Abstract
We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to threshold or to study large scale synchronization phenomena and dynamical phase transitions when operating above the threshold. We consider the modelling of polariton graphs using the complex Ginzburg–Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them.
Highlights
Engineering a physical system to reproduce a many-body Hamiltonian has been at the heart of Feynman’s idea of an analogue Hamiltonian simulator [1]
The design of an analogue Hamiltonian simulator consists of several important ingredients [14]: (i) mapping of the Hamiltonian of the system to be simulated into the elements of the simulator and the interactions between them; (ii) preparation of the simulator in a state that is relevant to the physical problem of interest: one could be interested in finding the ground or excited equilibrium state at a finite temperature; (iii) performing measurements on the simulator with the required precision
We demonstrated that the search for the global ground state of a polariton graph is equivalent to the minimization of the XY Hamiltonian HXY = -åJij cos(qij)
Summary
Original content from this Abstract work may be used under We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the licence. Polariton simulators have the potential to reach the global minimum of the XY. Hamiltonian in a bottom-up approach by gradually increasing excitation density to threshold or to attribution to the author(s) and the title of study large scale synchronization phenomena and dynamical phase transitions when operating above the work, journal citation the threshold. We consider the modelling of polariton graphs using the complex Ginzburg–Landau and DOI. Model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them
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