  In the quest to understand high-temperature superconductivity in copper
oxides, a vigorous debate has been focused on the pseudogap - a partial gap
that opens over portions of the Fermi surface in the 'normal' state above the
bulk critical temperature ($T_{c}$). The pseudogap has been attributed to
precursor superconductivity, to the existence of preformed pairs, or to
competing orders such as charge-density waves. A direct determination of the
charge of carriers as a function of temperature and bias could help resolve
among these alternatives. Here, we report measurements of the shot noise of
tunneling current in high-quality
La$_{2-x}$Sr$_{x}$CuO$_{4}$/La$_{2}$CuO$_{4}$/La$_{2-x}$Sr$_{x}$CuO$_{4}$
(LSCO/LCO/LSCO) heterostructures fabricated using atomic-layer-by-layer
molecular beam epitaxy, for several doping levels. The data delineate three
distinct regions in the bias voltage-temperature ($V-T$) space. Well outside
the superconducting gap region, the shot noise agrees quantitatively with
independent tunneling of charge-e carriers. Deep within the gap, shot noise is
greatly enhanced, reminiscent of multiple Andreev reflections. Starting above
$T_{c}$ and extending to biases much larger than the gap, there is a broad
region in which the noise substantially exceeds the expectations of
single-charge tunneling, indicating pairing of carriers. Pairs are detectable
deep into the pseudogap region of temperature and bias.
