Cassettari Donatella, Mussardo Giuseppe, Trombettoni Andrea
SUPA School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK.
SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy.
PNAS Nexus. 2022 Dec 12;2(1):pgac279. doi: 10.1093/pnasnexus/pgac279. eCollection 2023 Jan.
We report the experimental realization of the prime number quantum potential (), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different 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 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.
我们报告了质数量子势（）的实验实现，该势定义为进入单粒子薛定谔哈密顿量的势，其本征值由前几个质数给出。利用计算机生成全息术，我们针对不同的 值创建了适合在这些势中光学捕获超冷原子的光强分布。作为进一步的应用，我们还实现了一种势，其谱由幸运数给出，幸运数是通过一种不同于用于质数的熟悉的埃拉托斯特尼筛法的不同筛法生成的整数序列。我们的结果为实现以任意整数序列作为能级的量子势铺平了道路，并从长远来看展示了建立用于算术运算或涉及质数的数学测试的量子系统的可能性。
