An Interesting New Revelation on Simultaneous Higher Order Squeezing in an Electro-Magnetic Field

We find that the superposition of coherent states Ψscs that generates |4m〉 Fock states can squeeze the electromagnetic field conjugate at both fourth order and sixth order 〈Ψscs|(∆Ei) |Ψscs〉 < 〈α|(∆Ei) |α〉coh (i = 1 and 2)(N = 2, 3). A very interesting point which the present calculation reveals is that the minimum squeezing in both the cases (i.e. N = 2, 3) occurs at |α| = 0.67. A further interesting point is that the smallest eigenvalue of E i obtained by using a superposition of |4m〉 Fock states remains nearly the same as the minimum squeezing value: 〈(∆Ei) 〉minimumsqueezing 〈(Ei) 〉smallesteigenvalue (i = 1 and 2; N = 2, 3).