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arXiv:1404.2721 · Applied Physics Letters

Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect

Xinxing Zhou, Xing Li, Hailu Luo, Shuangchun Wen

Published Feb 3, 2014• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.4864782

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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.
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.
Weak measurements, which offer a significant signal enhancement with pre- and post-selections, have proven to be powerful for precision metrology. However, the measured precision of the parameter of interest is always limited by the post-selection-induced probe loss, especially in the presence of technical noise. In this paper, we investigate the optimal pre- and post-selections of weak measurements for precision metrology in the presence of technical noise. While weak measurements apply more generally, we experimentally measure the spin splitting induced by the spin Hall effect of light (SHEL) to approach this issue. The highest measured precision of the spin splitting can be obtained with the post-selected state in the nonlinear intermediate regime. Surprisingly, the pre- and post-selections for the largest weak-value amplification are incapable of estimation of the spin splitting, since the amplified shift is independent of the spin splitting. Our results are not restricted to the SHEL and could be applied to other parameter estimations with weak measurements.
We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.
We study quantum measurements with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength. For a qubit system, we derive the maximum measurement results by choosing appropriate initial and finial states. Significant amplification effect is obtained when the interaction between the system and the measuring device is very weak; and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measure sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can both be significantly improved by weak measurements; surprisingly, neither SNR nor MS can be effectively improved when the probability decrease is considered.