Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.

Figure 1

Final transition probability $P_{\uparrow \to \downarrow }(\infty )$ as a function of intrinsic interaction $\Delta$, for several values of the coupling angle $\theta$. Parameters: $E_0=2\sqrt{\hslash v}$ and $S=0.5\hslash v$.