Spin squeezing in internal bosonic Josephson junctions via enhanced shortcuts to adiabaticity

We investigate a time-efficient and robust preparation of spin-squeezed states - a class of states of interest for quantum enhanced metrology - in internal bosonic Josephson junctions with a time-dependent nonlinear coupling strength between atoms in two different hyperfine states. We treat this state-preparation problem, which had previously been addressed using shortcuts to adiabaticity (STA), using the recently proposed analytical modification of this class of quantum control protocols that has become known as the enhanced STA (eSTA) method. We characterize the state-preparation process by evaluating the time dependence of the coherent spin-squeezing and number-squeezing parameters and the target-state fidelity. We show that the state-preparation times obtained using the eSTA method compare favorably to those found in previously proposed approaches. We also demonstrate that the increased robustness of the eSTA approach - compared to its STA counterpart - leads to additional advantages for potential experimental realizations of strongly spin-squeezed states in internal bosonic Josephson junctions.