Effects of mode profile on tunneling and traversal of ultracold atoms through vacuum-induced potentials

We consider the resonant interaction of an ultracold two-level atom with an electromagneticfield insidea high-Qmicromaser cavity. In particular, we study the tunneling and traversal of ultracold atomsthrough vacuum-induced potentials for secant hyperbolic square and sinusoidal cavity mode functions.The phase time which may be considered as an appropriate measure of the time required for the atomsto cross the cavity, significantly modifies with the change of cavity mode profile. For example, switchingbetween the sub and superclassical behaviors in phase time can occur due to the mode function. Si-milarly, negative phase time appears for the transmission of the two-level atoms in both excited andground states for secant hyperbolic square mode function which is in contrast to the mesa mode case