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Journal of Physics D Applied Physics

Improved model of weak measurement for detecting the photonic spin Hall effect

Zirui Qin, Qinggang Liu, Chong Yue, Yaopu Lang, Xinglin Zhou

Published Sep 4, 2019• 15 citations

Abstract

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.

DOI: 10.1088/1361-6463/ab415a

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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.

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.

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.

The basics of weak measurement and its various applications are discussed here. The optical analogue of weak measurement. which was predicted by E C G Sudarshan was also demonstrated with the experimental results. The optical activity of chiral molecules is also calculated with the help of weak measurement. We also demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of a fundamental Gaussian beam at planar dielectric interfaces. We employ pre and post selection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both of these shifts.We also studied these GH and IF shifts for higher order beams (for example Vortex beams)and how its get coupled. Geometric Hall effect of light is also studied with the help of weak measurement and we get the expected nature according to the 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.

Since its first introduction over twenty years ago, weak measurements have gradually became an useful metrology tool in the laboratory. Due to its desirable amplification effect, a small physical variable can be detected with weak measurements. Spin splitting of light, which stems from the interaction between the spin and orbital angular momentum in optical reflection or refraction at the interface of mediums, is always a weak effect. However, the spin splitting of light can be detected easily with weak measurements. Remarkably, the spin splitting of light is sensitive to the physical parameter variations of system. Using the spin splitting as a probe, the physical parameter can be accurately estimated with weak measurements. Here, we review some of our works on precision metrology with weak measurements using the spin splitting of light as a probe, such as estimation of the magneto-optical constant of a magnetic film, determination of the focused beam waist, and measurement of the polarization state of light.

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.