Cosmic microwave background constraints on the duration and timing of
  reionization from the South Pole Telescope
  The epoch of reionization is a milestone of cosmological structure formation,
marking the birth of the first objects massive enough to yield large numbers of
ionizing photons. The mechanism and timescale of reionization remain largely
unknown. Measurements of the CMB Doppler effect from ionizing bubbles embedded
in large-scale velocity streams (the patchy kinetic Sunyaev-Zel'dovich effect)
can constrain the duration of reionization. When combined with large-scale CMB
polarization measurements, the evolution of the ionized fraction can be
inferred. Using new multi-frequency data from the South Pole Telescope (SPT),
we show that the ionized fraction evolved relatively rapidly. For our basic
foreground model, we find the kinetic Sunyaev-Zel'dovich power sourced by
reionization at l=3000 to be <= 2.1 micro K^2 at 95% CL. Using reionization
simulations, we translate this to a limit on the duration of reionization of
Delta z <= 4.4 (95% CL). We find that this constraint depends on assumptions
about the angular correlation between the thermal Sunyaev-Zel'dovich power and
the cosmic infrared background (CIB). Introducing the degree of correlation as
a free parameter, we find that the limits on kSZ power weaken to <= 4.9 micro
K^2, implying Delta z <= 7.9 (95% CL). We combine the SPT constraint on the
duration of reionization with the WMAP7 measurement of the integrated optical
depth to probe the cosmic ionization history. We find that reionization ended
with 95% CL at z > 7.2 under the assumption of no tSZ-CIB correlation, and
z>5.8 when correlations are allowed. Improved constraints from the full SPT
data set in conjunction with upcoming Herschel and Planck data should detect
extended reionization at >95% CL provided Delta z >= 4. (abbreviated)
