Coherence in the radial degree of freedom.

Coherence quantifies the statistical fluctuations in an optical field and has been extensively studied in the space, time, and polarization degrees of freedom. In the context of space, coherence theory has been formulated between two transverse positions as well as between two azimuthal positions, referred to as transverse spatial coherence and angular coherence, respectively. In this paper, we formulate the theory of coherence for optical fields in the radial degree of freedom and discuss the associated concepts of coherence radial width, radial quasi-homogeneity, and radial stationarity with some physically realizable examples of radially partially coherent fields. Furthermore, we propose an interferometric scheme for measuring radial coherence.

Quantifying polarization changes induced by rotating Dove prisms and K-mirrors.

Dove prisms and K-mirrors are devices extensively used for rotating the wavefront of an optical field. These devices have several applications, including the measurement of orbital angular momentum, microscopy, beam steering, and pattern recognition. However, the wavefront rotation achieved through these devices is always accompanied by polarization changes in the incident field, which is an undesirable feature in many of these applications. Although the polarization changes induced by a Dove prism have been explored to quite some extent, no such study is available for a K-mirror. In this paper, we theoretically and experimentally investigate polarization changes induced in the transmitted field by a rotating K-mirror. For quantifying such polarization changes, we define a quantity, mean polarization change D, which ranges from 0 to π. We find that K-mirrors can reduce D to about 0.03π for any incident state of polarization; however, reducing D to the same extent with a Dove prism is practically unviable. Therefore, K-mirrors are better alternatives to Dove prisms in applications in which the polarization changes accompanying wavefront rotation need to be minimum.

Cavity Optomechanical Sensing and Manipulation of an Atomic Persistent Current.

This theoretical work initiates contact between two frontier disciplines of physics, namely, atomic superfluid rotation and cavity optomechanics. It considers an annular Bose-Einstein condensate, which exhibits dissipationless flow and is a paradigm of rotational quantum physics, inside a cavity excited by optical fields carrying orbital angular momentum. It provides the first platform that can sense ring Bose-Einstein condensate rotation with minimal destruction, in situ and in real time, unlike demonstrated techniques, all of which involve fully destructive measurement. It also shows how light can actively manipulate rotating matter waves by optomechanically entangling persistent currents. Our work opens up a novel and useful direction in the sensing and manipulation of atomic superflow.

Experimental demonstration of structural robustness of spatially partially coherent fields in turbulence.

Structured fields that are spatially completely coherent have been extensively studied in the context of long-distance optical communication, as the structure in the intensity profile of such fields is used for encoding information. This method of doing optical communication works very well in the absence of turbulence. However, in the presence of turbulence, the intensity structures of such fields start to degrade because of the complete spatial coherence of the field, and this structural degradation increases with the increase in turbulence strength. On the other hand, several theoretical studies have now shown that the structured fields that are spatially only partially coherent are less affected by turbulence. However, to the best of our knowledge, no such experimental demonstration has been reported until now. In this Letter, we experimentally demonstrate the structural robustness of partially coherent fields in the presence of turbulence, and we show that for a given turbulence strength, the structural robustness of a partially coherent field increases as the spatial coherence length of the field is decreased.

Angular lens.

We propose a single phase-only optical element that transforms different orbital angular momentum (OAM) modes into localized spots at separated angular positions on a transverse plane. We refer to this element as an angular lens since it separates out OAM modes in a manner analogous to how a converging lens separates out transverse wave-vector modes at the focal plane. We also simulate the proposed angular lens using a spatial light modulator and experimentally demonstrate its working. Our work can have important implications for OAM-based classical and quantum communication applications.

Propagation-induced revival of entanglement in the angle-OAM bases.

Although the continuous-variable position-momentum entanglement of photon pairs produced by parametric down-conversion has applicability in several quantum information applications, it is not suitable for applications involving long-distance propagation. This is because entanglement in the position-momentum bases, as seen through Einstein-Podolsky-Rosen (EPR)-correlation measurements, decays very rapidly with photons propagating away from the source. In contrast, in this article, we show that in the continuous-variable bases of angle-orbital angular momentum (OAM), the entanglement, as seen through EPR-correlation measurements, exhibits a remarkably different behavior. As with the position-momentum bases, initially, the entanglement in the angle-OAM bases also decays with propagation, and after a few centimeters of propagation, there is no angle-OAM entanglement left. However, as the photons continue to travel further away from the source, the entanglement in the angle-OAM bases revives. We theoretically and experimentally demonstrate this behavior and show that angle-OAM entanglement revives even in the presence of strong turbulence.

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

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 single-shot 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.

Quantum correlations in optical angle-orbital angular momentum variables.

Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.