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.
Highlights
The Fermi-edge singularity (FES) problem [1–4] and Anderson’s orthogonality catastrophe (OC) [5] are the concepts behind one of the first and most important examples of how a quench can drive a strongly correlated quantum response of a fermionic conductor
The results above provide an extension to our understanding of FES/OC physics to how the excitation extends nonlocally through space and time
With the finite propagation velocity the transition amplitudes are strongly peaked at the characteristic run time, and the FES causes a reduction of the peak amplitude together with the modification of the power-law tails
Summary
The Fermi-edge singularity (FES) problem [1–4] and Anderson’s orthogonality catastrophe (OC) [5] are the concepts behind one of the first and most important examples of how a quench can drive a strongly correlated quantum response of a fermionic conductor. Picking up the signal at some distance causes a coupling with the source of the quench We formalize this aspect and formulate the FES signal as a time delayed, long ranged effective interaction with a strong memory effect due to the slow power-law decay of response functions. The time delay in the signal is due to the finite Fermi velocity vF and does not require the FES itself The latter, causes a significant renormalization of the transmission amplitude and decoherence even after extraction unless special fine tuned conditions are met. These are permanently present and time and FES are of no significance If they are intended to be switched on and off as required for a quantum gate operation [58] our paper shows that time delay, entanglement with the conductor.
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