Mixed Squeezing for a Pair of Two-Mode Squeezed States

Based on the neat <η| representation of two-mode squeezing operator which entangles signal-mode and idle-mode, where <η| is the common eigenvector of two particles' relative position and the total momentum exhibiting a maximal entanglement between the two modes, we study some kind of squeezing mixing 1-3 modes and 2-4 modes for a pair of two-mode (1-2 modes and 3-4 modes) squeezed states. The explicit form of such mixed squeezed states is derived and the new entanglement is analysed.