Quantum sensing of rotation velocity based on Bose-Hubbard model

Abstract: This work theoretically study the Bose-Hubbard model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge of the Bose-Hubbard model not only depends on the particle numbers and the ring radius, but also depends on the rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose-Hubbard model. At the exact phase transition edge where this sensing method is most sensitive, the resolution depends on the rotation velocity, the particle numbers and the ring radius, while is independent of the parameters in the Bose-Hubbard model such as the hopping constant and the on-site interaction.