Steady state coherence in a qubit is incompatible with a quantum map

Abstract

We consider the recent proposal of steady state coherences in a single qubit in the case of a composite system-bath interaction. Based on a field theoretical approach we reanalyse the issue within a Redfield description. We find that the Redfield approach in accordance with a recent proposal yields steady state coherences but also violates the properties of a quantum map yielding negative populations. The issue is resolved by applying the Lindblad equation which is in accordance with a proper quantum map. The Lindblad equation, however, also implies the absence of steady state coherence. We conclude that steady state coherence in a a qubit is incompatible with a quantum map.

Figures (1)

• Figure 1: Plot of the population $\rho^{st}_{++}$ versus the qubit energy splitting $\omega_0$ in the Redfield and Lindblad cases. Temperature $T=10$, cut off frequancy $\omega_c=100$, ohmic case for $s=1$, and spectral strength $g=1$. The Redfield case (blue) for $f_1=1$ and $f_2=1$. The Lindblad case (red) for $f_1=0$ and $f_2=1$. The Redfield case yields negative population $\rho_{++}<0$ in the range $\omega_0\gtrsim 25$ in violation of a quantum map.