Tailoring population inversion in Landau-Zener-St\"uckelberg interferometry of flux qubits

We distinguish different mechanisms for population inversion in flux qubits driven by dc+ac magnetic fields. We show that for driving amplitudes such that there are Landau-Zener-St\"uckelberg intereferences, it is possible to have population inversion solely mediated by the environmental bath at long driving times. We study the effect of the resonant frequency $\Omega_p$ of the measuring circuit, finding different regimes for the asymptotic population of the state of the flux qubit. By tailoring $\Omega_p$ the degree of population inversion can be controlled. Our studies are based on realistic simulations of the device for the Josephson flux qubit using the Floquet-Born-Markov formalism.