Manipulating Topological Edge Spins in a One-Dimensional Optical Lattice

Abstract

We propose to observe and manipulate topological edge spins in a one-dimensional optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In the free-fermion case the SPT phase is classified by a Z invariant which reduces to Z(4) with interactions. The zero edge modes of the SPT phase are spin polarized, with left and right edge spins polarized to opposite directions and forming a topological spin qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in an optical lattice. The manipulation of TSQs has potential applications to quantum computation.

Topological superradiant state in Fermi gases with cavity induced spin–orbit coupling

“…(21) can be simplified, as the summation over band index n contains only the lowest band with n = 1. After employing the gauge transformationψ (1) j↓ → (−1) jψ(1) j↓ , we can derive a concise form in momentum space [22]: s . Note that we have used the winding number as the topological invariant; it is defined as…”

“…Of particular interest is the possibility of preparing and probing topological states in cold atomic gases under synthetic SOC. Although solidstate materials with topologically nontrivial properties have been extensively studied in recent years [15][16][17], ultracold atomic gases may serve as ideal platforms for quantum simulation of exotic topological matter [18][19][20][21][22][23]. For instance, the highly tunable parameters of cold atoms should offer unprecedented control over interatomic interactions in a topological material and thus would provide the intriguing opportunity of simulating topological * Electronic address: phyliuxiongjun@gmail.com † Electronic address: wzhangl@ruc.edu.cn ‡ Electronic address: wyiz@ustc.edu.cn states in a strongly interacting system.…”

Edge state preparation in a one-dimensional lattice by quantum Lyapunov control

“…Similarly, for topological Bi(111) bilayer nanoribbon, through first-principle simulations, the desirable edge state engineering can be realized by chemical decoration [9]. Besides, in one dimensional lattice systems, by coupling the atomic spin states to a laserinduced periodic Zeeman field, a novel scheme is proposed to manipulate the edge state [10]. This attracts both theoretical and experimental interests.…”

“…Usually the topological character is indicated by the emergence of edge states for a bulk system. Recently, there have been a great deal of work to explore topological systems related to such states [2][3][4][5][6][7][8][9][10]. In two dimensional systems such as the Bi 2 Te 3 nanoribbon, manipulation of edge state by modulating a gate voltage has been reported in experiments [8].…”

Spin measurements and control of cold atoms using spin-orbit fields

“…[10][11][12]), topological states (e.g. [13]), and nontrivial spin dynamics [14][15][16]. Flexibility in designing the fields suggests new applications of cold atoms in dynamical systems, for example, developing of new quantum measurement techniques.…”