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Modification of the initial state a the mapping of quantum state in parametric amplifier.

Transformaiton of the rectangular mesh at the mapping of the phase space. At the input of the amplifier, there is the coherent sate with parameters $\alpha=\alpha_1+{\rm i}\alpha_2$. During the evolution with Hamiltonian $\frac{-\rm i}{2}\Big( a^2 b^\dagger - (a^\dagger)^2 b \Big)$. The state of pump mode with filed $b$ is also coherent with parameter $\beta\!=\!2$. Furation of evolution: $t\!=\!0$, $t\!=\!0.3$, $t\!=\!0.5$ (at the bottom).

Source: Figure 1 from the article D. Kouznetsov, D. Rohrlich. Quantum noise in the mapping of phase space. 40R. Russian version: Optika y Spectroscopia, 1997, v.82, N6, p.990-995 40E. English version: Optics and Spectroscopy, July 1997, v.83, N6, p.909-913. Reprint: http://www.ils.uec.ac.jp/~dima/PAPERS/rohrlich.pdf (English version) Reprint: http://www.ils.uec.ac.jp/~dima/PAPERS/mappingr1.pdf (Russian version)

Copyleft 1997 by Dmitrii Kouznetsov and Daniel Rohrlich.

Quantum noise in the mapping of phase space