By John Bonnycastle, James Ryan
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Additional info for An introduction to mensuration and practical geometry
3. Weak Nonresonant Field Example - Dynamic Stark Effect We first consider a single-mode weak nonresonant laser and work in the second. (p' A) gauge. 7). Clearly the question of the utility of the definition will be answered positively in this case: The energy levels of the atom will be shifted by an amount proportional to the square of the laser field which is assumed to be small compared to the energy level spacings. The decay rates will also be proportional to the square of the laser field so that the widths will be small compared to the energy level spacings.
1). 5) d nm and the relation d nn = 0 which comes from the fact that the bare atomic states, Un' are parity eigenfunctions. 3) and the unit vector u specifies the details of the laser-atom coupling. We obtain 49 Sec. 7) and u' u = u* . 8) 0. There are two types of time dependence in the dipole operator. e±iWIJ. and two types of time dependence in the electric field operator. e±iWk'. Therefore. anticipating that Wk ~ W L • the product of the two will have both slow time dependence. e± i(w k - Wd'.
10) where x = 41AI2/ WI20 and IE is the complete elliptic integral of the second kind This gives the energy of the atomic states dressed by the laser field. 8) and (3. 9) may be exploited so that it can be written as a Fourier series Sec. 8) and (3. 9). This explicitly demonstrates the Floquet-like behavior of the dressed wave function. 11), which will only be a good approximation to (3. 11) in the weak coupling limit. 5, give a better approximation to these states, and as the number of terms in the projection operator becomes larger, the method produces the exact states.
An introduction to mensuration and practical geometry by John Bonnycastle, James Ryan