Phys.org February 2, 2023
An international team of researchers (UK, Italy) has reported the experimental realization of the prime number quantum potential VN(x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, they created light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, they 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. According to the researchers their 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…read more. Open Access TECHNICAL ARTICLE
Experimental setup, showing the phase profile imprinted by the SLM and the resulting light intensity profile in the trapping plane. Credit: PNAS Nexus, Volume 2, Issue 1, January 2023, pgac279Â Â Â Â Â