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Based on the recent twisting-tensor approach [T. Opatrny, ArXiv:1408.3265(2014)], a specific scenario for fast and deep spin squeezing is proposed.Initially the state is subjected to one-axis twisting under optimumorientation, enabling the maximum squeezing rate allowed by the systemnonlinearity. Later on, when for highly squeezed states the one-axis twistingdeforms the uncertainty ellipse and deteriorates the squeezing properties, theprocess is switched to an effective two-axis counter-twisting by a sequence of$\pi/2$ pulses. The squeezing rate then slows to 2/3 of the maximum value, butthe process can continue for longer to achieve a very high degree of squeezing.

Dynamical spin squeezing: combining fast one-axis twisting and deep two-axis counter-twisting