The Properties Of Polaron In Quantum Ring

In this paper, first of all, electronic energy states are studied by solving precisely the time-independent Schr?dinger equation and the properties of a qubit that is formed by overlapping the ground state and the first excited state of the electron in the quantum ring are discussed. Then, the properties of polaron in quantum ring are investigated by using a combinative approach of the LLP unitary transformations and variational method.When investigating electronic energy states and the properties of a qubit in quantum ring, the numerical results show that the energy levels of the electron increase as the confinement of quantum ring is strengthened, the energy levels of the electron decrease as the confinement of quantum ring is weakened. If the outer radius (or the inner radius ) of quantum ring are given , the energy spacing ( E_{l( m +1 )n}- E_lmn) decrease as the inner radius (or the outer radius) increases; the energy spacing ( E( l +1 )mn ? Elmn) increase as the radial confinement of quantum ring is strengthened, the energy spacing ( E( l +1 )mn ? Elmn) decrease as the radial confinement of quantum ring is weakened; the energy spacings ( E( l +1 )mn ? Elmn) and ( E( l +1 )mn ? Elmn) are not dependent on the height of quantum ring. when the size of quantum ring has been determined, probability density distribution of electron in qubit has something to do with the space position in the quantum ring and time, there is maximum in the center position of quantum ring and there is zero in the boundary of quantum ring for the determined angle and time, and probability density distribution of electron does periodically oscillating with time and angle.For investigation of the properties of the polaron in quantum ring, the dependence of the ground-state energy of the polaron, the polaron energy shift and the mean phonon number on the frequency and the averaging radius of the ring in the absence of magnetic field ,and the dependence of the energy of the polaron and the polaron energy shift on the cyclotron frequency in the presence of magnetic field have all been discussed. The numerical results show that the ground state energy of the polaron increases with increasing the frequency (or the averaging radius) of the ring, the polaron energy shift decreases with increasing the frequency (or decreasing the averaging radius of the ring), the mean phonon number increases with increasing the frequency (or decreasing the averaging radius) of the ring. When a perpendicular magnetic field is present, the energy levels of the polaron occur cross, the ground state changes from the state with m=0 to the ones with m = -1,-2,-3, ... with increasing magnetic field and the ground state energy oscillates non-periodically with increasing magnetic field; the polaron energy shift will decrease with increasing magnetic field, the energy levels that have the same absolute value of quantum number m have the same the polaron energy shift; the bigger absolute value of quantum number m is, the bigger the polaron energy shift is. One may change the energy levels of the electron, properties of qubit and the polaron effect in the quantum ring by adjusting the size of quantum ring and magnetic field.