Topological quantum matter in synthetic dimensions

Abstract

In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of 'synthetic dimensions' has recently emerged as a powerful way to emulate phenomena such as topological phases of matter, which are now of great interest across many areas of physics. The main idea of a synthetic dimension is to couple together suitable degrees of freedom, such as a set of internal atomic states, in order to mimic the motion of a particle along an extra spatial dimension. This approach provides a way to engineer lattice Hamiltonians and enables the realisation of higher-dimensional topological models in platforms with lower dimensionality. We give an overview of the recent progress in studying topological matter in synthetic dimensions. After reviewing proposals and realizations in various setups, we discuss future prospects in many-body physics, applications, and topological effects in three or more spatial dimensions.

Coherent spin mixing via spin-orbit coupling in Bose gases

“…Therefore, we can construct the Casimir elementL 2 = L 2 z +L 2 y +L 2 z , and re-express Hamiltonian (35) aŝ…”

“…Moreover, it is worth mentioning that while the total "angular momentum" l is not preserved byĤ 2 , the magnetization m z is. A trademark of the Hamiltonian derived in this work is the emergence of effective spin-changing collisions that couple the edge well states with the central one, described by the effective HamiltonianĤ 1 (35). These processes prevent the Fock basis states of the lowest band modes to be an eigenstate of the system, and can give rise to nontrivial dynamics when the interactions dominate over the noninteracting trapping-mediated tunneling dynamics.…”

“…This is the case, for instance, in optical lattices where, by downplaying the kinetic terms and enhancing the gas density without further losses, many-body physics at strong coupling may become experimentally accessible [25]. The experimental observation of integer quantum Hall (Hofstadter model on 2D square lattice [26,27], and on narrow strips [28][29][30][31][32] in real or synthetic lattices [33][34][35]) and spin-Hall (Haldane model in honeycomb-like lattices [36,37]) effect for noninteracting gases with synthetic gauge fields, the lattice equivalent of SOC, paves the way to the experimental realization of fractional quantum Hall effect and quantum magnetism with interacting gases. Remarkably, beyond-mean-field effects can dominate the dynamics in weakly-interacting dilute gases when mean-field effects largely cancel and lead to the stabilization of quantum droplets [38], as experimentally demonstrated for contact [39][40][41] and dipolar interactions [42][43][44].…”

Tunable super- and subradiant boundary states in one-dimensional atomic arrays

“…In this paper, we investigate 1D atomic arrays subjected to a spatially periodic magnetic field. The spatial phase of the magnetic field is an external parameter, and can be used to map one momentum dimension in a 2D system [31,32]. Therefore, 1D atomic arrays with the synthetic momentum dimension manifests important topological features associated with 2D systems.…”

“…Therefore, 1D atomic arrays with the synthetic momentum dimension manifests important topological features associated with 2D systems. Systems with synthetic dimensions simplify experimental design and enable capabilities of manipulating atomic quantum states or photons along the synthetic dimension [31][32][33][34][35][36]. By changing the periodicity of the magnetic field, we show that the 1D atomic arrays exhibit a butterfly-like spectrum, which has not been discussed in the 2D atomic arrays under a uniform magnetic field [13,28].…”