Joint probability analysis of the dynamics of strong field ionization of atoms

We describe an approach to the description of time-development of the processes of ionization of

atoms in electromagnetic fields based on the notion of joint probability of occurrence of two events,

event B being finding atom in a given state after the end of the laser pulse,

event A being finding a particular value of a given physical observable at a moment of time inside the laser

pulse duration. This approach allows to tackle the questions which are somewhat difficult to

address, in particular, to study the characteristics of the ionized electron for times

inside the interval of the laser pulse duration. For the moments of time inside the interval of the laser pulse duration, when

the wave-packet describing ionized electron is not fully formed and is still partly inside

the atom, it is not easy to unambiguously single out the part of the wave-function describing ionized

electron from the total wave-function of the system. By choosing the event B appropriately we may circumvent

this difficulty. We may require, for instance, that B is detection of atom in an ionized state and study development of the

ionization process, or we may choose B to be detection of atom in a Rydberg state and study development of the

frustrated tunneling ionization (FTI) process. We apply this technique to study time-development of lateral velocity distribution

of ionized electrons and time-development of the FTI.