Topology in engineered quantum systems

Louis Hirsch Kauffman, Samuel J. Lomonaco

Zina Lippo, Elizabeth Louis Pereira, José Luis Lado +1 more

Topological phases of matter provide a flexible platform to engineer unconventional quantum excitations in quantum materials. Beyond single particle topological matter, in systems with strong quantum many-body correlations, many-body effects can be the driving force for non-trivial topology. Here, we propose a one-dimensional engineered Kondo lattice where the emergence of topological excitations is driven by collective many-body Kondo physics. We first show the existence of topological zero modes in this system by solving the interacting model with tensor networks, and demonstrate their robustness against disorder. To unveil the origin of the topological zero modes, we analyze the associated periodic Anderson model showing that it can be mapped to a topological non-Hermitian model, enabling rationalizing the origin of the topological zero modes. We finally show that the topological invariant of the many-body Kondo lattice can be computed with a correlation matrix pumping method directly with the exact quantum many-body wave function. Our results provide a strategy to engineer topological Kondo insulators, highlighting quantum magnetism as a driving force in engineering topological matter.

Revista, Zen, PHYSICS, 10

The interplay between topology and quantum entanglement holds profound implications for fundamental physics and the advancement of quantum technologies. Topological phases of matter are characterized by robust properties impervious to local perturbations, while entanglement serves as a critical resource for quantum information processing. Floquet engineering, the manipulation of quantum systems through periodic driving, offers a powerful non-equilibrium pathway to realize novel topological states that may not exist in static systems. This paper explores the theoretical and experimental avenues for realizing topological quantum entanglement within Floquet-engineered lattices. We review the foundational concepts of Floquet topological phases and various measures of entanglement, such as entanglement entropy and entanglement spectrum. We then delve into the methodologies for designing such systems across diverse platforms, including ultracold atoms in optical lattices, photonic waveguide arrays, and superconducting circuits. The discussion highlights how Floquet driving can induce robust entanglement in topological edge and bulk states, paving the way for fault-tolerant quantum information storage and processing. We propose specific protocols for generating and detecting topologically-protected entangled states, considering the challenges associated with heating and decoherence in periodically driven systems. Ultimately, this work emphasizes the potential of Floquet engineering as a versatile tool for synthesizing exotic entangled topological states, fostering new frontiers in quantum science and engineering.

Lay Nam Chang, Yigao Liang

Laura Ortiz Martín

Takuto Tsuno, Shintaro Taie, Yosuke Takasu +3 more

Recent advances in quantum technology have highlighted the importance of controlling quantum states, especially in open quantum systems, where the system interacts with the environment. Non-Hermitian quantum mechanics describes these systems. Photonic systems are a key platform for studying non-Hermitian quantum mechanics owing to their ability to engineer gain and loss. Ultracold atomic gases also have been used to study non-Hermitian quantum mechanics; however, unlike photonics, gain control is challenging, limiting exploration to control of loss. In this paper, we report engineering of effective gain through evaporative cooling of judiciously selected initial thermal atoms, leading to Bose-Einstein condensation (BEC) in the excited eigenstates of a synthetic lattice. We achieve BEC formation in a topological edge state of the Su-Schrieffer-Heeger lattice in the synthetic hyperfine lattice, akin to atomic laser oscillations at a topological edge mode, that is, a topological atom laser.