  We investigate the charge-states coherence underlying the nonequilibirum
transport through a spinless double-dot Aharonov-Bohm (AB) interferometer. Both
the current noise spectrum and real-time dynamics are evaluated with the
well-established dissipaton-equation-of-motion method. The resulted spectrums
show the characteristic peaks and dips, arising from coherent Rabi oscillation
dynamics, with the environment-assisted indirect inter-dot tunnel coupling
mechanism. The observed spectroscopic features are in a quantitative agreement
to the real-time dynamics of the reduced density matrix off-diagonal element
between two charge states. As the aforementioned mechanism, these
characteristics of coherence are very sensitive to the AB phase. While this is
generally true for cross-correlation spectrum, the total circuit noise spectrum
that is experimentally more accessible shows remarkably rich interplay between
various mechanisms. The most important finding of this work is the existence of
Coulomb-blockade-assisted Rabi interference, with very distinct signatures
arising from the interplay between the AB interferometer and the interdot
Coulomb interaction induced Fano resonance.
