Ultrafast Generation of Large Schrodinger Cat States*

Using a series of spin-dependent kicks on a trapped Yb$+$ ion, we create large, entangled, Schrodinger cat states. We prepare the ion in a superposition of its two m$_{\mathrm{f}}=$0 hyperfine ground states, representing an effective spin-1/2 system. Trapped in a harmonic potential, the ion is illuminated with a specially shaped, 1.5 ns pulse that imparts a momentum kick on the ion with a spin-dependent direction. A fast Pockels cell allows us to change the direction of the spin-dependent kick from each subsequent pulse out of an 80MHz mode-locked laser. By concatenating a series of these very high fidelity spin-dependent kicks, we separate the ion's wave packet into two, spatially distinct states separated by about 200 recoil momenta and involving about 70 phonons. This method for creating a Schrodinger cat state is not time-limited by the trap frequency, and does not rely on confinement in the Lamb-Dicke regime.