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Laser Beam Shaping

Two-photon interferences and twisted NOON-states using structured photons

Markus Hiekkamäki, Robert Fickler

Published Jul 30, 2021• 0 citations
Publisher

Abstract

Structured photons often serve as physical realizations of high-dimensional quantum states beneficial to quantum information. One popular way of discretizing the space is through Laguerre-Gaussian modes that can have twisted phase front and, thus, orbital angular momentum (OAM). We demonstrate that using multi-plane light-conversion techniques enables the performance of complex unitary transformations between multiple input-modes and output-modes in the quantum regime. We demonstrate various complex two-photon interferences observed in spatial modes, thereby realizing a linear optical network along a single beam path. Finally, we show that using this ability allows the generation of spatial-mode NOON-states, which offer angular super-sensitivity.

DOI
10.1117/12.2595715

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Structured photons often serve as physical realizations of high-dimensional quantum states beneficial to quantum information. One popular way of discretizing the space is through Laguerre-Gaussian modes that can have twisted phase front and, thus, orbital angular momentum (OAM). We demonstrate that using multi-plane light-conversion techniques enables the performance of complex unitary transformations between multiple input-modes and output-modes in the quantum regime. We demonstrate various complex two-photon interferences observed in spatial modes, thereby realizing a linear optical network along a single beam path. Finally, we show that using this ability allows the generation of spatial-mode NOON-states, which offer angular super-sensitivity.
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A powerful way to describe a transverse field spatial structure are Laguerre-Gauss modes, which are known for their theoretically unbound quanta of orbital angular momentum (OAM) caused on their twisted phase structure. Moreover, spatial structures serve as a promising way to high-dimensional quantum states, known to be advanta-geous in various quantum information tasks. To enable arbitrary unitary operations on any desired set of spatial modes, Multi-plane light-conversion (MPLC) schemes have been demonstrated recently [1].
Photonic N00N-states, i.e. states of light where N photons are in an extremal superposition between two orthogonal states 12(∣N,0⟩+∣0,N⟩)\frac{1}{{\sqrt 2 }}\left({\left| {N,0} \right\rangle + \left| {0,N} \right\rangle }\right)2​1​(∣N,0⟩+∣0,N⟩) , have an increased phase-sensitivity in comparison to their classical counterparts. This phase sensitivity has been harnessed in multiple proof-of-principle experiments with one implementation even showing this advantage unconditionally [1] . Using the increased phase sensitivity, that quantum states of light offer, in conjunction with the increased angular sensitivity of states with large orbital angular momentum (OAM) [2] , has been the target of theoretical studies [3] as well experiments utilizing squeezed states [4] and entangled photon pairs [5] . Until recently however [6] , a reliable way of generating two-photon OAM N00N-states, in a single beam-line and for arbitrary OAM-values, had not been demonstrated.
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.
Structured light carrying Orbital Angular Momentum (OAM) enables high-dimensional photonic quantum information processing. In this work, we propose and theoretically demonstrate a four-dimensional controlledNOT (CNOT) quantum gate implemented using the radial (p) and azimuthal (l) degrees of freedom of Laguerre–Gaussian modes. Quantum information is encoded within a single photon, with the radial mode acting as the control qubit and the OAM mode as the target qubit. The gate is realized using fully linear and unitary optical transformations based on Fourier transform based radial mode sorting and OAM inversion within the architecture. This approach enables deterministic two-qubit logic in an expanded Hilbert space, providing a scalable pathway toward high-dimensional quantum gates using structured light.