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Physical Review A

Precisely measuring the orbital angular momentum of beams via weak measurement

Jiangdong Qiu, Changliang Ren, Zhiyou Zhang

Published Jun 23, 2016• 20 citations

Abstract

We proposed and analyzed a scheme of precisely measuring orbital angular momentum (OAM) of the vortex beams with the help of weak measurement process. The orbital angular momentum information $l$ of the unknown OAM state can be obtained by its spatial displacements. The valid condition of precisely measuring orbital angular momentum was completely discussed. Interestingly, it is shown that the measurement by using the two-dimensional spatial displacements jointly is very useful for precisely measuring the OAM state with a large orbital angular momentum $l$. The signal-to-noise ratio of the measurement can be enhanced by increasing the weak-coupling $\ensuremath{\gamma}$ linearly as the valid condition is still satisfied. For fixed $\ensuremath{\gamma}$, the maximal signal-to-noise ratio for each weak value increases with the decrease of the weak value.

DOI: 10.1103/physreva.93.063841

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We proposed and analyzed a scheme of precisely measuring orbital angular momentum (OAM) of the vortex beams with the help of weak measurement process. The orbital angular momentum information

l

of the unknown OAM state can be obtained by its spatial displacements. The valid condition of precisely measuring orbital angular momentum was completely discussed. Interestingly, it is shown that the measurement by using the two-dimensional spatial displacements jointly is very useful for precisely measuring the OAM state with a large orbital angular momentum

l

. The signal-to-noise ratio of the measurement can be enhanced by increasing the weak-coupling

\ensuremath{\gamma}

linearly as the valid condition is still satisfied. For fixed

\ensuremath{\gamma}

, the maximal signal-to-noise ratio for each weak value increases with the decrease of the weak value.

Weak measurement, which can amplify a weak signal, has shown great significance in precision measurements. The amplification is usually realized through the weak value and the propagation factor. We show that the orbital angular momentum (OAM) can provide another dimension for amplification that is linearly proportional to the OAM number. We employ OAM to measure the spin Hall effect of light and demonstrate that the OAM-enabled amplification is compatible with the weak value amplification and the propagation amplification. This work is probable to promote the application of OAM in precision measurements.

As a special experimental technique, weak measurement extracts very little information about the measured system and will not cause the measured state collapse. When coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there is an indirect coupling between position and topological charge (TC) of OAM state. Based on these ideas, we propose an experimental scheme that experimentally measure the TC of OAM beams from -14 to 14 through weak measurement.

According to the principle of weak measurement, when coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there will be an indirect coupling between position and topological charge (TC) of OAM state. Based on this we propose an experiment scheme and experimentally measure the TC of OAM beams from -14 to 14 according to the weak measurement principle. After the experiment the intrinsic OAM of the beams changed very little. Weak measurement, Topological Charge, OAM beams.

Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.

Tiny but universal beam shifts occur when a polarized light beam is reflected upon a planar interface. Although the beam shifts of Gaussian beams have been measured by the weak measurement technique, the weak measurement for orbital angular momentum (OAM)-induced spatial shifts of vortex beams is still missing. Here, by elaborately choosing the preselection and postselection states, the tiny OAM-induced Goos–Hanchen and Imbert–Fedorov shifts are amplified at an air–prism interface. The maximum shifts along directions both parallel and perpendicular to the incident plane are theoretically predicted and experimentally verified with optimal preselection and postselection states. These maximum shifts can be used to determine the OAM of vortex beams.