Optical Weak Measurement Research Articles

Connection between weak measurement in quantum physics and analytic phase retrieval in classical wave optics

Recently, various precision optical experiments have been proposed that utilize the concept of weak measurement in quantum physics. Since it is known that the results appearing in weak measurements are related to the phase of the quantum system, it is important to investigate the phase in order to understand the weak measurements. We present that one of phase-retrieval methods in classical wave optics, the analytic phase retrieval, has a close connection with quantum weak measurement. We explain such a connection for two emblematic optical weak measurements that have the same mathematical formalism as quantum systems: one is a system for the anomalous probe displacement of polarized light in a birefringent crystal, and the other is a system for the direct measurement of a wave function by polarization. We reveal that the same physical operation as the analytic phase retrieval is behind these two systems, namely the use of filtering effects.

Tunable quantized spin Hall effect of light in graphene

The spin Hall effect of light is an appealing toolset for metrology that holds incredible potential for precision measurements due to its high sensitivity to the refractive index and nanostructure physical parameters. Here, we theoretically examine the quantized spin Hall effect of light on the surface of a monolayer graphene–substrate system subjected to an external perpendicular magnetic field. We discuss the impact of Landau levels induced by the external magnetic field B and the photon energy on magneto-optical conductivities and Fresnel reflection coefficients. We find that the spin-dependent splittings in graphene exhibit quantized characteristics due to the Landau levels quantization of the magneto-optical conductivities and Fresnel’s reflection coefficients near the Brewster angle. Moreover, the spin-dependent shifts are quantized and show oscillatory behavior with changes in the magnetic field and the photon energy. Our results manifest that the quantized photonic spin-dependent separations are sensitive to variations in the incidence angle, magnetic field, and incident photonic energies. The quantized spin-dependent splitting opens a promising route to find the quantized Hall conductivity and discrete Landau levels in the monolayer graphene by a direct optical weak measurement.

In Situ Detection of Electrochemical Reaction Surface Area by Optical Weak Measurement.

The surface area is key to electrochemical systems, including those in electrocatalysis and energy storage. Studies have shown that the surface area of the electrocatalyst directly affects the electrochemical activity, adsorption performance, and stability of the electrocatalyst. This paper used an optical weak measurement (WM) method, which has little impact on the analyte, to measure the reaction surface area (RSA) that actually participated in the electrochemical reaction. Then compared the RSA obtained by the WM with the total surface area (TSA) obtained by the standard Brunauer-Emmett-Teller (BET) measurement and the active surface area (ASA) obtained by the electrochemical double-layer capacitance (EDLC) method. Their growth trend was consistent, indicating the reliability of the WM method. Compared with the above two methods, the WM method is an in situ detection and easy to operate experimentally, which can help researchers to consider the effect of surface area on electrocatalyst performance more rationally.

Optical weak measurement for the precise thickness determination of an ultra-thin film.

A total internal reflection system based on the weak value amplification principle is set up for the precise measurement of the thickness of an ultra-thin film. In this system, the film thickness is derived from the change of the double-peak pointer caused by the effective refractive index of the film, which is correlated to its thickness. The sensitivity and resolution of this system reached 2727.21nm/RIU and 7.2×10-6 R I U, respectively, determined by using a sodium chloride solution with a refractive index of 1.331911. The growth process of TA/Fe(III) assembled films with thicknesses in the few nanometers range is monitored using the as-set-up system, and the experimental results are consistent with a theoretical calculation based on the Maxwell Garnett effective medium. Additionally, we theoretically calculated the detection limit for the thickness measurement of the film as 22pm. We clearly provide a potential method for the precise measurement of the thickness of an ultra-thin film.

Experimentally monitoring of the rapid biomolecular hydrolysis reaction with optical weak measurement

The real-time measurement of optical activity is of great significance for studying the chemical reactions of chiral molecules. In this study, we have built a set of linear common path optical weak measurement chiral sensor system in frequency domain, and the optical sensitivity of the system feasibly reaches 1524 for activity. Using this system, we have realized the state measurement of the ultrafast alkaline hydrolysis reaction of gluconolactone under different concentrations of catalyst. This study shows that the optical weak measurement chiral sensor can well monitor and compare the degree of hydrolysis reaction, and partly reflect the approximate change of the optical rotation in the real-time process of hydrolysis. Optical weak measurement chiral sensing does not require separation and labeling molecules, and has great application potential for the production and development of chiral compounds, especially chiral drugs.

Real-time monitoring the hydrolysis of chiral molecules by optical weak measurement

As one of important optical properties of chiral molecules, the real-time monitoring of the optical rotation is of great significance to study the reaction characteristics of chiral molecules. In this study, we have built an optical frequency domain weak measurement system with linear common-path method for chiral sensing, in which the response between optical rotation and central wavelength shift can reach more than 1200 nm/rad. The high-precision measurement of the optical rotation of chiral molecules and the high-sensitivity real-time monitoring of the decomposition rate in the acidic hydrolysis of sucrose under different concentrations of catalysts are realized using this system. The experimental results are basically consistent with the theoretical prediction. This study shows that optical weak measurement chiral sensing can monitor the hydrolysis degree of chiral molecules in real time without separating and labeling molecules. It has great application potential in the production and research of chiral compounds, especially chiral medicine.

Specific detection of glucose by an optical weak measurement sensor.

Diabetes is an important public health problem and finding quick testing methods with high accuracy, reliability, and convenience are important to control the blood glucose of diabetic patients. In this study, a sensor based on a weak measurement scheme was developed for the specific detection of glucose for the first time. The detection of glucose using the proposed method was completed by the high sensitivity and resolution of the weak measurement based on optical rotation detection, as well as the change in the optical rotation before and after the specific oxidation of glucose. The resolution of the as-obtained glucose sensor was around 2.71×10-3 g/L (1.50×10-2 mmol/L), and the detection range was 0-11 g/L (0-61 mmol/L).

Weak Measurements in Nano-optics

Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to weak value that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics. Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domains. The applications involve measuring ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics. Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device. Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as a natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signals or effects. Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.

The Atacama Cosmology Telescope: Weighing Distant Clusters with the Most Ancient Light

Abstract We use gravitational lensing of the cosmic microwave background (CMB) to measure the mass of the most distant blindly selected sample of galaxy clusters on which a lensing measurement has been performed to date. In CMB data from the the Atacama Cosmology Telescope and the Planck satellite, we detect the stacked lensing effect from 677 near-infrared-selected galaxy clusters from the Massive and Distant Clusters of WISE Survey (MaDCoWS), which have a mean redshift of . There are currently no representative optical weak lensing measurements of clusters that match the distance and average mass of this sample. We detect the lensing signal with a significance of . We model the signal with a halo model framework to find the mean mass of the population from which these clusters are drawn. Assuming that the clusters follow Navarro–Frenk–White (NFW) density profiles, we infer a mean mass of . We consider systematic uncertainties from cluster redshift errors, centering errors, and the shape of the NFW profile. These are all smaller than 30% of our reported uncertainty. This work highlights the potential of CMB lensing to enable cosmological constraints from the abundance of distant clusters populating ever larger volumes of the observable universe, beyond the capabilities of optical weak lensing measurements.

A Bio-molecular Sensor Based on Optical Weak Measurement

We developed a phase-sensitive sensor based on the optical weak measurement for label-free detection of biomolecular interaction. The weak value amplification system can be implemented in common-path with total internal reflection structure. The phase difference between p and s polarizations caused by biomolecular recognition is measured by the central wavelength shift of the frequency domain weak measurement system. Structure of p and s polarizations in common-path makes system robust and stable. The applicability is illustrated by real-time monitoring interaction of biomolecules.

Optical quantum weak measurement coupled with UV spectrophotometry for sensitively and non-separatedly detecting enantiopurity.

Based on the theories of quantum weak measurement, we built a set of linear common-path optical weak measurement systems in frequency domain for detecting chiral molecules. The polarization resolution with this system to detect the optical rotation of chirality molecules is nearly two orders of magnitude higher than that of conventional polarizers. Combined with ultraviolet spectroscopy, the purity of the proline enantiomers mixture was detected. The purity resolution can reach to 0.14%, which is comparable to the liquid chromatography. Weak measurement combined with ultraviolet spectroscopy to non-separatedly detect the purity of chiral enantiomers has great application potential in the pharmaceutical industry.

The real-time determination of d- and l-lactate based on optical weak measurement

A simple transmission optical rotation (OR) configuration based on weak measurement was developed for the real-time determination of d- and l-lactate.

Weak Measurement of Elliptical Dipole Moments by C-Point Splitting.

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-field polarization basis. Projecting the far field onto a spatially varying postselected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.

Weak Measurement Enhanced Spin Hall Effect of Light for Particle Displacement Sensing.

A spherical nanoparticle can scatter tightly focused optical beams in a spin-segmented manner, meaning that the far field of the scattered light exhibits laterally separated left- and right-handed circularly polarized components. This effect, commonly referred to as giant spin Hall effect of light, strongly depends on the position of the scatterer in the focal volume. Here, a scheme that utilizes an optical weak measurement in a cylindrical polarization basis is put forward to drastically enhance the spin-segmentation and, therefore, the sensitivity to small displacements of a scatterer. In particular, we experimentally achieve a change of the spin-splitting signal of 5% per nanometer displacement.

A chiral sensor based on weak measurement for the determination of Proline enantiomers in diverse measuring circumstances

A new chiral sensor based on weak measurement to accurately measure the optical rotation (OR) has been developed for the estimation of a trace amount of chiral molecule. With the principle of optical weak measurement in frequency domain, the central wavelength shift of output spectra is quantitatively relative to the angle of preselected polarization. Hence, a chiral molecule (e.g., L-amino acid, or D-amino acid) can be enantioselectively determined by modifying the preselection angle with the OR, which will cause the rotation of a polarization plane. The concentration of the chiral sample, corresponding to its optical activity, is quantitatively analyzed with the central wavelength shift of output spectra, which can be collected in real time. Immune to the refractive index change, the proposed chiral sensor is valid in complicated measuring circumstance. The detections of Proline enantiomer concentration in different solvents were implemented. The results demonstrated that weak measurement acted as a reliable method to chiral recognition of Proline enantiomers in diverse circumstance with the merits of high precision and good robustness. In addition, this real-time monitoring approach plays a crucial part in asymmetric synthesis and biological systems.

Optical weak measurements without removing the Goos–Hänchen phase

Optical weak measurements are a powerful tool for measuring small shifts of optical paths. When applied to the measurement of the Goos–Hänchen shift, in particular, a special step must be added to its protocol: the removal of the relative Goos-Hänchen phase, since its presence generates a destructive influence on the measurement. There is, however, a lack of description in the literature of the precise effect of the Goos–Hänchen phase on weak measurements. In this paper we address this issue, developing an analytic study for a Gaussian beam transmitted through a dielectric structure. We obtain analytic expressions for weak measurements as a function of the relative Goos–Hänchen phase and show how to remove it without the aid of waveplates.

Molecular imprinting sensor based on quantum weak measurement

A new type of sensing protocol, based on a high precision metrology of quantum weak measurement, was first proposed for molecularly imprinted polymers (MIP) sensor. The feasibility, sensitivity and selectivity of weak measurement based MIP (WMMIP) sensor were experimentally demonstrated with bovine serum albumin (BSA). Weak measurement system exhibits high sensitivity to the optical phase shift corresponding to the refractive index change, which is induced by the specific capture of target protein molecules with its recognition sites. The recognition process can be finally characterized by the central wavelength shift of output spectra through weak value amplification. In our experiment, we prepared BSA@MIP with modified reversed-phase microemulsion method, and coated it on the internal surface of measuring channels assembled into the Mach-Zehnder (MZ) interferometer based optical weak measurement system. The design of this home-built optical system makes it possible to detect analyte in real time. The dynamic process of the specific adsorption and concentration response to BSA from 5×10−4 to 5×10−1μg/L was achieved with a limit of detection (LOD) of 8.01×10−12g/L. This WMMIP shows superiority in accuracy, fast response and low cost. Furthermore, real-time monitoring system can creatively promote the performance of MIP in molecular analysis.

Optical weak measurement system with common path implementation for label-free biomolecule sensing.

A reflection-type phase-sensitive weak measurement for biosensing and chemical label-free sensing is presented. The phase difference between p and s polarizations in total internal reflection caused by biomolecular recognition is measured by weak value amplification. The system with p and s polarizations in a common path is stable and robust. The sensing process occurring on the silicon dioxide surface is achieved with a resolution of 3.6×10^-6 refractive index units. The applicability is demonstrated by real-time monitoring biomolecular interaction of IgG and protein A.

Axial dependence of optical weak measurements in the critical region

The interference between optical beams of different polarizations plays a fundamental role in reproducing the optical analog of the electron spin weak measurement. The extraordinary point in optical weak measurements is represented by the possibility of estimating with great accuracy the Goos–Hänchen (GH) shift by measuring the distance between the peaks of the outgoing beams for two opposite rotation angles of the polarizers located before and after the dielectric block. Starting from the numerical calculation of the GH shift, which clearly shows a frequency crossover for incidence near the critical angle, we present a detailed study of the interference between s and p polarized waves in the critical region. This makes it possible to determine in which conditions axial deformations can be avoided and the GH curves reproduced. In view of a possible experimental implementation, we give the expected weak measurement curves for Gaussian lasers of different beam waist sizes propagating through borosilicate (BK7) and fused silica dielectric blocks.

The analogy between optical beam shifts and quantum weak measurements

We describe how the notion of optical beam shifts (including the spatial and angular Goos–Hänchen shift and Imbert–Federov shift) can be understood as a classical analogue of a quantum measurement of the polarization state of a paraxial beam by its transverse amplitude distribution. Under this scheme, complex quantum weak values are interpreted as spatial and angular shifts of polarized scalar components of the reflected beam. This connection leads us to predict an extra spatial shift for beams with a radially-varying phase dependance.