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arXiv:2305.03409 · Physical Review Letters

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System

Joana Fraxanet, Alexandre Dauphin, Maciej Lewenstein, Luca Barbiero, Daniel González-Cuadra

Published Dec 27, 2023• 16 citations
arXivHTMLPDF

Abstract

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

DOI
10.1103/physrevlett.131.263001

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In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.
We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.
Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.
Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.
Ultracold atom arrays in optical lattices emerge as an excellent playground for the integration of topological photonics and quantum optics. Here, we study high-order topological quantum optics in an ultracold atom metasurface intended to mimic the two-dimensional Su-Schrieffer-Heeger model. We find the existence of long-range interactions beyond nearest-neighbor ones leads to isolated corner states in the band gap, and show a corner atom can be addressed by a laser drive far away from it via these nontrivial states. We demonstrate the Purcell factor can be used as a powerful tool to examine the existence of topological edge and corner states. We predict topological edge states can mediate strong coherent interactions between two remote impurity quantum emitters while suppressing dissipative losses thanks to the higher-order topology, generating robust and long-lived quantum entanglement, without the need for additional photonic structures.
We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.
We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity, the homogeneous gas density breaks a Z_{2} symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization, the resulting Bloch bands can have a nontrivial topological structure characterized by a nonvanishing Zak phase. In the case where the Fermi momentum is close to half of the cavity-mode wave number, a Peierls-like instability here creates a topological insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be nondestructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well-defined frequency window of the cavity spectrum.