Higher-order squeezing for even- and odd-displaced squeezed states

We study even- and odd-displaced squeezed states, which were proposed by us as 1/Ne(D(z)+D(-z))S(r) mod 0) and 1/N0(D(z)-D(-z))S(r) mod 0). We find: (i) when z is real, the 2Nth moments in both states are larger than in the ordinary squeezed state; (ii) for the same z= mod z mod , the two states can not exhibit stronger squeezing than the squeezed state in the same order; (iii) under the condition mod z mod e-r square root 2>>1, the even (odd)-displaced squeezed state can respectively exhibit stronger (4k-2) (4k)-order (k=1,2,3,...) squeezing than the squeezed state.