6. (20 points) (a) A two-level atom is interacting with a continuum of electromagnetic field modes in their vacuum state, causing it to spontaneously decay with rate y. The atom is driven on resonance by a classical laser field with intensity described by 12. The probability that the atom is in the excited state, p(t), evolves according to the equation of motion dp 3ydp 72 122 + + 1122 + p= dt2 2 dt 2 2 (i) (2 points) Identify the equation of motion and give an interpretation for each of the terms. (ii) (2 points) Find the stationary solution Pss, and give the value of Pss when 12>r (iii) (2 points) Write the second order equation of motion in an equivalent first order form. 6. (20 points) (a) A two-level atom is interacting with a continuum of electromagnetic field modes in their vacuum state, causing it to spontaneously decay with rate y. The atom is driven on resonance by a classical laser field with intensity described by 12. The probability that the atom is in the excited state, p(t), evolves according to the equation of motion dp 3ydp 72 122 + + 1122 + p= dt2 2 dt 2 2 (i) (2 points) Identify the equation of motion and give an interpretation for each of the terms. (ii) (2 points) Find the stationary solution Pss, and give the value of Pss when 12>r (iii) (2 points) Write the second order equation of motion in an equivalent first order form