Efficient scheme for realizing beam-splitter-type coupling for two cavity modes

We propose a scheme for realizing the beam-splitter-type coupling between two cavity modes. In the scheme a collection of Λ-type three-level atoms are coupled with the two cavity modes with large detunings. Under certain conditions, the effective Hamiltonian for the cavity modes describes the frequency-up conversion, which is decoupled with the atomic system. The effective coupling strength increases with the number of the atoms, which allows the procedure to be completed in a reasonable time. The atoms have no probability of being populated in the excited states and thus the scheme is insensitive to atomic spontaneous emission.