Edge state preparation in one dimensional lattice by quantum Lyapunov control

Abstract

Quantum Lyapunov control uses a feedback control methodology to determine control fields which are applied to control quantum systems in an open-loop way. In this work, we adopt two Lyapunov control schemes to prepare an edge state for a fermionic chain consisted of cold atoms loaded in an optical lattice. Such a chain can be described by the Harper model. Corresponding to the two schemes, state distance and state error Lyapunov functions are considered. The results show that both the schemes are effective to prepare the edge state within a wide range of parameters. We found that the edge state can be prepared with high fidelity even \textbf{if} there are moderate fluctuations in on-site or hopping potentials. Both control schemes can be extended to similar chains (3$m+d$, $d$=2) of different lengths. Since regular amplitude control field is easier to apply in practice, amplitude-modulated control fields are used to replace the unmodulated one to prepare the edge state. Such control approaches provide tools to explore edge states for one dimensional topological materials.

References in corpus (26)

• Topological Insulators
• Topological insulators and superconductors
• Anderson localization of a non-interacting Bose-Einstein condensate
• Perfect state transfer in quantum spin networks
• Topological States and Adiabatic Pumping in Quasicrystals
• Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
• Superfluid-insulator transition in a periodically driven optical lattice
• One-dimensional Topological Edge States of Bismuth Bilayers
• Edge states and topological phases in one-dimensional optical superlattices
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• In situ observation of strongly interacting ferromagnetic domains in a shaken optical lattice
• Exponential localization in one-dimensional quasiperiodic optical lattices
• Phase coherence of an atomic Mott insulator
• Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
• Manipulating Topological Edge Spins in One-Dimensional Optical Lattice
• Interference pattern and visibility of a Mott insulator
• Optimal Lyapunov-based quantum control for quantum systems
• Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control
• Period-doubling Instability of Bose-Einstein Condensates Induced in Periodically Translated Optical Lattices
• Topological Bose-Mott Insulators in a One-Dimensional Optical Superlattice
• Driving Quantum System into Decoherence-free Subspaces by Lyapunov Control
• Effect of interactions on the localization of a Bose-Einstein condensate in a quasi-periodic lattice
• The edge engineering of topological Bi(111) bilayer
• Exploiting boundary states of imperfect spin chains for high-fidelity state transfer
• Realization of quantum gates by Lyapunov control
• Entanglement of localized states