A quantum control protocol is proposed for the creation of NOON states with $N$ ultracold bosonic atoms on two modes, corresponding to the coherent superposition $|N,0\rangle +|0,N\rangle$. This state can be prepared by using a third mode where all bosons are initially placed and which is symmetrically coupled to the other two modes. Tuning the energy of this third mode across the energy level of the other modes allows the adiabatic creation of the NOON state. While this process normally takes too much time to be of practical use, due to the smallness of the involved spectral gap, it can be drastically boosted through counterdiabatic driving which allows for efficient gap engineering. We demonstrate that this process can be implemented in terms of static parameter adaptations that are experimentally feasible with ultracold quantum gases. Gain factors in the required protocol speed are obtained that increase exponentially with the number of involved atoms and thus counterbalance the exponentially slow collective tunneling process underlying this adiabatic transition. Besides optimizing the protocol speed, our NOON state preparation scheme achieves excellent fidelities that are competitive for practical applications.

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• BEC tunneling
• Cold gases in optical lattices
• Entanglement in quantum gases
• Entanglement production
• Quantum control
• Quantum many-body systems
• Ultracold gases
• Adiabatic approximation