  Abstract We report the experimental observation of molecular unidirectional
rotation (UDR) echoes, and analyze their origin and behavior both classically
and quantum mechanically. The molecules are excited by two time-delayed
polarization-twisted ultrashort laser pulses and the echoes are measured by
exploding the molecules and reconstructing their spatial orientation from the
detected recoil ions momenta. Unlike alignment echoes which are induced by
linearly polarized pulses, here the axial symmetry is broken by the twisted
polarization, giving rise to molecular unidirectional rotation. We find that
the rotation sense of the echo is governed by the twisting sense of the second
pulse even when its intensity is much weaker than the intensity of the first
pulse. In our theoretical study, we rely on classical phase space analysis and
on three-dimensional quantum simulations of the laser-driven molecular
dynamics. Both approaches nicely reproduce the experimental results. Echoes in
general, and the unique UDR echoes in particular, provide new tools for studies
of relaxation processes in dense molecular gases.
