Donatella Cassettari

Abstract

We report the experimental realization of the prime number quantum potential V_N(x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers [1].

[1] D. Cassettari, G. Mussardo and A. Trombettoni, Holographic realization of the prime number quantum potential, PNAS Nexus 2, Issue 1, pgac279 (2023).

Presentation

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