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

TL;DR

This paper explores how non-equilibrium many-body effects like Fermi-edge singularity influence long-range interactions in conductors, revealing limitations on using time-controlled RKKY interactions for quantum gate operations.

Contribution

It introduces a detailed analysis of the spatiotemporal propagation of quenches and their impact on RKKY-like interactions in conductors, highlighting conditions for coherence.

Findings

Coherence between localized states requires finely tuned interactions.

Long-range RKKY-type interactions are limited by many-body dynamics.

Speed of quantum gates based on these interactions may be constrained.

Abstract

Fermi-edge singularity and Anderson's orthogonality catastrophe are paradigmatic examples of non-equilibrium many-body physics in conductors, appearing after a quench is created by the sudden change of a localised potential. We investigate if the signal carried by the quench can be used to transmit a long ranged interaction, reminiscent of the RKKY interaction, but with the inclusion of the full many-body propagation over space and time. We calculate the response of a conductor to two quenches induced by localised states at different times and locations. We show that building up and maintaining coherence between the localised states is possible only with finely tuned interaction between the localised states and the conductor. This puts bounds to the use of time controlled RKKY type interactions and may limit the speed at which some quantum gates could operate.