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The Riemann hypothesis, which states that the non-trivial zeros of theRiemann zeta function all lie on a certain line in the complex plane, is one ofthe most important unresolved problems in mathematics. Inspired by theP\'olya-Hilbert conjecture, we propose a new approach to finding a physicalsystem to study the Riemann zeros, which in contrast to previous examples, isbased on applying a time-periodic driving field. This driving allows us tomould the quasienergies of the system (the analogue of the eigenenergies in theabsence of driving), so that they are directly governed by the zeta function.We further show by numerical simulations that this allows the Riemann zeros tobe measured in currently accessible cold atom experiments.

Finding zeros of the Riemann zeta function by periodic driving of cold atoms