Twisting tensor and spin squeezing

Abstract: A unified tensor description of quadratic spin squeezing interactions is proposed, covering the single- and two-axis twisting as special cases of a general scheme. A closed set of equations of motion of the first moments and variances is derived in Gaussian approximation and their solutions are discussed from the prospect of fastest squeezing generation. It turns out that the optimum rate of squeezing generation is governed by the difference between the largest and the smallest eigenvalues of the twisting tensor. A cascaded optical interferometer with Kerr nonlinear media is proposed as one of possible realizations of the general scheme.