  Optical "Schr\"odinger cat" states, the non-classical superposition of two
quasi-classical coherent states, serve as a basis for gedanken experiments
testing quantum physics on mesoscopic scales and are increasingly recognized as
a resource for quantum information processing. Here, we report the first
experimental realization of optical "Schr\"odinger cats" by adding a photon to
a squeezed vacuum state, so far only photon-subtraction protocols have been
realized. Photon-addition gives us the advantage of using heralded signal
photons as experimental triggers, and we can generate "Schr\"odinger cats" at
rates exceeding $8.5 \times 10^4$ counts per second; at least one order of
magnitude higher than all previously reported realizations. Wigner
distributions with pronounced negative parts are demonstrated at down to -8.89
dB squeezing, even when the initial squeezed vacuum input state has low purity.
Benchmarking against such a degraded squeezed input state we report a maximum
fidelity of more than 80% with a maximum cat amplitude of $|\alpha| \approx
1.66$. Our experiment uses photon-addition from pairs, one of those photons is
used for monitoring, giving us enhanced control; moreover the pair production
rates are high and should allow for repeated application of photon-addition via
repeat-stages.
