Holographic Realization of the Prime Number Quantum Potential

2022/02/07 by Donatella Cassettari, Cassettari, Donatella, Giuseppe Mussardo +3
Mathematics · Physics and Astronomy · #Arithmetic #Combinatorics #Computer science #Holography #Mathematics #Physics #Prime (order theory) #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Realization (probability) #Statistics #Theoretical physics #cond-mat.other #hep-th #math.NT #quant-ph

paper · pdf · doi:10.48550/arxiv.2202.03446

published in arXiv (Cornell University) (Cornell University) · 12 pages, 6 ifgures

arxiv created 2022/02/07 · openalex publication_date 2022/02/07 · arxiv updated 2022/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We report the first 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. We use holographic optical traps and, in particular, a spatial light modulator to tailor the potential to the desired shape. As a further application, we also implement a potential with lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes's sieve used for the primes. Our results pave the way towards 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.

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