Fraction-order sideband generation in an optomechanical system

We propose a scheme for generating a new kind of sideband, i.e., the fraction-order sideband, in an optomechanical system. In the conventional scheme of high-order sideband generation [Opt. Lett.38, 353 (2013)OPLEDP0146-959210.1364/OL.38.000353], the sideband interval has a minimum frequency limitation, which is equal to the mechanical frequency ω_b, and this limits the precision of the sideband comb. With our proposed fraction-order sidebands, the sideband interval can break that limitation and reach ω_b/n (n is an integer). The scheme we propose can be realized by driving the optomechanical system with three laser fields, including a control field (ω_c) and two probe fields (ω, ω), in which the detuning between ω_c and ω is equal to the mechanical frequency ω_b, while the detuning between ω_c and ω is equal to ω_b/n. In this case, we find that not only the integer-order (high-order) sidebands, but also the fraction-order sidebands, and the sum and difference sidebands between the integer- and fraction-order sidebands, will appear in the output spectrum. Moreover, the sideband interval becomes ω_b/n, and it can be decreased by increasing n. Our work paves the way to achieve a tunable optical frequency comb based on the optomechanical system.