Abstract
An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).
Highlights
In the strongly correlated regime of interacting light matter physics, it is possible to generate an effective strong repulsion between the photons, and from this study, one can understand and quantum simulate different interesting physical properties of strongly correlated quantum condensed matter many body system
We would like to find out the emergence of different relativistic modes, for this interacting light-matter physics in a nonlinear cavities array, based on the exact solutions
We explicitly show that the topological quantum phase transition of the system occurs through a change of topological invariant quantity, i.e., the winding number
Summary
An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system We study this system, in a one dimensional array of nonlinear cavities. 40 have proposed a model for a one dimensional array of nonlinear cavities where they have quantum simulated p-wave pairing effectively arising from the interplay between the strong on-site interaction and two-photon parametric driving This model may have ingredient for the existence of topological properties. The authors have tried to quantum simulate the Majorana like modes for this one-dimensional array of nonlinear cavities, but the detail study of the topological properties and emergence of different relativistic modes have not addressed there. We will use the same model Hamiltonian for the present study but in a different context
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