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Optics Express

Sorting photons of different rotational Doppler shifts (RDS) by orbital angular momentum of single-photon with spin-orbit-RDS entanglement

Lixiang Chen, Weilong She

Published Sep 3, 2008• 16 citations
Publisher

Abstract

We demonstrate that single photons from a rotating q-plate exhibit an entanglement in three degrees of freedom of spin, orbital angular momentum, and the rotational Doppler shift (RDS) due to the nonconservation of total spin and orbital angular momenta. We find that the rotational Doppler shift deltaomega = Omega((delta)s + deltal) , where s, l and Omega are quantum numbers of spin, orbital angular momentum, and rotating velocity of the q-plate, respectively. Of interest is that the rotational Doppler shift directly reflects the rotational symmetry of q-plates and can be also expressed as deltaomega = (Omega)n , where n = 2(q-1) denotes the fold number of rotational symmetry. Besides, based on this single-photon spin-orbit-RDS entanglement, we propose an experimental scheme to sort photons of different frequency shifts according to individual orbital angular momentum.

DOI
10.1364/oe.16.014629

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We demonstrate that single photons from a rotating q-plate exhibit an entanglement in three degrees of freedom of spin, orbital angular momentum, and the rotational Doppler shift (RDS) due to the nonconservation of total spin and orbital angular momenta. We find that the rotational Doppler shift deltaomega = Omega((delta)s + deltal) , where s, l and Omega are quantum numbers of spin, orbital angular momentum, and rotating velocity of the q-plate, respectively. Of interest is that the rotational Doppler shift directly reflects the rotational symmetry of q-plates and can be also expressed as deltaomega = (Omega)n , where n = 2(q-1) denotes the fold number of rotational symmetry. Besides, based on this single-photon spin-orbit-RDS entanglement, we propose an experimental scheme to sort photons of different frequency shifts according to individual orbital angular momentum.
The rotational Doppler shift of a photon with orbital angular momentum ±ℓℏ is shown to be an even multiple of the angular frequency Ω of the reference frame rotation when the photon is reflected from the phase-conjugating mirror. The one-arm phase-conjugating interferometer is considered. It contains N Dove prisms or other angular-momentum-altering elements rotating in opposite directions. When such interferometer is placed in the rotating vehicle, the δω=4(N+1/2)ℓ·Ω rotational Doppler shift appears. As a result, the helical interference pattern will rotate with angular frequency δω/2ℓ. The accumulation of angular Doppler shift via successive passages through the N image-inverting prisms is due to the phase conjugation; for a conventional parabolic retroreflector, the accumulation is absent. The features of such a vortex phase-conjugating interferometry at the single-photon level are discussed.
We investigate two-photon entangled states using two important degrees of freedom of the electromagnetic field, namely orbital angular momentum (OAM) and spin angular momentum. For photons propagating in the same direction we apply the idea of entanglement duality and develop schemes to do entanglement sorting based on either OAM or polarization. In each case the entanglement is tested using appropriate witnesses. We finally present generalizations of these ideas to three- and four-photon entangled states.
Single photons emerging from Pancharatnam-Berry phase optical elements (q plates) exhibit entanglement in the degrees of freedom of spin and orbital angular momentum. We put forward an experimental scheme for probing the spin-orbit correlations of single photons. It is found that the Clauser-Horne-Shimony-Holt parameter S for the single-photon spin-orbit entangled state could be as high as 2√2, evidently violating the Bell-like inequality and thus invalidating the noncontextual hidden variable theories.
The optical "spin-orbit" coupling occurring in a suitably patterned nonuniform birefringent plate known as a "q plate" allows entangling the polarization of a single photon with its orbital angular momentum (OAM). This process, in turn, can be exploited for building a bidirectional "spin-OAM interface," capable of transposing the quantum information from the spin to the OAM degree of freedom of photons and vice versa. Here, we experimentally demonstrate this process by single-photon quantum tomographic analysis. Moreover, we show that two-photon quantum correlations such as those resulting from coalescence interference can be successfully transferred into the OAM degree of freedom.
Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.
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.