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arXiv:2106.08709 · Physical Chemistry Chemical Physics

Topology detection in cavity QED

Beatriz Pérez-González, Álvaro Gómez-León, Gloria Platero

Published Jan 1, 2022• 21 citations
arXivHTMLPDF

Abstract

We explore the physics of topological lattice models immersed in c-QED architectures for arbitrary coupling strength with the photon field. We propose the use of the cavity transmission as a topological marker and study its behaviour. For this, we develop an approach combining the input-output formalism with a Mean-Field plus fluctuations description of the setup. We illustrate our results with the specific case of a fermionic Su-Schrieffer-Heeger (SSH) chain coupled to a single-mode cavity. Our findings confirm that the cavity can indeed act as a quantum sensor for topological phases, where the initial state preparation plays a crucial role. Additionally, we discuss the persistence of topological features when the coupling strength increases, in terms of an effective Hamiltonian, and calculate the entanglement entropy. Our approach can be applied to other fermionic systems, opening a route to the characterization of their topological properties in terms of experimental observables.

DOI
10.1039/d2cp01806c

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Quantum entanglement is studied in the context of its use as a probe of quantum phases within fermionic non-interacting quantum wires. In particular, we consider the uniform lattice, as well as the Su-Schreiffer-Heeger (SSH) model, and use the bipartite entropy of entanglement to characterize their quantum phases. In 1D, it has been shown analytically that the von Neumann entropy defined for a subsystem HA⊂HA⊗HB\mathcal{H}_A \subset \mathcal{H}_A\otimes\mathcal{H}_BHA​⊂HA​⊗HB​ takes distinct forms dependent on the whether or not the state is thermodynamically gapped. It is also known that entanglement can be used to identify topological phases of a quantum system, such as the symmetry protected phase found in the SSH model. These results are confirmed numerically, and some common techniques for the calculation of bipartite entanglement are compared according to their aptitude for simulating larger and more complicated systems.
Witnessing and tracking topological phase transitions induced by interactions with the environment is a crucial challenge. Among the various experimental approaches to detect topological properties, the Mean Chiral Displacement (MCD) has emerged as a powerful bulk probe in one-dimensional chiral systems, allowing the extraction of the topological invariant from single-particle dynamics. Here we study the dynamics of a single particle in a one-dimensional Su-Schrieffer-Heeger chain coupled to multiple cavity modes via inter-cell hopping terms, focusing on the out-of-equilibrium behavior of the MCD. We show that, whenever the frequency is larger than the static hopping amplitudes, the coupling induces a discontinuous jump in the MCD, already at small times, signaling that such a coupling also leaves a signature in the survival edge probability when the dynamics are initialized at one of the two edges. For frequencies comparable to the static hopping amplitudes, topological order competes with dissipative effects, which makes the MCD behave smoothly, retaining information about the driven-dissipative topology.
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Entanglement entropy (EE) provides a powerful probe of quantum phases, yet its role in identifying topological phase transitions in disordered systems remains underexplored. We introduce an exact EE-based framework that captures topological phase transitions even in the presence of disorder. Specifically, for a class of Su-Schrieffer-Heeger (SSH) model variants, we show that the difference in EE between half-filled and near-half-filled ground states,ΔSA, vanishes in the topological phase but remains finite in the trivial phase, a direct consequence of edge-state localization. This behavior persists even in the presence of quasiperiodic or binary disorder. By analyzing domain-wall configurations in the SSH chain, we further show how subsystem tuning allows one to distinguish genuine topological zero-energy eigenstates from trivial localized states. Exact phase boundaries, derived from Lyapunov exponents via transfer matrices, agree closely with numerical results fromΔSAand the topological invariant𝓠, with instances whereΔSAoutperforms𝓠. Our results highlight EE as a robust diagnostic tool and a potential bridge between quantum information and condensed matter approaches to topological matter.