Spin-Nematic Squeezed State Sensitivity to Spin Rotation in Atomic Systems

The interaction described by Equation (/ref{Ham_approx}) generates a spin-nematic squeezed state, as shown in Figure /ref{fig:schematic}(a). This state exhibits similarities to the two-mode squeezed vacuum state, widely discussed in the context of the SU(1,1) interferometer [gross2011atomic, hamley2012spin]. By introducing a $/pi$ phase shift in the |F=1, m_F= 0⟩ component, we can easily reverse the sign of Equation (/ref{Ham_approx}), facilitating time-reversed evolution [linnemann2016quantum]. This work demonstrates that the spin-nematic squeezed state, an atomic counterpart to the two-mode squeezed vacuum state, is sensitive to spin rotation transformations characterized by two phases, $/varphi_1$ and $/varphi_2$, represented by the form $e^{-i(/varphi_1L_x+/varphi_2 L_y)}$.