Search

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0, \pi/2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0, \pi)$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology., Comment: 23 pages, 11 figures

Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understanding about their fundamental characteristics and demonstrate their superior performance, we develop a comprehensive statistical analysis based on the Bayesian optimal design of experiments, which provides a natural description of these non-Gaussian strategies. This mathematical framework, together with numerical analysis and Monte Carlo methods, allows us to determine the asymptotic limits in sensitivity of strategies based on photon counting designed to maximize information gain, which up to now had been a challenging problem. Moreover, we show that these non-Gaussian phase estimation strategies have the same functional form as the canonical phase measurement in the asymptotic limit differing only by a scaling factor, thus providing the highest sensitivity among physically-realizable measurements for single-shot phase estimation of coherent states known to date. This work shines light into the potential of optimized non-Gaussian measurements based on photon counting for optical quantum metrology and phase estimation., Comment: 14 pages, 4 figures

The problem of determining the porous silicon (PSi) optical constants, thickness, porosity, and surface quality using just reflectance data is board employing evolutionary algorithms. The reflectance measurements were carried out of PSi films over crystalline silicon (c-Si) substrate, and the fitting procedure was done by using a genetic algorithm. The PSi is treated as a mixture of c-Si and air. Therefore, its effective optical constants can be correlated with the porosity trough effective medium approximation (EMA). The results show that genetic fitting has a good match with the experimental measurements (Near UV-Vis reflectance) and the thickness obtained by scanning electron microscopy (SEM)., Comment: 18 pages, 4 figures

Within this work, the kinetics of the growing stage of porous silicon (PS) during the etching process was studied using the photoacoustic technique. A p-type Si with low resistivity was used as a substrate. An extension of Rosencwaig and Gersho model is proposed in order to analyze the temporary changes that take place in the amplitude of the photoacoustic signal during the PS growth. The solution of the heat equation takes into account the modulated laser beam, the changes in the reflectance of the PS-backing heterostructure, the electrochemical reaction, and the Joule effect as thermal sources. The model includes the time-dependence of the sample thickness during the electrochemical etching of PS. The changes in the reflectance are identified as the laser reflections in the internal layers of the system. The reflectance is modeled by an additional sinusoidal-monochromatic light source and its modulated frequency is related to the velocity of the PS growth. The chemical reaction and the DC components of the heat sources are taken as an average value from the experimental data. The theoretical results are in agreement with the experimental data and hence provided a method to determine variables of the PS growth, such as the etching velocity and the thickness of the porous layer during the growing process., Comment: 7 pages, 7 figures, 2 tables

There are a few methodologies to monitoring the Porous Silicon (PS) formation in-situ. One of these methodologies is photoacoustic. Previous works that reported the use of photoacoustic to study the PS formation do not provide the physical explanation of the origin of the signal. In this paper, a physical explanation is provided of the origin of the photoacoustic signal during the PS etching. The incident modulated radiation and changes in the reflectance are taken as thermal sources. In this paper, a useful methodology is proposed to determine the etching rate, porosity, and refractive index of a PS film by the determination of the sample thickness, using SEM images. This method was developed by carrying out two different experiments using the same anodization conditions. The first experiment consisted of the growth of samples with different etching times to prove the periodicity of the photoacoustic signal and the second considered the growth samples using three different wavelengths that are correlated with the period of the photoacoustic signal. The last experiment showed that the period of the photoacoustic signal is proportional to the laser wavelength., Comment: 6 pages, 7 figures