  Quantum interferometry and quantum information processing have been proposed
for Bose-Einstein condensates (BECs), but BECs are described in complicated
ways such as using quantum field theory or using a nonlinear differential
equation. Nonlinear quantum mechanics does not mesh well with the superposition
principle at the heart of interferometry and quantum information processing but
could be compatible. Thus, we develop a rigorous foundation for quantum gates,
obtained by solving the equation for evolution, and then we employ this
foundation, combined with quantum-control techniques and appropriate
state-sampling techniques, to devise feasible nonlinear Hadamard gates and
thereby feasible, i.e., high-contrast, nonlinear Ramsey interferometry. Our
approach to BEC interferometry and quantum logic shifts the paradigm by
enlarging to the case of nonlinear quantum mechanics, which we apply to the
cases of BEC interferometry and quantum information processing.
