Weak-value Amplification Technique Research Articles

Extension of Linear Response Regime in Weak-Value Amplification Technique

The achievable precision of parameter estimation plays a significant role in evaluating a strategy of metrology. In practice, one may employ approximations in a theoretical model development for simplicity, which, however, will cause systematic error and lead to a loss of precision. We derive the error of maximum likelihood estimation in the weak-value amplification technique where the linear approximation of the coupling parameter is used. We show that this error is positively related to the coupling strength and can be effectively suppressed by improving the Fisher information. Considering the roles played by weak values and initial meter states in the weak-value amplification, we also point out that the estimation error can be decreased by several orders of magnitude by averaging the estimations resulted from different initial meter states or weak values. These results are finally illustrated in a numerical example where an extended linear response regime to the parameter is observed.

Computing metasurfaces enabled chiral edge image sensing

SummaryComputing metasurfaces have shown the extraordinary ability to precisely perform optical analog operations to the input light wave, and therefore exhibit greater potentials toward sensing applications. Here, we propose a unique application of computing metasurface for chiral edge sensing by incorporating a weak-value amplification technique. The computing metasurface performs the spatial differentiation operations of phase objects and extracts the edge-enhanced images, because the phase gradient generally occurs at the edge. The chirality-induced polarization rotation acts as the preselection state and the spatial differentiation operations in the metasurface provide weak coupling. The amplified pointer shift related to the tiny polarization rotation will eventually lead to an asymmetric edge-enhanced image. Owing to the high sensitivity of the weak-value amplification, we experimentally demonstrate a high-contrast recognition of chirality by edge detection, which may have potential applications in real-time measurement and separation of chiral enantiomers.

Estimation of an optomechanical parameter via weak-value amplification

In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak-value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak-value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same level of precision from a Fisher information perspective. In the presence of strongly correlated noise, the weak-value amplification method is preferable, from a Fisher information perspective, than a standard measurement strategy that does not employ postselection and that is affected by the same type of noise.

Enhancing the precision of detecting weak magnetic fields based on weak-value amplification

We study the amplification of a weak magnetic field with the weak-value amplification (WVA) technique based on the Faraday magneto-optic effect. By using a different scheme to perform the Mach–Zehnder interferometer with the probe in momentum space, we have demonstrated a new, to the best of our knowledge, weak measure protocol to detect the small weak magnetic field by amplifying the phase shift of the Faraday magneto-optic effect. Our numerical results show that our scheme with the WVA technique has a higher signal-to-noise ratio than the traditional optical fiber scheme with the open-loop modulation technique. Besides, considering the instrument limitations of our scheme, we have demonstrated the magnetic field resolution at the 10 − 13 T level.

Realization of ultra-small stress birefringence detection with weak-value amplification technique

How to realize the detection of tiny birefringence is an important but challenging issue for investigations and applications in optics. In weak measurements, weak-value amplification has been widely applied to the precise estimation of time delay. Here, we show that the linear amplification in weak measurements has the potential to outperform standard weak-value amplification for ultra-small parameter characterization. The higher measurement accuracy in the linear amplification enables us to achieve a measurement of stress-induced birefringence with a high resolution of 5×10−10. Compared with existing methods, the accuracy based on weak measurements for birefringence detection can improve two orders of magnitude. Our method may have important applications in a variety of fields involving the precise measurement of time delay or birefringence.

Tunable and high-sensitivity temperature-sensing method based on weak-value amplification of Goos–Hänchen shifts in a graphene-coated system

We propose a tunable and high-sensitivity temperature-sensing method via weak-value amplification of Goos–Hänchen (GH) shifts in a graphene-coated system. The GH shifts were sensitive to the temperature, which was mainly attributed to the variations in the substrate’s refractive index with the temperature. By introducing the weak-value amplification technique, a temperature-sensing method was produced, in which the sensing sensitivity was two orders of magnitude higher and could be effectively manipulated by adjusting the amplified angle. The sensitivity was improved by regulating the graphene’s Fermi energy. Based on these findings, we obtained a maximum sensitivity of 1.3×105 nm/∘C by using the appropriate Fermi energy and amplification angle. These studies expand the practical applications of GH shifts, and provide the potential for developing high-sensitivity temperature sensors based on weak-value amplification.

High-Precision Multiparameter Weak Measurement with Hermite-Gaussian Pointer

The weak-value amplification technique has been proved to be useful for precision metrology in both theory and experiment. To explore the ultimate performance of weak-value amplification for multiparameter estimation, we investigate a general weak-measurement formalism with the assistance of the high-order Hermite-Gaussian (H-G) pointer and the quantum Fisher information matrix. Theoretical analysis shows that the ultimate precision of our scheme is improved by a factor of the square root of $2n+1$, where $n$ is the order of the Hermite-Gaussian mode. Moreover, the parameters' estimation precision can approach the precision limit with the maximum-likelihood estimation method and the homodyne method. We also present a proof-of-principle experimental setup to validate the H-G--pointer theory and explore its potential applications in precision metrology.

Precision Measurement of the Optical Conductivity of Atomically Thin Crystals via the Photonic Spin Hall Effect

How to measure the optical conductivity of atomically thin crystals is an important but challenging issue due to the weak light-matter interaction at the atomic scale. Photonic spin Hall effect, as a fundamental physical effect in light-matter interaction, is extremely sensitive to the optical conductivity of atomically thin crystals. Here, we report a precision measurement of the optical conductivity of graphene, where the photonic spin Hall effect acts as a measurement pointer. By incorporating with the weak-value amplification technique, the optical conductivity of monolayer graphene taken as a universal constant of $(0.993\pm0.005)\sigma_0$ is detected, and a high measuring resolution with $1.5\times10^{-8}\Omega^{-1}$ is obtained. For few-layer graphene without twist, we find that the conductivities increase linearly with layer number. Our idea could provide an important measurement technique for probing other parameters of atomically thin crystals, such as magneto-optical constant, circular dichroism, and optical nonlinear coefficient.

Realization of entanglement-assisted weak-value amplification in a photonic system

Weak-value amplification has been used to enhance the sensitivity of a linear detector response to small interaction parameters. However, the generation of a large weak value gives rise to reduction in postselection probability, which restricts the feasibility of the weak-value amplification technique. Recently, theoretical works have shown that the use of entanglement can increase the efficiency of the weak-value amplification method. Specifically, it is proven that by entangling $n$ particles of a system, the maximum postselection probability scales quadratically with $n$ [Pang, Dressel, and Brun, Phys. Rev. Lett. 113, 030401 (2014)]. In this work, we demonstrate an experimental realization of entanglement-assisted weak-value amplification in a photonic system, which shows that importing quantum entanglement can indeed improve the efficiency of weak-value amplification.

Surface roughness detection by spin Hall effect of light with sub-nanometer resolution

We report here a novel measurement method for detecting a rough surface with sub-nanometer accuracy by using the spin Hall effect of light (SHEL). Reflecting an inspection light at a sample surface, a slightly position shift, which is called “the SHEL,” occurs at the reflection surface. The shift corresponds to polarization difference between an incident and a reflected lights. The difference depends on a conditions of a surface roughness of a sample surface or a thickness of a thin film. Because a rough surface within λ/10 can be approximated to thin film by the theory of the effective medium theory. We measured the SHEL of some Au thin films and surface roughness of a optical flat sample via the weak value amplification technique. Sub-nanometer resolution for the measurement of the film thickness is obtained and some experimental results are shown in this paper.

Anomalous amplification of a homodyne signal via almost-balanced weak values.

We propose precision measurements of ultra-small angular velocities of a mirror within a modified Sagnac interferometer, where the counter-propagating beams are spatially separated, using the recently proposed technique of almost-balanced weak values amplification (ABWV) [Phys. Rev. Lett.116, 100803 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.100803]. The separation between the two beams provides additional amplification with respect to using collinear beams in a Sagnac interferometer. Within the same setup, the weak-value amplification technique is also performed for comparison. Much higher amplification factors can be obtained using the almost-balanced weak values technique, with the best one achieved in our experiments being as high as 1.2×107. In addition, the amplification factor monotonically increases with decreasing of the post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification (WVA) at small post-selection phases. Both techniques consist of measuring the angular velocity. The sensitivity of the ABWV technique is ∼38 nrad/s per averaged pulse for a repetition rate of 1 Hz and ∼33 nrad/s per averaged pulse for the WVA technique.

Quantum sensors based on weak-value amplification cannot overcome decoherence

Sensors that harness exclusively quantum phenomena (such as entanglement) can achieve superior performance compared to those employing only classical principles. Recently, a technique based on postselected, weakly-performed measurements has emerged as a method of overcoming technical noise in the detection and estimation of small interaction parameters, particularly in optical systems. The question of which other types of noise may be combatted remains open. We here analyze whether the effect can overcome decoherence in a typical field sensing scenario. Benchmarking a weak, postselected measurement strategy against a strong, direct strategy we conclude that no advantage is achievable, and that even a small amount of decoherence proves catastrophic to the weak-value amplification technique.