Topological pumping assisted by Bloch oscillations

Abstract

Adiabatic quantum pumping in one-dimensional lattices is extended by adding a tilted potential to probe better topologically nontrivial bands. This extension leads to almost perfectly quantized pumping for an arbitrary initial state selected in a band of interest, including Bloch states. In this approach, the time variable offers not only a synthetic dimension as in the case of the Thouless pumping, but it assists also in the uniform sampling of all momenta due to the Bloch oscillations induced by the tilt. The quantized drift of Bloch oscillations is determined by a one-dimensional time integral of the Berry curvature, which is effectively an integer multiple of the topological Chern number in the Thouless pumping. Our study offers a straightforward approach to yield quantized pumping, and it is useful for probing topological phase transitions.

Uncover band topology via quantized drift in two-dimensional Bloch oscillations

“…Indeed, C l,x and C l,y defined by a one dimensional integral can be effectively regarded as a reduced expression for the Chern number C l , which we call Reduced Chern number (RCN) [33].…”

“…The above dilemma may be solved by utilizing Bloch oscillations under external tilted fields, which have been proved to be a powerful method for exacting various geometric features of Bloch bands, including Berry phase [26,27], Berry curvature [15,28,29] and Chern number [30][31][32][33]. In particular, Berry curvature was proposed to be mapped from semiclassical dynamics by using two-dimensional Bloch oscillations (i.e., applying external forces in two dimensions) [28].…”

“…However, to further extract Chern number, this protocol needs to measure the displacement difference under positive and negative forces to cancel the contribution of group velocity from energy dispersion, and then to average the displacement difference under different initial momenta. Recently, we have shown how to directly extract Chern number via a one-dimensional quantized topological pumping assisted by Bloch oscillations that does not require uniform band occupation [33]. This is because Bloch oscillations uniformly sample all the momenta.…”

Asymmetric topological pumping in nonparaxial photonics

“…An alternative topological pumping is to transfer a localized light field from one side to another, realized in optical frequency regime 16 . Up to now, the topological pumping of light was studied in the framework of quantum simulations, where specific optical properties do not play any role 38 , 52 – 55 . In the low-frequency regime, the nonparaxial light propagation cannot be simply mapped to a Schrödinger-type wave equation.…”

Asymmetric topological pumping in nonparaxial photonics

“…An alternative topological pumping is to transfer a localized light field from one side to another, realized in high-frequency regime [12]. Up to now, the topological pumping of light was studied in the framework of quantum simulations, where specific optical properties do not play any role [34,[48][49][50][51].…”