Right-unitary transformation theory and applications

Abstract

We develop a new transformation theory in quantum physics, where the transformation operators, defined in the infinite dimensional Hilbert space, have right-unitary inverses only. Through several theorems, we discuss the properties of state space of such operators. As one application of the right-unitary transformation (RUT), we show that using the RUT method, we can solve exactly various interactions of many-level atoms with quantized radiation fields, where the energy of atoms can be two levels, three levels in Lambda, V and equiv configurations, and up to higher (>3) levels. These interactions have wide applications in atomic physics, quantum optics and quantum electronics. In this paper, we focus on two typical systems: one is a two-level generalized Jaynes-Cummings model, where the cavity field varies with the external source; the other one is the interaction of three-level atom with quantized radiation fields, where the atoms have Lambda-configuration energy levels, and the radiation fields are one-mode or two-mode cavities.