in three step model when a intense laser field interact with atom the coulomb potential distorted and a potential barrier is formed through which electron can tunnel, i am confused about barrier suppression that how it get suppress and how this potential barrier is created and also how this suppression depends on the phase of applied laser field
Check out "Anatomy of Strong Field Ionisation" by Ivanov, Spanner & Smirnova, it's a nice introduction to the case when the oscillation of the laser field is slow.
Article Anatomy of strong field ionization
The electron definitely see not only atom's intrinsic potential from protons in core and other electrons but also see AC potential from laser field. With linear polarization in laser, you can imagine that one side is suppressed while other side enhanced. As tunneling is depending on potential depth and its width, If one side suppression is enough then electron can go outside. In ultrafast laser. especially few-cycle pulse (~few fs in FWHM) Carrier-Envelop-Off set (CEO) which is measure of how much envelope and phase are matched is really important to study this phenomena.
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