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Frontiers in Optics

Measuring Pure States in the Orbital Angular Momentum Basis Using Nine Image Acquisitions

Girish Ashok Kulkarni, Suman Karan, Anand K. Jha

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We propose a novel technique for measuring high-dimensional pure states of light in the orbital-angular-momentum (OAM) basis using only nine multipixel image acquisitions. We experimentally demonstrate the technique for laboratory-generated states up to 25 dimensions, reporting a mean fidelity greater than 90 % up to 11 dimensions.
DOI
10.1364/fio.2020.fm7c.1

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APL Photonics•Feb 1, 2026•1 citation
The existing techniques for measuring high-dimensional pure states of light in the orbital angular momentum (OAM) basis either involve a large number of single-pixel data acquisitions and substantial postselection errors that increase with dimensionality, involve substantial loss, or require interference with a reference beam of known phase. Here, we propose an interferometric technique that can measure an unknown pure state using only nine multipixel image acquisitions without involving postselection, loss, or a separate reference beam. The technique essentially measures two complex correlation functions of the input field and then employs a recursive postprocessing algorithm to infer the state. We experimentally demonstrate the technique for pure states up to dimensionality of 25, reporting a mean fidelity greater than $90\mathrm{%}$ up to 11 dimensions. Our technique can significantly improve the performance of OAM-based information processing applications.
The orbital angular momentum of light (OAM) is a fundamental property of light. Beams with OAM have a helical wave front that carries quantized orbital angular momentum L hbar per photon, where L is any integer. This unbounded Hilbert space can increase information capacity of both classical and quantum communications and also improve and extend qubit and qudit quantum algorithms. Additionally, the use of the OAM modes allows for novel imaging techniques to directly observe and measure various topological properties of objects ranging from defects in semiconductors to rotating black holes and extrasolar planets. However, measuring such higher dimensional OAM states is fundamentally important, albeit challenging, in order to use this rich degree of freedom. In the work that follows, I present two novel OAM to time mapping schemes and an application using the higher dimensionality of OAM to non-destructively probe quantum states. These are the first OAM measuring schemes to use the temporal degree of freedom to measure OAM. The use of the novel loop nature allows for high fidelity and high speed measurements of a large number of OAM states without significant increase in experimental resources. The first scheme experimentally demonstrates a compact and practical device to measure the OAM spectrum. I report a fidelity of -21.3 dB for 5 different OAM states. The second scheme extends the first, but uses non-demolition measurements to iteratively test for specific OAM values. While this increases experimental complexity, it allows for the detection of an arbitrarily large OAM value from a single photon. I also discuss details of each technique investigate the affects of misalignment on the OAM spectrum. In the remaining part, I discuss my novel generalized quantum Zeno interrogation. The original quantum Zeno interrogation is limited to the two-dimensional state of a single object; while the generalized version has the ability to non-destructively probe the quantum state a set of objects, and deterministically imprint that information onto a single photon using the OAM degree of freedom.
The high-dimensional basis of orbital angular momentum (OAM) has several added and unique advantages for photonic quantum technologies compared to the polarization basis, which is only two-dimensional. However, one of the major roadblocks in implementing OAM-based applications with their full potentials is the absence of an ideal OAM-mode detector. Despite the plethora of efforts in the last three decades, currently, there is no OAM detector that can detect a broad OAM-mode spectrum, has uniform detection-efficiency over all the modes, measures the true spectrum, and works for an arbitrary quantum state without the need for any previous information. Here, we experimentally demonstrate just such an OAM detector. We report detection of pure and mixed OAM states with fidelities more than 98% and with measurement times of only a few minutes for dimensionalities up to 100. We expect our work to substantially boost the OAM-based photonic quantum technology efforts.
High-dimensional entangled states in an orbital-angular-momentum (OAM) basis offer several unique advantages for quantum information applications. However, for the optimal performance of a given application, one requires a generation technique for OAM entangled states that is completely postselection-free and fully controllable. Nonetheless, despite several efforts in the past, no such technique currently exists. In this paper, we propose just such a technique and experimentally demonstrate postselection-free generation of up to about 150-dimensional OAM entangled states. We report the generation accuracy, which is a measure of the control, to be more than $98\mathrm{%}$ for states with Gaussian and triangular OAM Schmidt spectra, and up to $90\mathrm{%}$ for the maximally entangled OAM states, which have rectangular spectra.
Photons with a spiral phase will carry orbital angular momentum (OAM), which can serve as a valuable resource for constructing high-dimensional Hilbert spaces due to its orthogonality and unbounded dimensionality. However, the fast measurement of high-dimensional OAM spectra remains a challenge. While intensity detection is relatively straightforward, full characterization requires phase retrieval. Although quantum state tomography allows full reconstruction, it demands a number of measurements scaling quadratically with the d2 of dimension (d), leading to a “curse of dimensionality” as the dimension d increases. Thus, there is an urgent need for efficient and simple methods for extracting phase information from high-dimensional OAM spectra. Here, we propose a generalized Poincaré sphere model with analog Stokes-like parameters, enabling full phase measurement of a d-dimensional OAM spectrum using only 4d measurements, significantly reducing the data acquisition requirement. We experimentally validated the method by performing intensity and phase measurements on 8-, 16-, and 32-dimensional OAM comb spectra. The results show excellent agreement with theoretical predictions, with measured fidelities ranging from 0.9829 to 0.9965. This approach facilitates an efficient characterization of high-dimensional OAM spectra and contributes to advancing their practical applications.