Photoelectron counting sequences for single-atom resonance fluorescence are studied. The distribution of waiting times between photoelectric counts is calculated, and its dependence on drivingfield intensity and detection efficiency is discussed. The photoelectron-counting distribution is derived from the waiting-time distribution. The relationship between photoelectron counting sequences and photon emission sequences is discussed and used to obtain an expression for the reduced state of the atom during the waiting times between photoelectric counts. The roles of irreversibility and the observer in atomic state reduction are delineated. The fluorescent photons emitted by a single coherently driven two-level atom exhibit the nonclassical property of photon antib~nchin~.l-~ The antibunching of fluorescent photons is seen in temporal correlations between photoelectric counts; the detection of one photon makes the detection of a second, after just a short delay, improbable. Photon antibunching is traditionally defined in terms of the degree of second-order temporal coherence g'2'( t, t +T). This is the joint probability for recording photoelectric counts in the intervals [t,t +At) and [t +T, t +7+At), normalized by the probability for two independent photoelectric counts. For antibunched light the joint probability for recording photoelectric counts closely spaced in time falls below the probability for statistically independent counts (separated by a time longer than the coherence time); thus, gi2'( t, t) < 1. The antibunching of fluorescent photons is also reflected in the sub-Poissonian character of the probability density p (n, t, t + TI for recording n photoelectric counts in the interval [r, t + T).~ p (n,t,t + T) can be derived from g'2'(t,t +T), although the detailed algebraic relationship is quite complicated. Both g'2'(t,t +T) and p (n, t, t + T) have been calculated for single-atom resonance fluorescence by a number of workers.'-lo Because of the complexity of general expressions in the time domain, some workers only give the Laplace transform for the photoelectron counting distribution, or give explicit time-dependent expressions only for limiting cases, such as short and long counting times. Recent theoretical work on "quantum j~rn~s""~~~ has drawn attention to the distribution of waiting times between photon emissions as another useful quantity for characterizing photon statistics-in terms of measured quantities, the distribution of waiting times between photoelectrons. By "waiting time" we mean the time T between a photoelectric count recorded at time t, and the next, recorded at time t +T. If photoelectron sequences can be described by a Markov birth process, a single conditional probability density w(~lt) specifies the distribution of waiting times between every pair of photoelectrons. We call this the photoelectron waiting-time distribution. Photoelectron waiting times for coherent light are exponentially distributed.I3 Antibunching implies that photons tend to be separated in time. The distribution of waiting times should then tend to peak around the average time between photoelectric counts. Photoelectron waiting times are certainly not new to