Topological insulator and particle pumping in a one-dimensional shaken optical lattice

Abstract

We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tightbinding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping.

Simulation and measurement of the fractional particle number in one-dimensional optical lattices

“…Finally, we note that a shallow-enough harmonic trap in practical experiments will not affect the particle transport [33,39] and the main results of this paper remain intact. In order to take the effect of the harmonic trap into account, we can add a term H t = V t n (n − L/2) 2ĉ † nĉ n into Hamiltonian (1), where V t is the trap strength and L is the lattice size.…”

“…The shift of the Wannier center encodes the adiabatic particle transport (the variation of polarization) as [33,39,40]…”

“…This is an analog of the adiabatic charge pumping proposed by Thouless [32]; however, the parametric driving in our case does not form a closed cycle but only a half one. The topological pumping in cold atom systems and photonic quasi-crystals has been discussed in the contexts of SSH model [33][34][35] and 1D quasi-periodic Harper model [36][37][38][39][40], where the pumping particle is shown to be quantized one over one period and can be fractional over a fraction of one period [40].…”

Effects of dephasing on quantum adiabatic pumping with nonequilibrium initial states

“…In particular, the sum of the Chern numbers of all the filled bands below the Fermi surface determines the number of pumped charges over one adiabatic cycle in a one-dimensional (1D) periodic lattice. To date various quantum pumps have been proposed to study topological phases and topological phase transitions [3][4][5][6][7][8][9][10][11][12]. Thouless's concept, which can be deemed as a dynamical version of the integer quantum Hall effect, is directly simulated this year in two cold-atom experiments [13,14].…”

Anomalous charge pumping in a one-dimensional optical superlattice

“…While recent studies have focused on the tight-binding limit (the Aubry-Andre model) [4-21], we study the continuous limit of the 1D superlattice, where, because of the weak potential, the single-particle spectra can be calculated perturbatively. Related cold atom proposals on quantized transport [22][23][24][25][26] have focused on the simplest superlattice where one sub-lattice constant is half of the other, and are therefore not in the anomalous regime which interests us.The 1D superlattice can be mapped onto the HarperHofstadter model [2,27]. The topological numbers (Chern numbers) associated with charge pumping can be mapped onto quantized Hall conductances [28,29].…”