Quantum Memory and Optical Transistor Based on Electromagnetically Induced Transparency in Optical Cavities

Abstract: We theoretically studied the implementation of a quantum memory and an optical transistor in a system composed by a single atom trapped inside a high finesse cavity. In order to store and map the quantum state of an input pulse onto internal states of the single atom (quantum memory) we employ the electromagnetically induced transparency (EIT) phenomenon (which can work out as an optical transistor) where the information can be transferred to the dark state of the atom modelled by a three-level system in a {\Lambda}-type configuration. In our model we consider a suitable temporal shape for the control field that ensures the adiabaticity of the storage process and retrieval of the probe pulse. The dynamic of the field inside the cavity was obtained by master equation approach, while the outside field was calculated by input-output formalism. We have analysed two different setups: i) two-sided and ii) single-sided cavities. While the first setup is the most appropriate and commonly used to observe cavity-EIT in the transmission spectrum, thus the best configuration for the optical transistor, the maximum quantum memory efficiency can not reach reasonable values, being limited to 50% for symmetric cavities. On the other hand, with single-sided cavity the quantum memory efficiency increases considerably and can reach values close to 100% in the strong atom-field coupling regime. However this specific setup is not favourable to observe the cavity-EIT effect in the transmission spectrum and then it is not appropriate to control the transmission of light pulses.