Effective Raman Hamiltonian revisited

Abstract

In this paper, the effective Raman Hamiltonian is revisited. A common way to obtain the effective Raman Hamiltonian is by using the time-dependent perturbation method (TDPT) along with Fermi’s golden rule to keep the total energy and probability constant. However, for a non-resonant Raman process the obtained effective Hamiltonian is not convenient because it is not Hermitian. Hence, we present the Magnus expansion method for obtaining the effective Raman Hamiltonian, which has the advantages of being Hermitian and featuring effects absent in the TDPT effective Hamiltonian. To our knowledge, this is the first time that the Magnus expansion is utilized as an alternative method. We compare the our obtained effective Hamiltonian to that obtained from canonical transformation method. We determine the extra piece in second-order time-dependent perturbation theory which causes loss or gain of total probability.