Generation and entanglement of multi-dimensional multi-mode coherent fields in cavity QED

We introduce generalized multi-mode superposition of multi-dimensional coherent field states and propose a generation scheme of such states in a cavity QED scenario. An appropriate encoding of information on these states is employed, which maps the states to the Hilbert space of some multi-qudit states. The entanglement of these states is characterized based on such proper encodings. A detailed study of entanglement in general multi-qudit coherent states is presented, and in addition to establishing some explicit expressions for quantifying entanglement of such systems, several important features of entanglement in these system states are exposed. Furthermore, the effects of both cavity decay and channel noise on these system states are studied and their properties are illustrated.