Topological order in interacting one-dimensional Bose Systems

De Gottardi, Wade Wells

Michael Fleischhauer, Fabian Grusdt, Michael Höning

Maciej Marciniak, Grigori E. Astrakharchik, Krzysztof Pawłowski +1 more

We investigate the coherence and correlations of many-body states appearing in topological pumping in a one-dimensional Bose gas. By analyzing the system at zero and infinite interaction strengths, we reveal a rescaling of momentum distributions accompanied by a self-similar behavior in first- and second-order correlation functions. In excited states of non-interacting bosons, the momentum distribution shows a comb-like structure similar to that of non-interacting fermions but at a higher density. This is mirrored by Friedel oscillations in the one-body density matrix. At the same time, the density-density correlations still exhibit the bosonic enhancement. Our work illustrates how topological pumping induces a nontrivial mapping between bosonic and fermionic correlations.

Revista, Zen, PHYSICS, 10

The exploration of novel quantum states of matter remains a central theme in condensed matter physics. Among these, topological order stands out for its robust properties against local perturbations and its potential applications in quantum information processing. While considerable progress has been made in understanding topological order in purely bosonic or fermionic systems, the interplay between different quantum statistics in interacting Bose-Fermi mixtures offers a rich platform for discovering new forms of topological order. This paper investigates the theoretical conditions and characteristic signatures for the emergence of topological order in these hybrid quantum systems. We propose that tunable interspecies interactions, combined with appropriate lattice geometries or synthetic gauge fields, can drive Bose-Fermi mixtures into exotic phases exhibiting non-trivial topological properties. Specifically, we explore scenarios where bosonic particles mediate effective interactions between fermions, or where bosonic condensation leads to a modification of the fermionic band structure, thereby inducing topological phases. Our analysis focuses on identifying key experimental observables, such as fractionalized excitations, robust edge modes, and entanglement properties, which can serve as hallmarks of emergent topological order. The theoretical framework incorporates mean-field approaches, variational methods, and numerical simulations to characterize the phase diagram of interacting Bose-Fermi mixtures, providing a pathway for experimental realization and verification of these fascinating quantum states.

Maciej Marciniak, Grigori E. Astrakharchik, Krzysztof Pawłowski +1 more

We investigate the coherence and correlations of many-body states appearing in topological pumping in a one-dimensional Bose gas. By analyzing the system at zero and infinite interaction strengths, we reveal a rescaling of momentum distributions accompanied by a self-similar behavior in first- and second-order correlation functions. In the excited states of noninteracting bosons, the momentum distribution shows a comblike structure similar to that of noninteracting fermions but at a higher density. This is mirrored by Friedel oscillations in the one-body density matrix. At the same time, the density-density correlations still exhibit a bosonic enhancement. Our work illustrates how topological pumping induces a nontrivial mapping between bosonic and fermionic correlations.

Titus Neupert, Huan He, Curt W. von Keyserlingk +2 more