  The at-will control of quantum states is a primary goal of quantum science
and technology. The celebrated Hahn echo exemplifies such quantum-state control
based on a time-reversal process in a few-level system. Here, we propose a
different echo phenomenon associated with the energy-band structure in quantum
many-body systems. We show that the dynamics of quasiparticle wavepackets can
be reversed by a driving electric-field pulse, yielding echoes with the
time-reversed waveform of the optical excitation pulse when the quasiparticles
recombine. The present echoes are observed not only in band insulators but also
in correlated insulators, including a Mott insulator and a
spontaneously-broken-symmetry charge-ordered insulator, in one- and
higher-dimensional systems, irrespective of the integrability of the models.
Analytical expressions reveal the conditions under which the echoes appear, and
they also indicate that the frequency of the echo pulses reflects the
dispersion relation for quasiparticles such as electron-hole pairs,
doublon-holon pairs, and kink-antikink pairs. These findings provide a
framework for all-optical momentum-resolved spectroscopy of the quasiparticles
in quantum many-body systems.
