The equations describing the resonant with a two-level atom with energy levels as shown in the figure are given below- du/dt- -bu 4fal where us (p21 tp12); v zij (p21-p12) and w = (p22-p"), and β- collision) dephasing time and a the spontaneous emission rate from level 2, and the rabi 1/e+ a/2 , τ the (elastic frequency χ-2nde/h. inelastic collisions are not present. the dipole moment connecting these two levels is given by d solve the following problems for the conditions specified. a. 40%) the incident laser is a cw laser. the collision dephasing rate 1/t is such that β 3a. the field strength of the laser is varied in unit of a, such that χ-2ndeh-- calculate the steady state population of level 2(i. c pz) in terms of the parameter n. 汃 b. [4096] for the same system, write down the rateequations describing the laser interaction with the system. solve for the steady state population of level 2 c. [20%] is it possible to achieve population inversion be achieved at steady state, using the results from either a or b above? briefly explain the physical explanations in your own words besides just quoting formulae from your calculation.