  In this work, transport properties of the nonadiabatically pumped
double-quantum-well (DQW) structure are studied. Different from a single
quantum well, band mixing in the DQW generates bonding and antibonding states,
whose wave functions have different spatial symmetry. By applying a
time-dependent electric potential to the two well regions simultaneously,
Floquet sidebands are formed, which constitutes additional quantum tunneling
paths. When one of the Floquet sidebands coincides with the bonding or
antibonding quasibound states within the DQW structure, sharp Fano resonances
are found in the transmission coefficients as well as in the differential shot
noise spectra. While such Fano resonances originate from quantum interference,
their shapes are strikingly different for transport via the bonding state and
via the antibonding state. The Fano resonance via the even-parity bonding state
shows a perfect transmission followed by a total reflection and the Fano
resonance via the odd-parity antibonding state has a reversed symmetry and
shows a total reflection before a perfect transmission.
