  The present qubit technology, in particular in Josephson qubits, allows an
unprecedented control of discrete energy levels. This motivates a new study of
the old pump-probe problem, where a discrete quantum system is driven by a
strong drive and simultaneously probed by a weaker one. The strong drive is
included by the Floquet method and the resulting quasienergy states are then
studied with the probe. We study a qubit where the harmonic drive has a
significant longitudinal component relative to the static equilibrium state of
the qubit. Both analytical and numerical methods are used to solve the problem.
We present calculations with realistic parameters and compare the results with
recent experimental results. A short introduction to the Floquet method and the
probe absorption is given.
