Engineering Hamiltonians through Nonlinearities
Following the formalism described in “Black-box superconducting circuit quantization” http://arxiv.org/abs/1204.0587 we can expand sin(a+b+…+h.c.) or cos(a+b+…+h.c.) or any other nonlinear f(a+b+…+h.c.) in order to obtain non-linear terms in the Hamiltonian (a, b, and other letters represent the annihilation operators of various oscillator modes). If we drive some of the modes classically we can create any non-linear term in the effective Hamiltonian. This module helps solve the constraint on the frequencies of the modes (both the requirement that some of the monomials in the expansion are resonant and that all the other terms in the expansion of the nonlinearity are off-resonant).