A convenient method for controlling transformation between optical bistability and multistability

We propose a convenient method to manipulate the behavior of optical bistability (OB) and optical multistability (OM) in a double Λ-type atomic system with hyperfine structure driven by a π-polarized probe field and a σ-polarized elliptically polarized field (EPF). In the scheme, the frequency detuning of two circularly polarized components of the EPF are determined by an applied magnetic field, and the amplitudes and the phase difference of that can be modulated by rotating a quarter-wave plate, which can be used to optimize quantum interference. Our numerical results show that not only the appearance and disappearance of OB can be transformed reciprocally, but also the switch from OB to OM or vice can be easily realized only by adjusting the magnetic field B or rotating the angle ϕ with the 1/4 wave plate.