We derive the evolution law of an initial two-mode squeezed vacuum state
\( \text {sech}^{2}\lambda e^{a^{\dag }b^{\dagger }\tanh \lambda }\left \vert 00\right \rangle \left \langle 00\right \vert e^{ab\tanh \lambda }\) (a pure state) passing through an
a-mode diffusion channel described by the master equation
$$\frac{d\rho \left( t\right) }{dt}=-\kappa \left a^{\dagger}a\rho \left( t\right) -a^{\dagger}\rho \left( t\right) a-a\rho \left( t\right) a^{\dagger}+\rho \left( t\right) aa^{\dagger}\right] , $$
since the two-mode squeezed state is simultaneously an entangled state, the final state which emerges from this channel is a two-mode mixed state. Performing partial trace over the
b-mode of
ρ(
t) yields a new chaotic field,
\(\rho _{a}\left (t\right ) =\frac {\text {sech}^{2}\lambda }{1+\kappa t \text {sech}^{2}\lambda }:\exp \left \frac {- \text {sech}^{2}\lambda }{1+\kappa t\text {sech}^{2}\lambda }a^{\dagger }a \right ] :,\) which exhibits higher temperature and more photon numbers, showing the diffusion effect. Besides, measuring
a-mode of
ρ(
t) to find
n photons will result in the collapse of the two-mode system to a new Laguerre polynomial-weighted chaotic state in
b-mode, which also exhibits entanglement.