The General Optical Transition

Abstract

In this chapter we discuss transitions, stimulated and spontaneous, in the two-level atom, described by an excited state │k〉 of energy W _k = hv _k , and a ground state │i〉 of energy W _i = hv _i . The transition frequency is v _k − v _i = v ₀. Strictly speaking, of course, at least one of the two levels must comprise a number of sublevels or Zeeman levels. In the simplest of all transitions, for example, that between a J = 0 state and a J = 1 state, the latter has three substates with different projections of angular momentum M = +1, 0, −1. True two-state behavior can exist if the J = 0 state is the lower one or ground state, the J = 1 state is the upper one or excited state, and the radiation is polarized pure linear or pure circular. If the stimulating radiation is polarized pure linear, then we may regard the transition as being stimulated between the J _i = 0, M _i = 0 ground state and the J _k = 1, M _k = 0 excited state. Since spontaneous decay from the excited state can only return the atom to the unique ground state, the general state of the atom remains always a superposition of those two states. A similar argument can be made, for example when the radiation is pure circular; if it is designated σ ⁺, the ground state is coupled only to the J _k = 1, M _k = 1 excited state, and this can return only to J _i = 0, M _i = 0. Such a simple situation cannot occur for the case where the ground state is J _i = 1 and the excited state is J _k = 0. If, for example, one excites with linearly polarized light, an atom in the J _i = 1, M _i = 0 ground state is excited to the J _k = 0, M _k = 0 state; the latter may decay by spontaneous emission to any of the three ground states, M _i = 0, ±1, and the system has lost its two-state character. Indeed, unless there is some mechanism for returning the population to the M _i = 0 state, the atom will become optically pumped into the J _i = 1, M _i = ±1 states, because no transitions can be stimulated from these states. However, other cases of pure two-level behavior are possible. For example, if an atom whose ground state has angular momentum J _i = J is stimulated to make transitions using σ ⁺-polarized radiation to an excited state with angular momentum J _k = J + 1, optical pumping will again occur. The combined effect of stimulation, which is always trying to transfer the atom to substates of higher component of angular momentum, and of spontaneous decay, is to pump the population by successive stimulations and decays, into the ground substate J _i = J, M _i = +J. From this, the incident radiation can stimulate transitions only to the excited substate J _k = J + 1, M _k = J + 1, and that state can return, by stimulated or spontaneous transition, only to J _i = J, M _i = J. The system, once pumped, can therefore be described as a superposition of these two states only.