Motivation: telegraphic fluorescence (driven spontaneous emission) of single atoms

Example single V-systems: two upper levels 1 (fast spontaneous emission) and 2 (slow spontaneous emission), one lower level 0 driven by two lasers. Transition $0\to 2$ traps the system in 2 for a long time. Resonance fluorescence intensity $I(t)$ therefore exhibits jumps: `telegraphic fluorescence' with random switching between bright and dark periods. Aim: calculate distribution of dark periods.

Length $T_D$ of dark period can be simply calculated from the density matrix element $\rho_{22}$

$$T_D^{-1} = \dot{\rho}_{22}(t=0),\quad \rho_{22}=0,$$ (138)

where the derivative is calculated from the underlying equation of motion (Master equation). However, the calculation of other, more complicated quantities related to the description of telegraphic fluorescence turns out to be technically complicated within the Master equation formalism. Example: `exclusive probability' $P_0(t)$ that, after an emission at time $t=0$, no other photon has been emitted in the time interval $[0,t]$.

• Some people raise `objections' against the traditional Master equation approach: the density operator $\rho$ describes ensembles of quantum systems and is therefore inappropriate to describe single quantum systems such as a single ion in an ion trap. However, these objections are unjustified; as long as one sticks with the probabilistic interpretation of Quantum Mechanics, the density operator description is perfectly valid for a single quantum system.
• `Single quantum systems' can not only be realised in ion traps, but also in `artificial atoms' and `artificial molecules' (solid state based quantum dots, superconducting charge or flux qubits). These will be discussed in a later chapter.