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.

6 pages, 3 figures, to appear in PRA

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• Quasi-continuous variable quantum computation with collective spins in multi-path interferometers
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• Spin squeezing an ultracold molecule
• Asymmetric Foucault pendulum dynamics with analogies to the Lipkin-Meshkov-Glick quantum phase transitions and other quantum phenomena