论文标题
质数量子电位的全息实现
Holographic Realization of the Prime Number Quantum Potential
论文作者
论文摘要
我们报告了质数量子潜力$ v_n（x）$的第一个实验实现，定义为进入单粒子schrödingerhamiltonian的潜力，并带有第一个$ n $ prime数字给出的特征值。我们使用全息光学陷阱，尤其是空间光调节器来调整潜在的形状。作为进一步的应用程序，我们还具有幸运数字的潜力，这是一个与熟悉的Eratosthenes筛子用于素数不同的筛子产生的整数。 我们的结果铺平了用任意整数序列作为能级的量子电位的道路，从角度来看，将量子系统设置用于算术操作或涉及质量数量的数学测试的可能性。
We report the first experimental realization of the prime number quantum potential $V_N(x)$, defined as the potential entering the single-particle Schrödinger 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.
