Impact of Boundary Conditions on the Double-Kicked Quantum Rotor

TL;DR

This paper investigates how boundary conditions influence topological properties in the on-resonance Spin-1/2 Double Kicked Rotor, revealing edge state formation and boundary-sensitive bulk responses relevant for experimental realizations.

Contribution

It provides a detailed analysis of boundary effects on topological phases in a driven quantum system, highlighting the role of edge states and the Mean Chiral Displacement as a bulk probe.

Findings

Boundary conditions significantly affect the MCD response.

Open boundaries lead to localized edge states in momentum space.

Bulk-edge correspondence remains observable despite boundary effects.

Abstract

We study the on-resonance Spin-1/2 Double Kicked Rotor, a periodically driven quantum system that hosts topological phases. Motivated by experimental constraints, we analyze the effects of open and periodic boundary conditions in contrast to the idealized case of infinite momentum space. As a bulk probe for topological invariants, we focus on the Mean Chiral Displacement (MCD) and show that it exhibits a pronounced sensitivity to boundary conditions, which can be traced to the dynamics in momentum space. Under open boundaries, states that would otherwise extend freely become localized at the edges of the finite momentum space, forming quasienergy edge states. While the bulk response measured by the MCD is strongly affected once the evolving wave packet reaches the boundaries, the persistence of these edge states still reflects the bulk-edge correspondence and provides reliable signatures of topological transitions.