We analyze the conditions for producing atomic number states in a one-dimensional optical box using the Bethe ansatz method. This approach provides a general framework, enabling the study of number state production over a wide range of realistic experimental parameters.
We analyze a system of fermionic $^{6}$Li atoms in an optical trap, and show that an atom on demand can be prepared with ultra-high fidelity, exceeding 0.99998. This process can be scaled to many sites in parallel, providing a realistic method to ini
tialize N qubits at ultra-high fidelity for quantum computing. We also show how efficient quantum gate operation can be implemented in this system, and how spatially resolved single-atom detection can be performed.
