Single-shot measurement of the orbital-angular-momentum spectrum of light

Abstract

The existing methods for measuring the orbital-angular-momentum (OAM) spectrum suffer from issues such as poor efficiency, strict interferometric stability requirements, and too much loss. Furthermore, most techniques inevitably discard part of the field and measure only a post-selected portion of the true spectrum. Here, we propose and demonstrate an interferometric technique for measuring the true OAM spectrum of optical fields in a singleshot manner. Our technique directly encodes the OAM-spectrum information in the azimuthal intensity profile of the output interferogram. In the absence of noise, the spectrum can be fully decoded using a single acquisition of the output interferogram, and, in the presence of noise, acquisition of two suitable interferograms is sufficient for the purpose. As an important application of our technique, we demonstrate measurements of the angular Schmidt spectrum of the entangled photons produced by parametric down-conversion and report a broad spectrum with the angular Schmidt number 82.1.

Measuring dimensionality and purity of high-dimensional entangled states

“…Unlike a conventional Schmidt decomposition, we do not assume the state is pure, and the dimension extracted from our technique is conditioned on the presence of entanglement: a maximally mixed and maximally entangled system cannot yield the same result. While our approach would benefit from the knowledge of the modal spectrum, which can be measured very quickly 57 , 58 , the outcome on purity and dimensionality are only modestly affected by typical spectrum shapes (see Supplementary Fig. 5 ); in our examples, the uncertainty in dimensionality is ≈5% with knowledge of the spectrum increasing to ≈10% without.…”

A classical model of spontaneous parametric down-conversion

“…Our model can be a useful theoretical tool for analysing high-gain SPDC [30,31,50,56] and induced coherence experiments [41,68,69]. Moreover, using the connection between Schmidt decomposition in quantum theory and the coherent-mode decomposition in classical coherence theory [32,51], our model can be used to extract important properties of the global quantum state such as the Schmidt spectrum and Schmidt modes [77]. A precise knowledge of these properties may not only lead to a better quantitative understanding of high-dimensional multiphoton entanglement of the high-gain SPDC field [78], but may also inform experiments aimed at harnessing the underlying correlations for applications in imaging [18,19], quantum state preparation [20], phase metrology [55], radiation shaping [56], microscopy [57], sensing [59], and spectroscopy [63].…”

“…The quantities S l , which include contributions from all the constituent radial modes, are collectively referred to as the OAM spectrum. The angular coherence function W (φ s1 , φ s2 ) = W (φ s1 − φ s2 ) defined as [51,52] W (φ s1 − φ s2 ) = dq s q s A s (q s , φ s1 )A * s (q s , φ s2 ) , (21) has been shown to be related to the OAM spectrum S l by the Fourier transform relation [51,52]…”

“…In our experiments, we employ the interferometric technique reported in Ref. [51] to measure the OAM spectrum of the high-gain SPDC field. As shown in Fig.…”

“…2, the SPDC field is incident into a Mach-Zehnder interferometer with an odd and even number of mirrors in the two arms, and its far-field interferograms are imaged using the EMCCD camera. The constructive and destructive interferograms are acquired by changing the interferometric phase δ using the translation stage, and their difference image is used to compute the OAM spectrum [51]. However, this direct procedure results in large errors in the value of S 0 due to shot-to-shot fluctuations in the pump energy.…”