Rabi Splitting In A Quantum Well System With Rashba Spin-orbital Coupling

Cavity quantum electro-dynamics is the research field about the interaction between the matter and the electromagnetic field with a boundary.The fundamental model is the Jaynes-Cumming model,with which the vacuum Rabi splitting is predicted,and so on.Rabi splitting is the behavior that the transmission spectrum of the atom will turn into two peaks from the initial one due to the resonant coupling with the cavity field.Recently the electrons in the quantum wells can be realized to be artificial manipulated.Quantum well materials are new man-made materials.It benefits from modern film growth techniques and is made by the technique.The periodicity of quantum well can be controlled artificially.So it has many special properties which are superior to the natural materials,and potential values.Therefore it becomes a considerable candidate in the field of materials science,and semiconductor science,quantum information and other fields.We study the Rabi splitting phenomenon in a quantum well system with Rashba spin-orbital coupling where the spin degree of freedom is driven weakly by an external field.The vertical magnetic field to the quantum well is used to drive the interaction system between the 2-dimentional quantum well and an atom.The dynamics of such system can be described by the Jaynes-Cummings model.As we increase the strength of spin-orbital coupling,the system undergoes an energy-level crossing which does not occur in the traditional cavity circuit QED setups.The Rotating-wave Approximation(RWA)and Non-rotating Wave Approximation(NRWA)interactions can be manipulated separately,that can not be reached in cavity quantum electro-dynamical systems.Herein,the RWA and NRWA items are the Rashba and Dresshaus spin-orbital couplings respectively in the quantum well system.We find that the Rabi splitting can be gotten as the Rashba coupling is retained in the quantum well system.With the increasing coupling the energy-level crossing occurs,which is impossible in the cavity QED or the circuit QED systems.In the above range of the parameters,the RWA item becomes the NRWA one.And the NRWA item becomes RWA one and determines the dynamics of the system.That is,the intuitive rotating wave approximation in the driving Hamiltonian is ineffective when the energy-level crossing occurs.We also give a physical understanding based on the dressed-state representation.The dynamic is analyzed based on the master equation and the slow-varying approximation is adopted for the solving the density matrix.