Leaky cavities with unwanted noise

A phenomenological approach is developed that allows one to completely describe the effects of unwanted noise, such as the noise associated with absorption and scattering, in high-$Q$ cavities. This noise is modeled by a block of beam splitters and an additional input-output port. The replacement schemes enable us to formulate appropriate quantum Langevin equations and input-output relations. It is demonstrated that unwanted noise renders it possible to combine a cavity input mode and the intracavity mode in a nonmonochromatic output mode. Possible applications to unbalanced and cascaded homodyning of the intracavity mode are discussed and the advantages of the latter method are shown.

Figure 1

One-sided cavity with unwanted internal losses.

Figure 2

Replacement scheme for modeling the unwanted noise in a one-sided cavity. The symmetrical SU(2)-type beam splitters ${\mathrm{BS}}_1$ and ${\mathrm{BS}}_2$ model the unwanted noise in the coupling mirror, and the asymmetrical U(2)-type beam-splitter ${\mathrm{BS}}_3$ simulates some feedback.

Figure 3

An example of a degenerate replacement scheme.

Figure 4

The mode structure of the external field: cavity-associated output mode (CAOM), additional output mode (AOM), and matched input mode (MIM).

Figure 5

The dependences of $ϵ$ and $\xi$ on ${\eta }_{\mathrm{ext}}$ for the reconstruction of the Husimi-Kano $Q$ function, $s=-1$, where $\xi$ is given for three different efficiencies of photocounting ${\eta }_c$.

Figure 6

Reconstruction of the Husimi-Kano $Q$ function for the odd superposition of the coherent states $\mid {\delta }_{-}⟩=\mathcal{N}(\mid \delta ⟩-\mid -\delta ⟩)$, $\delta =0.7$, by unbalanced homodyning: (a) numerical simulation with $1.7\times {10}^5$ sampling events for each point; (b) exact function.

Figure 7

Cascaded homodyne detection of the intracavity mode.