  We prove a nonperturbative duality concerning the dynamics of
harmonic-oscillator-type Unruh-DeWitt detectors in curved spacetimes.
Concretely, using the Takagi transformation we show that the action of a
harmonic oscillator Unruh-DeWitt detector with one frequency in a spacetime is
equal to that of a detector with a different frequency in a conformally related
spacetime. As an example, we show that the dynamics of simple stationary
detectors in flat spacetime is dual to that of detectors in a cosmological
scenario. The nonperturbative duality enables us to investigate entanglement
harvesting in new scenarios in curved spacetime by using results obtained in
simpler, conformally related spacetimes.
