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Frontiers in Optics

Spatial Mode N00N-States and the Quantum Gouy Phase

Markus Hiekkamäki, Rafael F. Barros, Marco Ornigotti, Robert Fickler

Published Jan 1, 2023• 0 citations
Publisher

Abstract

Photonic N00N states can be realized in spatial modes of light in a single beam. Here, their enhanced phase sensitivity translates to improved angular sensing and enables the observation of the quantum Gouy phase.
DOI
10.1364/fio.2023.fm1b.2

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Photonic N00N states, i.e., states of light where N photons are in an extremal superposition between two orthogonal states12(∣N,0⟩+∣0,N⟩)\frac{1}{\sqrt{2}}(\vert N,0\rangle +\vert 0,N\rangle)2​1​(∣N,0⟩+∣0,N⟩), have an increased phase-sensitivity in comparison to their classical counterparts. Using the sensitivity offered by N00N states, in conjunction with the intrinsic properties of transverse-spatial modes, enables new measurement schemes with sensitivities beyond the classically allowed limits and opens up possibilities to investigate the behaviour of different quantum states.
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.
Multi-photon entangled states of light such as N00N (N is the photon number) and squeezed states are routinely used in quantum metrological experiments. Spatially structuring these quantum optical states improves the sensitivity and enhances resolution by using the high dimensional spatial degree of freedom. However, progress in quantum structured light mainly focused on either increasing the number of photons, or increasing the mode numbers, separately [1]. The reason is that generating high (mode number>> 10) dimensional structured light states is usually a lossy process that degrades multi-photon states of light.
Abstract Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.
The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100 ℏ, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular supersensitivity and accessible generation of N00N states between any transverse light fields.