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

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 optimum orientation, enabling the maximum squeezing rate allowed by the system nonlinearity. Later on, when for highly squeezed states the one-axis twisting deforms the uncertainty ellipse and deteriorates the squeezing properties, the process 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, but the process can continue for longer to achieve a very high degree of squeezing.