Translating Uncontrolled Systems in Time

Abstract

We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This ``time translation'' effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which we can effect on multiple target systems through a scattering protocol of fixed duration. The core results are: a) when the target is a single system, we can translate it backwards in time for an amount proportional to the experimental runtime; b) when $n$ targets are present in the scattering region, we can make a single system evolve $n$ times faster (backwards or forwards), at the cost of keeping the remaining $n-1$ systems stationary in time. For high $n$ our protocols therefore allow one to map, in short experimental time, a system to the state it would have reached with a very long unperturbed evolution in either positive or negative time.