Photon Anti-Bunching Properties of the Anti-Jaynes-Cummings Model

Abstract

This thesis present anti-Jaynes interaction, an interaction where anti-rotating light mode couples to a two-level atom. The anti-bunching properties of the anti-Jaynes-Cummings model was explicitly demonstrated, a model which researchers have always shied away from studying due to the notion that it was non-energy conserving. The energy conservation property was recently addressed hence creating a wider gap which need to be addressed. The anti-Jaynes-Cummings interaction was redefined as a generator of the anti-polariton qubit. Anti-polariton qubit is a two-state quantized particle specified by state vectors, Hamiltonian, conserved excitation number, identity, state transition, U(1) symmetry operators. Formation of anti-polariton qubit involves absorption or emission of negative energy photon by field mode triggered by initial emission or absorption of negative energy photon by the atom. Superposition of qubit state vectors provides the eigenvectors and eigenvalues of the anti JC Hamiltonian. The mean photon number, photon number fluctuation, density operator and atomic inversion are easily evaluated. The result of the mean and its fluctuation were used in the Mandel operator to explicitly demonstrate the anti-bunching properties of the anti-JC interaction. Exact solution of the long standing problem is of importance in understanding the statistical properties and physical properties of the interacting two level atom system which shall be of great importance in the optimization of the technological application, especially in the emerging areas of quantum teleportation and quantum computing. Attention can now be refocused in studying the practical application of the anti JC model such as quantum computing.