Local vs global dynamics in a dissipative qubit-impurity system

Abstract

We analyse the dynamics of a qubit coupled to a dissipative impurity by comparing local and global derivation schemes of a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation within the Born-Markov and full secular (FS) approximations. We show that the local approach correctly captures a crossover in the dynamics of the qubit coherence, while the FS approximation restricts the validity of the global approach to regimes with well-separated energy scales. Our results clarify the domains of validity of the two approaches and show that the local scheme provides a better GKSL description of the qubit dynamics in the experimentally relevant parameter regime.

Figures (1)

• Figure 1: (a) Sketch of the qubit (blue) coupled to an incoherent impurity (yellow), in turn coupled to a bath (orange). The impurity undergoes emission (absorption) processes with rate $\gamma_-$ ($\gamma_+$) and the coupling $v$ induces a conditional shift of the qubit energy splitting. (b) Diagram in the $(v,\gamma)$ plane showing the regions where a GKSL master equation can be derived within the FS approximation. The blue/red regions correspond to the global (FG)/ local (FL) approach; in the yellow region no GKSL description is assured. In the region marked by "$\times$" both approaches are valid. (c) Modulus of the qubit coherence in the FL approach, showing the crossover from monotonic decay ($g<1$) to dynamics with revivals ($g>1$). The dotted curve shows the FG solution for $g=6$, which converges to the FL solution. Parameters: $\epsilon=20$, $\Delta=0$, $\epsilon_I=20$, $\delta\bar{p}=\delta p_0=0$.