Equivalence of second-order sub-Poissonian statistics and fourth-order squeezing for intense light

We study the simultaneous occurrence of second-order sub-Poissonian photon statistics and fourth-order squeezing for the operator X-theta = X-1 coS theta + X-2 sin theta, in the displaced state vertical bar psi'> = D(alpha)vertical bar psi >, where the Hermitian operators X-1,X-2 are defined by X-1 + iX(2) = a, the annihilation operator, D (alpha) = exp(alpha a(+) - alpha*a) is the displacement operator, alpha = vertical bar a vertical bar e(i theta) and vertical bar psi > is the state of the weak optical field. We show that the two phenomena occur simultaneously when the amplitude vertical bar alpha vertical bar of the displacement is very large as compared to the amplitude of the weak optical field. We also propose a balanced homodyne method for detection of fourth-order squeezed light in the same fashion as that for normal squeezing.