Holographic realisation of the prime number quantum potential

Seminars | Tuesday, January 31, 2023 | 10:00:00
Giuseppe Mussardo
I discuss a recent paper with Donatella Cassettari and Andrea Trombettoni where we report the experimental realization of the prime number quantum potential, defined as the potential entering the single-particle Schrodinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we have created light intensity profiles suitable to optically trap ultracold atoms in these potentials for different values of N. As a further application, we have also implemented a potential whose spectrum is given by the 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.  
References: D. Cassettari, G. Mussardo and A. Trombettoni, Holographic realisation of the prime number quantum potential, PNAS-Nexus  https://doi.org/10.1093/pnasnexus/pgac279