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Physical Review A

High-dimensional quantum nature of ghost angular Young’s diffraction

Lixiang Chen, Jonathan Leach, Barry Jack, Miles J. Padgett, Sonja Franke‐Arnold, Weilong She

Published Sep 20, 2010• 27 citations
Publisher

Abstract

We propose a technique to characterize the dimensionality of entangled sources affected by any environment, including phase and amplitude masks or atmospheric turbulence. We illustrate this technique on the example of angular ghost diffraction using the orbital angular momentum (OAM) spectrum generated by a nonlocal double slit. We realize a nonlocal angular double slit by placing single angular slits in the paths of the signal and idler modes of the entangled light field generated by parametric down-conversion. Based on the observed OAM spectrum and the measured Shannon dimensionality spectrum of the possible quantum channels that contribute to Young's ghost diffraction, we calculate the associated dimensionality ${D}_{\mathrm{total}}$. The measured ${D}_{\mathrm{total}}$ ranges between 1 and 2.74 depending on the opening angle of the angular slits. The ability to quantify the nature of high-dimensional entanglement is vital when considering quantum information protocols.

DOI
10.1103/physreva.82.033822

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We propose a technique to characterize the dimensionality of entangled sources affected by any environment, including phase and amplitude masks or atmospheric turbulence. We illustrate this technique on the example of angular ghost diffraction using the orbital angular momentum (OAM) spectrum generated by a nonlocal double slit. We realize a nonlocal angular double slit by placing single angular slits in the paths of the signal and idler modes of the entangled light field generated by parametric down-conversion. Based on the observed OAM spectrum and the measured Shannon dimensionality spectrum of the possible quantum channels that contribute to Young's ghost diffraction, we calculate the associated dimensionality Dtotal{D}_{\mathrm{total}}Dtotal​. The measured Dtotal{D}_{\mathrm{total}}Dtotal​ ranges between 1 and 2.74 depending on the opening angle of the angular slits. The ability to quantify the nature of high-dimensional entanglement is vital when considering quantum information protocols.
We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing N angular slits placed in the path of twin photons define a qudit space of dimension N2, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical results for the Concurrence as a function of the angular aperture size for the case of high-dimensional OAM entanglement and for the case of high-dimensional path entanglement, produced by N × M angular slits. Our results provide additional means for preparation and characterization of entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
The orbital angular momentum (OAM) of light has become a central topic in quantum information and optical communication. In applications OAM is typically probed by observing a beam's diffraction through binary amplitude and phase masks. Distinguishing the different OAM states of the beam is usually difficult, though, so here the authors program a digital micromirror array to shift the setup's slit transversely, to exploit the unique phase of an OAM beam. By observing how diffraction varies as the slit changes, one can probe higher OAM values than usual, allowing access to theoretically unlimited OAM states for high-dimensional quantum systems, or for multiplexing in communication.
Using angular position–orbital angular momentum entangled photons, we propose an experiment to generate maximally entangled states in D-dimensional quantum systems, the so called qudits, by exploiting correlations of parametric down-converted photons. Angular diffraction masks containing N angular slits in the arms of each twin photon define a qudit space of dimension N2, spanned by the alternative pathways of the photons. Numerical results for N angular slits with N = 2, 4, 5, 10 are reported. We discuss relevant experimental parameters for an experimental implementation of the proposed scheme using Spatial Light Modulators (SLMs), and twin-photons produced by Spontaneous Parametric Down Conversion (SPDC). The entanglement of the qudit state can be quantified in terms of the Concurrence, which can be expressed in terms of the visibility of the interference fringes, or by using Entanglement Witnesses. These results provide an additional means for preparing entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.
We implement an interferometric method using two angular slits to measure the orbital-angular-momentum (OAM) mode spectrum of a field with partial angular coherence. As the angular separation of the slits changes, an interference pattern for a particular OAM mode is obtained. The visibility of this interference pattern as a function of angular separation is equivalent to the angular correlation function of the field. By Fourier transforming the angular correlation function obtained from the double-angular-slit interference, we are able to calculate the OAM spectrum of the partially coherent field. This method has potential application for characterizing the OAM spectrum in high-dimensional quantum information protocols.