  An ambipolar $n$-$p$ double quantum dot defined by potential variation along
a semiconducting carbon-nanotube is considered. We focus on the (1e,1h) charge
configuration with a single excess electron in the conduction band state
confined in the $n$-type dot and a single missing electron in the valence band
state of the $p$-dot for which lifting of the Pauli blockade of the current was
observed in the electric-dipole spin resonance [E. A. Laird et al. Nat.
Nanotech. 8 , 565 (2013)]. The dynamics of the system driven by periodic
electric field is studied with the Floquet theory and the time-dependent
configuration interaction method with the single-electron spin-valley-orbitals
determined for atomistic tight-binding Hamiltonian. We find that the
transitions lifting the Pauli blockade are strongly influenced by coupling to a
vacuum state with an empty $n$ dot and a fully filled $p$ dot. The coupling
shifts the transition energies and strongly modifies the effective $g$ factors
for axial magnetic field. The coupling is modulated by the bias between the
dots but it appears effective for surprisingly large energy splitting between
the (1e,1h) ground state and the vacuum (0e,0h) state. Multiphoton transitions
and high harmonic generation effects are also discussed.
