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arXiv:1402.6039 · International Journal of Theoretical Physics

Quantum Phase Transition of Polaritonic Excitations in a Multi-Excitation Coupled Array

Li-Tuo Shen, Rongxin Chen, Huai‐Zhi Wu, Zhen‐Biao Yang, E. K. Twyeffort Irish, Shi‐Biao Zheng

Published Sep 23, 2017• 0 citations
arXivHTMLPDF
DOI
10.1007/s10773-017-3532-2

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We propose a physical system where photons could exhibit strongly correlated effects. We demonstrate how a Mott-insulator phase of atom-photon excitations (polaritons) can arise in an array of individually addressable coupled electromagnetic cavities when each of these cavities is coupled resonantly to a single two-level system (atom, quantum dot, or Cooper pair). This Mott phase is characterized by the same integral number of net polaritonic excitations with photon blockade providing the required repulsion between the excitations in each site. Detuning the atomic and photonic frequencies suppresses this effect and induces a transition to a photonic superfluid. Finally, on resonance the system can straightforwardly simulate the dynamics of many-body spin systems.
We discuss the Jaynes–Cummings–Hubbard model describing the superfluid–Mott insulator transition of polaritons (i.e., dressed photon–qubit states) in coupled qubit–cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave-boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory for a generalized multi-mode Dicke model. We show that a remarkable relation between the two theories exists in the limit of large photon bandwidth and large negative detuning, i.e., when the nature of polariton quasiparticles becomes qubit-like. In this regime, the weak-coupling theory predicts the existence of a single Mott lobe with a change of the universality class of the phase transition at the tip of the lobe, in perfect agreement with the SBT. Moreover, the spectra of low energy excitations, i.e., the sound velocity of the Goldstone mode and the gap of the amplitude mode match exactly as calculated from both theories.