Nonclassical Light Sources and Frequency Converters with Integrated Opto-Mechanical

Hbs = Gab†+ h.c., (6.5) which is also called beam-splitter Hamiltonian. This effective Hamiltonian is useful for laser sideband cooling of mechanical oscillators (Wilson et al., 2007; Marquardt et al., 2007), and light frequencies converter, which we will discuss in Section 6.3.We take the detuning as = m, and assume m » G, under the rotating wave approximation, the effective Hamiltonian becomes Hsq = Gab + h.c., (6.6)which can generate the two-mode squeezed state between cavity and mechanical modes. Combining both beam splitter and two-mode squeezing Hamiltonian, we may generate two-mode squeezed lights with opto-mechanical systems (Yin and Han, 2009), which will be discussed in Section 6.3.