Phase-dependent ionization of hydrogen by intense sub-cycle pulses

We have performed simulations and analytic calculations that show strong carrier-envelope phase dependence in the ionization of hydrogen atoms using intense sub-cycle sub-femtosecond laser pulses. When the pulse width is comparable to the classical orbit time of the initial bound state, sine-like pulses can ionize more than cosine-like pulses that have the same fluence. This result is the opposite of what is expected from a tunneling-like model, where the ionization probability primarily depends on the peak amplitude of the electric field during the pulse.