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arXiv:1802.07755 · Physical review. B./Physical review. B

Emergent light crystal from frustration and pump engineering

Matteo Biondi, G. Blatter, Sebastian Schmidt

Published Sep 17, 2018• 8 citations
arXivHTMLPDF

Abstract

We demonstrate how pump engineering drives the emergence of frustration-induced quasi-long-range order in a low-dimensional photonic cavity array. We consider a Lieb chain of nonlinear cavities as described by the Bose-Hubbard model and featuring a photonic flatband in the single-particle spectrum. Incoherent pumping of the Lieb lattice leads to a photonic density wave which manifests an algebraic decay of correlations with twice the period of the lattice unit cell. This work opens up other directions for the emergence of strongly correlated phases in quantum optical frustrated systems through pump design.

DOI
10.1103/physrevb.98.104204

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We demonstrate how pump engineering drives the emergence of frustration-induced quasi-long-range order in a low-dimensional photonic cavity array. We consider a Lieb chain of nonlinear cavities as described by the Bose-Hubbard model and featuring a photonic flatband in the single-particle spectrum. Incoherent pumping of the Lieb lattice leads to a photonic density wave which manifests an algebraic decay of correlations with twice the period of the lattice unit cell. This work opens up other directions for the emergence of strongly correlated phases in quantum optical frustrated systems through pump design.
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The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of density wave ordered superradiant photonic fluid phase can be realized and a first order transition between two different density wave ordered states is found. This proposal shows us a new way to produce coherent "solid" phase without the help of long range interactions.
Understanding how frustration and symmetry breaking shape collective behavior is a central problem in quantum many-body systems. In this work, we investigate this problem in large one- and two-dimensional arrays of coupled Dicke models on a periodic lattice, where strong light-matter coupling gives rise to a superradiant phase and competition between neighboring order parameters induces spontaneous translational symmetry breaking. Such Dicke lattice models constitute a fundamentally new class of quantum many-body systems, as they simultaneously realize the thermodynamic limit associated with the lattice size and an intrinsic thermodynamic limit arising from collective on-site interactions with quantum emitters. We show that frustration drives photonic density-wave ordering, and that the resulting broken periodicity can be predicted from the excitation spectrum of the symmetric phase, without requiring computationally prohibitive thermodynamic energy minimization. Furthermore, we demonstrate that an emergent Nambu-Goldstone mode arises near the critical point in a one-dimensional chain despite the presence of only discrete symmetry, and uncover the mechanism that enables this otherwise forbidden gapless excitation. We also find quasi-periodic ordering in the superradiant phase, reminiscent of quasicrystals, and demonstrate that synthetic magnetic flux provides a powerful knob to control the nature of translational symmetry breaking. Our results establish a new direction in quantum many-body physics where the coexistence of local and global thermodynamic limits gives rise to unconventional symmetry breaking and emergent collective behavior.
We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the intercavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the U(1)\text{U}(1)U(1) symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.