Riemann zeros from a periodically-driven trapped ion

TL;DR

This paper demonstrates an experimental method to observe the lowest non-trivial Riemann zeros using a periodically-driven trapped ion, linking number theory with quantum physics through engineered ion dynamics.

Contribution

It introduces a novel quantum simulation approach to measure Riemann zeros by controlling ion dynamics with tailored microwave driving fields.

Findings

Successfully observed the lowest non-trivial Riemann zeros experimentally.

Engineered ion dynamics reveal zeros of the zeta function with high accuracy.

Provides a physical realization of mathematical objects in quantum systems.

Abstract

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in Random Matrix Theory and Quantum Chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.