protection--new technique for distant encryption key generation which might be capable of providing thorough security. The method is based on high-precision phase measurements of radio signal propagation time performed simultaneously in both forward and backward directions. These measurements are possible only if the communicants' time scales are synchronized with nanosecond precision, which is shown to be possible by meteor time transfer. In order to account for short-term instability of quantum frequency standards, considering irregularity and variable precision of meteor measurements, we use optimal linear filtration and experimental measurement analogue, based on the results of meteor synchronization experiment conducted on the Mendeleevo(Moscow)-Kazan radio path. The possibility of using a meteor channel in two modes for remote time scale synchronization and encryption key generation is shown together with estimates for the capacity of this procedure.