Fig. 4: Dynamic synthesis of TAT squeezing.
From: Dynamic synthesis of Heisenberg-limited spin squeezing
a An illustration of the pulse sequence for the synthesis of TAT squeezing. Each period Tc = 8τ, twice as long as aforementioned OAT pulse scheme, contains four π/2 rotation pulses (orange rectangles) and four − π/2 rotation pulses (green rectangles) imposed on subsystem J, and an additional pair of ∓ π/2 pulses (blue and red rectangles) imposed on subsystem S. b Evolution of the squeezing parameters ξ2 for the TAT pulse scheme (red solid curve: criterion of Kitagawa and Ueda1; green solid curve: criterion of Wineland2,3) and for the effective TAT Hamiltonian (12) (black and blue solid curves for the two parameters), compared with the OAT dynamics (blue dashed and orange dot-dashed curves) governed by Hamiltonian (5). c and d The optimal spin squeezing parameter \({\xi }_{\min }^{2}\) for Kitagawa and Ueda criterion and the optimal squeezing time \({t}_{\min }\) as functions of the particle number Ns for the TAT pulse scheme (red solid balls), compared with the effective TAT results (blue solid curves). The black dashed line in c corresponds to \({\xi }_{\min }^{2}=1.8/{N}_{{{{\rm{s}}}}}\). The parameters are given in each subgraph.
