Nov 14 – 15, 2022
Europe/Rome timezone

Holographic Realization of the Prime Number Quantum Potential

Nov 15, 2022, 11:40 AM
Aula Specola (Bologna)

Aula Specola


Palazzo Poggi Via Zamboni 33
Teoria Martedi


Prof. Giuseppe Mussardo (SISSA-INFN Trieste)


We report the experimental realization of the prime number quantum potential $V_N(x)$, defined as the potential entering the single-particle Schroedinger 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. As a further application, we also implement 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, including the factorisation of integers, essentially for quantum cryptography.

Primary authors

Prof. Andrea Trombettoni (Universita' di Trieste & INFN Trieste) Prof. Giuseppe Mussardo (SISSA-INFN Trieste) Prof. Donatella Cassettari (University of St. Andrew (Scotland))

Presentation materials