Quantum Mpemba effect from Stark localization
In classical systems, rugged potential energy landscapes provide a transparent mechanism for the celebrated Mpemba effect, in which hotter initial states cool down faster. This picture generally does not survive in quantum systems. Here we show how to design a quantum energy landscape with local dissipation leading to an Mpemba effect with parametrically separated timescales. Our approach uses Stark localization to design an energy landscape and localized incoherent hopping as cooling mechanism. The hops are triggered by rare "detection" events whose rate grows with energy, allowing hotter states to cool faster and producing super-exponentially separated cooling rates for localized initial states. We further show that the effect is dramatically enhanced by collective hopping of bound pairs in the presence of attractive on-site interactions. These findings have clear experimental signatures accessible in present-day setups.