Fast and robust cat state preparation utilizing higher order nonlinearities. 

Abstract.

Cat states are a valuable resource for quantum metrology applications, promising to
enable sensitivity down to the Heisenberg limit. Moreover, Schroeinger cat states, 
based on a coherent superposition of coherent states, show robustness against 
phase-flip errors making them a promising candidate for bosonic quantum codes. 
A pathway to realize cat states is via utilizing single Kerr-type anharmonicities 
as found in superconducting devices as well as in Rydberg atoms. Such platforms 
nevertheless utilize only the second order anharmonicity, which limits the time it 
takes for a cat state to be prepared. Here we show how proper tuning of multiple 
higher order nonlinear interactions leads to shorter cat state preparation time. 
We also discuss practical aspects including an optimal control scheme which allows 
us to start the state preparation from the vacuum state under standard single mode 
driving. Lastly, we propose an ensemble of Rydberg atoms that exhibits higher order
nonlinearities as a platform to prepare cat states in the laboratory.