Fast-forward ground-state preparation in finite two-site Bose–Hubbard systems

Abstract

Abstract We present a method to accelerate the adiabatic quantum dynamics of two-site Bose–Hubbard systems by using the fast-forward method proposed by Masuda and Nakamura. The accelerated scheme is constructed by adding a driving Hamiltonian to the original Hamiltonian and introducing a large time-scaling factor together with an adiabatic parameter, enabling adiabatic quantum dynamics within a shortened timescale. We apply this protocol to a finite-time ground-state preparation in the two-site Bose–Hubbard model. For two bosons, the dynamics reduces to a two-level problem in the symmetric Fock subspace, which yields an analytic current-like auxiliary coupling that suppresses diabatic transitions during an initial ground-state configuration to a desired final ground-state configuration. For three bosons, the Hamiltonian separates into symmetric and antisymmetric parity blocks; the symmetric block governs ground-state preparation from the normalized state 1 2 | 2 , 1 ⟩ + 1 2 | 1 , 2 ⟩ ), while the antisymmetric correction is relevant only for transitionless driving in the full-parity sector. For four bosons, the exchange-symmetric sector is three dimensional. This three-level structure constitutes the principal multilevel extension presented in this work. Numerical solutions of the time-dependent Schrödinger equation show that the fast-forward Hamiltonian maintains high instantaneous ground-state fidelity and reproduces the target population distribution within the prescribed finite protocol time, whereas evolution under the bare Hamiltonian produces appreciable diabatic excitations. The protocol provides an analytically tractable example of fast-forward control in an interacting bosonic dimer.