  Doublon-hole pair production which takes place during dielectric breakdown in
a Mott insulator subject to a strong laser or a static electric field is
studied in the one-dimensional Hubbard model. Two nonlinear effects cause the
excitation, i.e., multi-photon absorption and quantum tunneling. Keldysh
crossover between the two mechanisms occurs as the field strength and photon
energy is changed. The calculation is done analytically by the Landau-Dykhne
method in combination with the Bethe ansatz solution and the results are
compared with those of the time dependent density matrix renormalization group.
Using this method, we calculate distribution function of the generated
doublon-hole pairs and show that it drastically changes as we cross the Keldysh
crossover line. After calculating the tunneling threshold for several
representative one-dimensional Mott insulators, possible experimental tests of
the theory is proposed such as angle resolved photoemission spectroscopy of the
upper Hubbard band in the quantum tunneling regime. We also discuss the
relation of the present theory with a many-body extension of electron-positron
pair production in nonlinear quantum electrodynamics known as the Schwinger
mechanism.
