Generation of ultrashort pulses of harmonics

We study harmonic generation by a single atom exposed to two short perpendicularly polarized laser pulses. The two perpendicular electric fields oscillate at two different frequencies ${\omega }_1$ and ${\omega }_2$. Hence, the resultant field has a polarization which depends on time. Since harmonics are emitted when the resultant oscillating field is linearly polarized, it is expected that a short pulse of harmonics may be emitted if the external field is linearly polarized during a short period of time. We show that, indeed, the atom may emit an ultrashort pulse of a given harmonic. This result has been obtained by time-frequency analyzing the acceleration of the induced dipole moment with a filter whose frequency bandwidth is smaller than twice the frequency of the external field. Our calculation of the dipole acceleration is based on the numerical solution of the time-dependent Schrödinger equation. We then address the question of how far it is possible to reduce the duration of the emitted pulse of one given harmonic by adjusting both ${\omega }_1$ and ${\omega }_2$ and keeping the amplitude of this pulse significant. In order to answer to this question, we used the quantum version of the two-step model [M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994)].