The response of a neutral atom to a strong laser field probed by transient absorption near the ionisation threshold

We present transient absorption spectra of an extreme ultraviolet attosecond pulse train in helium dressed by an 800 nm laser field with intensity ranging from $2\times10^{12}$ W/cm$^2$ to $2\times10^{14}$ W/cm$^2$. The energy range probed spans 16-42 eV, straddling the first ionisation energy of helium (24.59 eV). By changing the relative polarisation of the dressing field with respect to the attosecond pulse train polarisation we observe a large change in the modulation of the absorption reflecting the vectorial response to the dressing field. With parallel polarized dressing and probing fields, we observe significant modulations with periods of one half and one quarter of the dressing field period. With perpendicularly polarized dressing and probing fields, the modulations of the harmonics above the ionisation threshold are significantly suppressed. A full-dimensionality solution of the single-atom time-dependent Schr\"odinger equation obtained using the recently developed ab-initio time-dependent B-spline ADC method reproduce some of our observations.