Helical Floquet Channels in 1D Lattices

Abstract

We show how dispersionless channels exhibiting perfect spin-momentum locking can arise in a 1D lattice model. While such spectra are forbidden by fermion doubling in static 1D systems, here we demonstrate their appearance in the stroboscopic dynamics of a periodically driven system. Remarkably, this phenomenon does not rely on any adiabatic assumptions, in contrast to the well known Thouless pump and related models of adiabatic spin pumps. The proposed setup is shown to be experimentally feasible with state of the art techniques used to control ultracold alkaline earth atoms in optical lattices.Introduction. Exploring the rich phenomenology of spin-orbit coupling is an active field of research in numerous branches of quantum physics [1][2][3]. The discovery of helical edge-states [4][5][6] has opened the route towards perfect spin-momentum locking, characterized by a oneto-one correspondence between the propagation direction of particles and their spin. Such exotic states have only been realized at the surface of 2D topological insulators [4,[7][8][9][10]. Without the 2D bulk, their occurrence is forbidden in 1D lattice systems [10], as the periodicity of band structures in the first Brillouin Zone (BZ) imposes fundamental constraints -referred to as fermion doubling [11] [cf. Fig. 1(a)]. Harnessing the unique properties of periodically driven quantum systems [12-17], here we show how these limitations can be circumvented: we find perfect spin-momentum locking in the stroboscopic dynamics of a periodically driven 1D lattice model. While conventional helical edge states require a time reversal symmetric topological 2D bulk [19], the spin-momentum locking in our 1D setting stems from topological properties in combined time-momentum (Floquet) space [see Fig. 1(d)], and relies on a spin-rotation symmetry of the stroboscopic dynamics. Our approach goes conceptually beyond adiabatically projected models such as the Thouless pump [20,21], in that we consider the full quasienergy spectrum without involving adiabatic projections.In Floquet systems, the quasi-energies are only defined modulo the driving frequency Ω, allowing for spectra that are only periodic in the BZ up to integer multiples of Ω. However, even in driven systems, unidirectional motion in 1D systems cannot be achieved without adiabatic assumptions, due to fundamental topological constraints [18]. The central result of this work is that the Floquet Bloch Hamiltonian ( = 1)

Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate

“…In a perfect helical Floquet channel, pseudo-spins with spin-down (spinup) polarization along the z axis should propagate to the left (right), demonstrating a "spin-momentum locking" behavior discussed in Ref. [65]. Such a behavior is clearly observed in Fig.…”

“…The topological phase transition is then confirmed experimentally through second-statistical-moment measurements. We further demonstrate helical Floquet channels in the one-dimensional momentum lattice [65,66], where atoms on different sublattice sites are locked into a leftward (rightward) unidirectional motion along the momentum lattice. These dispersionless channels originate from the winding of Floquet quasi-energy bands, and are protected by a pair of dynamic Chern numbers in parameter space.…”

Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems

“…The transformed HamiltonianŴ (ωt) no longer contains the time-periodic termV (r) f (ωt). The periodic driving is now represented by the operator A (r, ωt) =Â (r, ωt + 2π) featured in the transformed Hamiltonian (7). This leads to the SOC to be studied in the next Subsection.…”

“…The position-dependence ofR (r, ωt) yields the spin-dependent momentum shift A (r, ωt) in Eq. (7), so the SOC appears directly from the unitary transformation.…”

“…The periodic driving enriches topological [1][2][3][4][5][6][7][8][9][10][11] and many body [8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] properties of physical systems. This can be used to generate the artificial gauge fields for ultracold atoms [30][31][32][33][34][35][36][37][38][39][40][41][42] and photonic systems [43][44][45][46][47][48], as well as to alter the topological properties of condensed matter systems [2,…”