Coherent Control of Lowest States of a Shallow Impurity in Graphene Monolayer by Phase Modulated Laser Pulses

The energies of the ground 1S and first excited states 2P, 2S of a shallow donor impurity in graphene monolayer with opened energy gap in a perpendicular magnetic field are obtained using a variational approach. It is shown that the energies of the lowest states and distance between them can be tuned in the region of few ten meV by changing the value of the fine structure parameter and magnitude of the magnetic field. A model of a soft Coulomb interaction is suggested. On the basis of the results obtained, the dipole matrix elements for optical transitions 1S –2P⁺ and 2S –2P⁺ are calculated. In the next step, coherent population transfer between the two metastable states 1S and 2S produced by a single phase modulated (frequency chirped) laser pulse is considered. It is demonstrated that such population transfer may be performed without considerable population of the excited state 2P⁺ if initially population of the quantum system under consideration is localized in one of the metastable states. Additionally, the case when the system is in superposition of two metastable states initially is investigated.