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      Experimental Implementation of the Fractional Vortex Hilbert's Hotel

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          Abstract

          The Hilbert hotel is an old mathematical paradox about sets of infinite numbers. This paradox deals with the accommodation of a new guest in a hotel with an infinite number of occupied rooms. Over the past decade, there have been many attempts to implement these ideas in photonic systems. In addition to the fundamental interest that this paradox has attracted, this research is motivated by the implications that the Hilbert hotel has for quantum communication and sensing. In this work, we experimentally demonstrate the fractional vortex Hilbert's hotel scheme proposed by G. Gbur [Optica 3, 222-225 (2016)]. More specifically, we performed an interference experiment using the fractional orbital angular momentum of light to verify the Hilbert's infinite hotel paradox. In our implementation, the reallocation of a guest in new rooms is mapped to interference fringes that are controlled through the topological charge of an optical beam.

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          Author and article information

          Journal
          23 June 2022
          Article
          2206.12013
          806df69c-9558-4323-becc-fd905e6cc3fb

          http://creativecommons.org/licenses/by/4.0/

          Custom metadata
          10 pages 4 figures
          quant-ph physics.optics

          Quantum physics & Field theory,Optical materials & Optics
          Quantum physics & Field theory, Optical materials & Optics

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