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Physical Review A

Modified weak measurements for the detection of the photonic spin Hall effect

Shizhen Chen, Xinxing Zhou, Chengquan Mi, Hailu Luo, Shuangchun Wen

Published Jun 5, 2015• 81 citations
Publisher

Abstract

Weak measurement is an important technique for the detection of the tiny spin-dependent splitting in photonic spin Hall effect. The weak measurement is only valid when the probe wave function remains almost undisturbed during the procedure of measurements. However, it does not always satisfy such condition in some practical situations, such as in the strong-coupling regime or when the preselected and postselected states are nearly orthogonal. In this paper, we develop a modified weak measurement for the detection of the photonic spin Hall effect when the probe wave function is distorted. We find that the measuring procedure with preselected and postselected ensembles is still effective. This scheme is important for us to detect the photonic spin Hall effect in the case where neither weak nor strong measurements can detect the spin-dependent splitting. The modified theory is valid not only in the weak-coupling regime but also in the strong-coupling regime, and especially in the intermediate regime. The theoretical models of conventional weak measurements and modified weak measurements are established and compared. We show that the experimental results coincide well with the predictions of the modified theory.

DOI
10.1103/physreva.91.062105

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Weak measurement is an important technique for the detection of the tiny spin-dependent splitting in photonic spin Hall effect. The weak measurement is only valid when the probe wave function remains almost undisturbed during the procedure of measurements. However, it does not always satisfy such condition in some practical situations, such as in the strong-coupling regime or when the preselected and postselected states are nearly orthogonal. In this paper, we develop a modified weak measurement for the detection of the photonic spin Hall effect when the probe wave function is distorted. We find that the measuring procedure with preselected and postselected ensembles is still effective. This scheme is important for us to detect the photonic spin Hall effect in the case where neither weak nor strong measurements can detect the spin-dependent splitting. The modified theory is valid not only in the weak-coupling regime but also in the strong-coupling regime, and especially in the intermediate regime. The theoretical models of conventional weak measurements and modified weak measurements are established and compared. We show that the experimental results coincide well with the predictions of the modified theory.
Weak measurement is an important technique for detecting the tiny spin-dependent splitting in photonic spin Hall effect. The weak measurement is only valid when the probe wavefunction remains almost undisturbed during the procedure of measurements. However, it does not always satisfy such condition in some practical situations, such as in the strong-coupling regime or the preselected and postselected states are nearly orthogonal. In this paper, we develop a modified weak measurement for detecting photonic spin Hall effect when the probe wavefunction is distorted. We find that the measuring procedure with preselected and postselected ensembles is still effective. This scheme is important for us to detect the photonic spin Hall effect in the case where neither weak nor strong measurements can detect the spin-dependent splitting. The modified theory is valid not only in weak-coupling regime but also in the strong-coupling regime, and especially in the intermediate regime. The theoretical models of conventional weak measurements and modified weak measurements are established and compared. We show that the experimental results coincide well with the predictions of the modified theory.
Photonic spin Hall effect (SHE) holds great potential applications in precision metrology. How to obtain a high measurement precision is an important issue to detect the photonic SHE. In this Letter, we propose using optimal preselection and postselection in weak measurements to enhance the measurement precision. We find that the maximum weak value and pointer shift can be obtained with an optimal overlap of preselection and postselection states. These findings offer the possibility for improving the precision of weak measurements and thereby have possible applications for accurately characterizing the parameters of nanostructures.
We have detected a spin-dependent displacement perpendicular to the refractive index gradient for photons passing through an air-glass interface. The effect is the photonic version of the spin Hall effect in electronic systems, indicating the universality of the effect for particles of different nature. Treating the effect as a weak measurement of the spin projection of the photons, we used a preselection and postselection technique on the spin state to enhance the original displacement by nearly four orders of magnitude, attaining sensitivity to displacements of approximately 1 angstrom. The spin Hall effect can be used for manipulating photonic angular momentum states, and the measurement technique holds promise for precision metrology.
Abstract Weak measurement is an important measurement method in quantum measurement, which has been widely used in detecting the photonic spin Hall effect (PSHE). The models of weak measurement for detecting PSHE have been derived in the frame of quantum mechanics. However, the existing models still have some drawbacks. For example, they are not suitable for the case where the reflection interface is composed of absorption medium, or the case when the reflection is in total internal reflection. A new improved model of weak measurement for detecting the PSHE of reflected Gaussian beam is derived in this article. The improved model is not derived in the framework of quantum mechanics, but is derived in the framework of classical optics which is easier to understand. In comparison to the existing models, the new improved model we derived no longer has the above restrictions. It is suitable for both the absorbent and non-absorbent medium interfaces, and is also suitable for both the partial and total internal reflection. Furthermore, the improved model is verified by experiments and the experimental results are in good agreement with the theoretical results. It is believed that this improved new model will help researchers to study the PSHE more widely and may provide more ways for the precise measurement of physical parameters. In addition, the derivation way based on classical optics theory also provides a new path to establish the quantum weak measurement models.
In this paper, a method to measure the tiny spin splitting of the spin Hall effect of light (SHEL) using the almost-balanced weak measurement (ABWM) is presented. The ABWM technique uses two orthogonal post-selected states to record all of the information, which is a precise measurement method being different from the standard weak measurement (SWM). The theory model to describe the SHEL measurement based on ABWM is established. As results, the ABWM scheme has a larger amplification factor, reaching ∼105, which is nearly one order of magnitude higher than that of the SWM. When the post-selected angle is less than a certain value, the sensitivity and amplification factor of the ABWM scheme are higher than those of the SWM scheme, while the measurement precision and SNR of the ABWM technique are comparable to those of the SWM scheme. This research may have great potential for the precision metrology or sensing field based on the SHEL measurement.
We report an experimental demonstration of generalized photonic spin splitting (PSS) using arbitrary linearly polarized higher-order orbital angular momentum (OAM) pointer states supported by a modified weak measurement model. The experimental findings show the dependence of longitudinal and transverse PSS on linear polarization angle, postselection angle, and azimuthal index (lll) of OAM states. PSS rises as lll increases, reaching a maximum of roughly 300 $\textmu{}\text{m}$ and 120 $\textmu{}\text{m}$ for the transverse and longitudinal shift values, respectively. Considering l=0l=0l=0, 1, and 2, the polarization-controlled variation of both shifts at three distinct angles of incidence is investigated for a fixed postselection angle. All the experimental results agree well with the developed theoretical model, proving the model's accuracy. This model is valid for both external and internal reflection of arbitrary linearly polarized incident light reflecting from absorbing as well as nonabsorbing mediums, considering arbitrary coupling strength and a very small postselection angle. The manipulation of PSS using higher-order OAM light beams shown in this study will have a wide range of applications in wavefront manipulation, optical sensors, and nanophotonics.