Twist-and-turn dynamics of spin squeezing in bosonic Josephson junctions: Enhanced shortcuts-to-adiabaticity approach

The twist-and-turn dynamics of spin squeezing results from the interplay of the one-axis-twisting (nonlinear in the collective-spin operators) and the transverse-field turning (linear) term in the underlying Lipkin-Meshkov-Glick-type Hamiltonian, both with constant (time-independent) prefactors. Using shortcuts to adiabaticity (STA) and the recently developed enhanced version thereof (eSTA), we demonstrate here that dynamics of this type can be utilized for a fast and robust preparation of spin-squeezed states in internal bosonic Josephson junctions, i.e., condensates of cold bosonic atoms in two different internal (hyperfine) states (single-boson modes) coupled through Rabi rotations. Assuming that the initial state of this system is its ground state for a given initial value of the (time-dependent) linear coupling strength and that the nonlinear coupling strength remains constant, we set out to determine the time dependence of the linear (Rabi) coupling strength that allows for the generation of spin-squeezed states using the STA- and eSTA-based approaches. We then characterize the modified twist-and-turn dynamics of this system by evaluating the coherent spin-squeezing and number-squeezing parameters, as well as the fidelity of the target spin-squeezed states. In this way, we show that the eSTA approach allows for a particularly robust realization of strongly spin-squeezed states in this system, consistently outperforming its adiabatic and STA-based counterparts, even for systems with several hundred particles. Our method could also be employed for the generation of metrologically-useful non-Gaussian states.