Coherent Control of a Shallow Impurity Quantum States in Graphene Monolayer by Bichromatic Phase Modulated Laser Pulses: Influence of Relaxation Processes

The dipole matrix elements for optical transitions 1S – $$2{{P}^{ + }}$$ and 2S – $$2{{P}^{ + }}$$ of a shallow donor impurity in a graphene monolayer with an opened energy gap are calculated in a perpendicular magnetic field using a variational approach. In the next step, population transfer between the two metastable states 1S and 2S by a bichromatic phase modulated (frequency chirped) laser pulse is analyzed taking into account relaxation processes in the system. It is demonstrated that such population transfer may be performed in a robust way without a considerable population of the excited state $$2{{P}^{ + }}$$ if the duration of the bichromatic pulse is much shorter than the relaxation times of the system. Spontaneous decay of the excited state and dephasing relaxation processes result in not complete transfer of the population between the metastable states.