Squeezing components in linear quantum feedback networks

The aim of this article is to extend linear quantum dynamical network theory to include static Bogoliubov components (such as squeezers). Within this integrated quantum network theory, we provide general methods for cascade or series connections, as well as feedback interconnections using linear fractional transformations. In addition, we define input-output maps and transfer functions for representing components and describing convergence. We also discuss the underlying group structure in this theory arising from series interconnection. Several examples illustrate the theory.

Figure 1

LQFN consisting of a beam splitter, squeezer, and cavity. The time delay around the optical loop is $\tau$.

Figure 2

General form of an LQFN, with the time delay due to the spatial extent of the feedback connection represented by ${\Theta }_{\tau }$ (see text).

Figure 3

LQFN of Fig. 1 redrawn in standard from Fig. 2.

Figure 4

Beam splitter feedback network with time delay.