Coherent backaction between spins and an electronic bath: Non-Markovian dynamics and low-temperature quantum thermodynamic electron cooling

Abstract

We provide a general analytical framework for calculating the dynamics of a spin system in contact with a bath beyond the Markov approximation. The approach is based on a systematic expansion of the Nakashima-Zwanzig master equation in the weak-coupling limit but makes no assumption on the time dynamics and includes all quantum coherent memory effects leading to non-Markovian dynamics. Our results describe, for the free induction decay, the full time range from the non-Markovian dynamics at short times, to the well-known exponential thermal decay at long times. We provide full analytic results for the entire time range using a bath of itinerant electrons as an archetype for universal quantum fluctuations. Furthermore, we propose a quantum thermodynamic scheme to employ the temperature insensitivity of the non-Markovian decay to transport heat out of the electron system and thus, by repeated re-initialisation of a cluster of spins, to efficiently cool the electrons at very low temperatures.

Controllable dynamics of a dissipative two-level system

“…One can see T −1 1 = 2T −1 2 , this relation is consistent with several previous studies [29,[49][50][51].…”