Dynamical dimerization phase in Jaynes–Cummings lattices

Abstract

We report on an emergent dynamical phase of a strongly-correlated light-matter system, which is governed by dimerization processes due to short-range and long-range two-body interactions. The dynamical phase is characterized by the spontaneous symmetry breaking of the translational invariance and appears in an intermediate regime of light-matter interaction between the resonant and dispersive cases. We describe the quench dynamics from an initial state with integer filling factor of a finite-sized array of coupled resonators, each doped with a two-level system, in a closed and open scenario. The closed system dynamics has an effective Hilbert space description that allows us to demonstrate and characterize the emergent dynamical phase via time-averaged quantities, such as fluctuations in the number of polaritons per site and linear entropy. We prove that the dynamical phase is governed by intrinsic two-body interactions and the lattice topological structure. In the open system dynamics, we show evidence about the robustness of dynamical dimerization processes under loss mechanisms. Our findings can be used to determine the light-matter detuning range, where the dimerized phase emerges.transitions from the Mott-insulating to superfluid phase [31]. Here, we introduce an effective Hilbert space in the two-excitations subspace using the criterion of discarding higher energy polaritonic states, which are out-ofresonance over the evolution [27,32]. This description allows us quantitative explanations for time-averaged quantities such as fluctuations in the number of polaritons per site and linear entropy. Besides, the computational cost is substantially diminished by using a reduced effective Hilbert space. As we extend the quench dynamics to complex finite-sized CRAs, we demonstrate the emergence of DDP, which is governed by intrinsic two-body interactions in the JC lattice. In the open system scenario, our numerical results show evidence about the robustness of dynamical dimerization processes under loss mechanisms, so our work may find inspiration for the observation of DDP within state-of-the-art quantum technologies such as superconducting circuits [15,17] and trapped ions [33,34].This paper is organized as follows. In section 2, we introduce the JCH model and the polariton mapping. In section 3, we describe the quench protocol for the closed JCH dimer. Here, we provide analytical expressions for time-averaged order parameters using an effective Hilbert space. In section 4, we highlight the emergence of a DDP as we extend the one-dimensional JC lattice to three and four sites. Here, section 4.1 describes DDP in a closed system, while in section 4.2, we introduce loss mechanisms in the JC lattice and discuss their effects on the dynamical phase transition. Finally, in section 5, we present our concluding remarks.