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arXiv:1403.5681 · Physical Review A

Hardy's paradox tested in the spin-orbit Hilbert space of single photons

Ebrahim Karimi, Filippo Cardano, Maria Maffei, Corrado de Lisio, Lorenzo Marrucci, Robert W. Boyd, Enrico Santamato

Published Mar 21, 2014• 29 citations
arXivHTMLPDF

Abstract

We test experimentally the quantum ``paradox'' proposed by L. Hardy [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same particle, namely, its spin angular momentum, determined by the photon polarization, and its orbital angular momentum, a property related to the optical transverse mode. Because our experiment involves a single particle, we cannot use locality to logically enforce noncontextuality, which must therefore be assumed based only on the observables' compatibility. On the other hand, our single-particle experiment can be implemented more simply and allows larger detection efficiencies than typical two-particle ones, with a potential future advantage in terms of closing the detection loopholes.

DOI
10.1103/physreva.89.032122

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We test experimentally the quantum ``paradox'' proposed by L. Hardy [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same particle, namely, its spin angular momentum, determined by the photon polarization, and its orbital angular momentum, a property related to the optical transverse mode. Because our experiment involves a single particle, we cannot use locality to logically enforce noncontextuality, which must therefore be assumed based only on the observables' compatibility. On the other hand, our single-particle experiment can be implemented more simply and allows larger detection efficiencies than typical two-particle ones, with a potential future advantage in terms of closing the detection loopholes.
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Abstract We report the realization of Hardy’s thought experiment in classical optical systems. Two different classical optical experiments are implemented. One is based on orbital angular momentum and polarization correlation in a classical optical beam, and the other is based on non-local classical correlation from two separated classical optical beams. All experimental results show that they are analogous to Hardy’s paradox experiments. This means that Hardy’s non-locality proof without inequalities, which is usually used in a quantum system, can also be achieved in classical optical systems.
The orbital angular momentum of photons, being defined in an infinite-dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called "q-plate", which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also have access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum m degree of freedom within the subspaces of |m| = 2h and |m| = 4h per photon.
Entanglement in higher dimensions is an attractive concept that is a chal- lenge to realise experimentally. To this end, the entanglement of the orbital angular momentum (OAM) of photons holds promise. The OAM state-space is discrete and theoretically unbounded. In the work that follows, we investi- gate various aspects of OAM entanglement. We show how the correlations in OAM and its conjugate variable, angular position, are determined by phase- matching and the shape of the pump beam in spontaneous parametric down- conversion. We implement tests of quantum mechanics which have been previously done for other variables. We show the Einstein-Podolsky-Rosen paradox for OAM and angle, supporting the incompatibility of quantum me- chanics with locality and realism. We demonstrate violations of Bell-type inequalities, thereby discounting local hidden variables for describing the correlations we observe. We show the Hardy paradox using OAM, again highlighting the nonlocal nature of quantum mechanics. We demonstrate violations of Leggett-type inequalities, thereby discounting nonlocal hidden variables for describing correlations. Lastly, we have looked into the entan- glement of topological vortex structures formed from a special superposition of OAM modes and show violations of Bell-type inequalities confined to a finite, isolated volume.
In this Letter we experimentally implement a single photon Bell test based on the ideas of S. Tan et al. [Phys. Rev. Lett. 66, 252 (1991)]] and L. Hardy [Phys. Rev. Lett. 73, 2279 (1994)]]. A double homodyne measurement is used to measure correlations in the Fock space spanned by zero and one photons. Local oscillators used in the correlation measurement are distributed to two observers by copropagating it in an orthogonal polarization mode. This method eliminates the need for interferometrical stability in the setup, consequently making it a robust and scalable method.