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arXiv:2107.12236 · Communications Physics

Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity

Christian Eckhardt, Giacomo Passetti, Moustafa Othman, Christoph Karrasch, Fabio Cavaliere, Michael A. Sentef, Dante Marvin Kennes

Published May 19, 2022• 52 citations

Abstract

Abstract Recent experimental advances enable the manipulation of quantum matter by exploiting the quantum nature of light. However, paradigmatic exactly solvable models, such as the Dicke, Rabi or Jaynes-Cummings models for quantum-optical systems, are scarce in the corresponding solid-state, quantum materials context. Focusing on the long-wavelength limit for the light, here, we provide such an exactly solvable model given by a tight-binding chain coupled to a single cavity mode via a quantized version of the Peierls substitution. We show that perturbative expansions in the light-matter coupling have to be taken with care and can easily lead to a false superradiant phase. Furthermore, we provide an analytical expression for the groundstate in the thermodynamic limit, in which the cavity photons are squeezed by the light-matter coupling. In addition, we derive analytical expressions for the electronic single-particle spectral function and optical conductivity. We unveil quantum Floquet engineering signatures in these dynamical response functions, such as analogs to dynamical localization and replica side bands, complementing paradigmatic classical Floquet engineering results. Strikingly, the Drude weight in the optical conductivity of the electrons is partially suppressed by the presence of a single cavity mode through an induced electron-electron interaction.

DOI: 10.1038/s42005-022-00880-9

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We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst ^{++} + + [Phys. Rev. A 108, 013323 (2023)]

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The ultrastrong coupling regime has emerged as a fascinating and distinctive phenomenon in cavity-QED and light-matter interactions, where the occupation of virtual excitations (e.g., photons) is possible in vacuum, which is a consequence of counter-rotating wave effects and breaking U(1) symmetry. However, an ongoing challenge is how to convert these virtual photons into real photons. We will first discuss how to “Floquet engineer” the quantum Rabi model for a two-level system coupled to a quantized cavity mode, under periodic modulation of the cavity-dipole coupling rate, leading to rich Floquet states. Exploiting the quantum vacuum, in the ultrastrong coupling regime, we show how purely mechanical driving can produce real photons. These periodic driving schemes are promising for the coherent manipulation of hybrid quantum systems and quantum vacuum effects, with applications for quantum state engineering and the study of nonequilibrium quantum phenomena.