Self-organized topological insulator due to cavity-mediated correlated tunneling

Titas Chanda1, Rebecca Kraus2, Giovanna Morigi2, and Jakub Zakrzewski1,3

1Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
2Theoretical Physics, Saarland University, Campus E2.6, D–66123 Saarbrücken, Germany
3Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland

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Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Like the fermionic Peierls instability, the emerging quantum phase is a topological insulator and is found at half fillings. Originating from quantum interference, this topological phase is found in "exact" density-matrix renormalization group calculations and is entirely absent in the mean-field approach. We argue that these dynamics can be realized in existing experimental platforms, such as cavity quantum electrodynamics setups, where the topological features can be revealed in the light emitted by the resonator.

Topological phases are robust states of matter with non-local orders that have potential applications for quantum computation. While they are well understood in the noninteracting limit, it is debated what is the effect of interactions on their onset and stability. Here, we show an instance where topology emerges from the quantum interference between global interactions and quantum fluctuations. The transition to a topological insulator is predicted for a one-dimensional gas of bosons in an optical lattice and is characterized by a spontaneous symmetry breaking. Since this topological insulator originates from quantum interference, mean-field approach fails to capture it while it appears in 'exact' density-matrix renormalization group calculations. We show that these dynamics can be realized in many-body cavity quantum electrodynamics setups, in the regime where photon scattering mediates global interactions, and this allows one to monitor the quantum phase.

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