Holographic Realization of the Prime Number Quantum Potential

TL;DR

This paper demonstrates the first experimental creation of a quantum potential based on prime numbers using holographic optical traps, enabling new avenues for quantum arithmetic and mathematical testing.

Contribution

It introduces a novel experimental method to realize quantum potentials with prime and lucky number sequences using holographic techniques.

Findings

Successfully realized prime number quantum potential experimentally.

Implemented a potential with lucky numbers as energy levels.

Showed potential for quantum arithmetic and mathematical applications.

Abstract

We report the first experimental realization of the prime number quantum potential $V_N(x)$, defined as the potential entering the single-particle Schr\"{o}dinger 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.