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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Observation of the Quantum Gouy Phase

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

Published Jun 26, 2023• 0 citations
Publisher

Abstract

Photonic N00N states, i.e., states of light where N photons are in an extremal superposition between two orthogonal states$\frac{1}{\sqrt{2}}(\vert N,0\rangle +\vert 0,N\rangle)$, 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.

DOI
10.1109/cleo/europe-eqec57999.2023.10231421

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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.
Two-photon interference is widely used in quantum information processing, e.g., state engineering and designing quantum gates, as well as in quantum sensing and metrology. This includes the generation and characterization of N00N states, which provide a phase measurement sensitivity that is beyond the shot-noise limit. There have been numerous efforts in generating N00N states with a photon number higher than 2, since their measurement sensitivity increases with N. Both photon number state and modal (temporal, spectral, and spatial) properties of light offer advantages in sensing, where the latter is achieved through mode-multiplexed measurements. Here, we experimentally demonstrate, with the aid of a recently developed photon-detection technology, measurement and characterization of up to tera-mode spatiotemporal correlations in two-photon interference and use it to generate high-dimensional two-photon N00N-states, which can be advantageous for multiphase estimation. We observe a high bi-photon interference and coalescence visibility of ∼64%\sim64\%∼64% and ∼88%\sim88\%∼88% for a tera (101210^{12}1012) and 0.2 tera (2×10112\times 10^{11}2×1011) spatiotemporal modes, respectively. These results open up a route for practical applications of using the spatiotemporal degrees of freedom in two-photon interference, and in particular, for quantum sensing and communication.
The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.