Quantum walk of ultracold atoms in optical lattices with quadratic gradients

Quantum walk of ultracold atoms in optical lattices has become a powerful platform for various applications, such as in quantum metrology and quantum simulation. A paradigmatic example is the Bloch oscillations in optical lattices with a linear gradient, which has been used to measure the gravity acceleration. In this talk, I will present our numerical results on quantum walk of ultracold atoms in optical lattices with a linear plus quadratic gradient. A modulated Bloch oscillation is observed, of which the frequency spectrum of the local density oscillations present equidistant splitting. Such frequency splitting has a potential use in measure, $e.g.$ the gravity gradients.