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Fermi-edge singularity and Anderson's orthogonality catastrophe areparadigmatic examples of non-equilibrium many-body physics in conductors,appearing after a quench is created by the sudden change of a localisedpotential. We investigate if the signal carried by the quench can be used totransmit a long ranged interaction, reminiscent of the RKKY interaction, butwith the inclusion of the full many-body propagation over space and time. Wecalculate the response of a conductor to two quenches induced by localisedstates at different times and locations. We show that building up andmaintaining coherence between the localised states is possible only with finelytuned interaction between the localised states and the conductor. This putsbounds to the use of time controlled RKKY type interactions and may limit thespeed at which some quantum gates could operate.

Spatiotemporal Spread of Fermi-edge Singularity as Time Delayed Interaction and Impact on Time-dependent RKKY Type Coupling