Long-range correlations and the random mass Dirac model on an integrated optical platform

Abstract

Summary form only given. The one-dimensional (1D) Dirac equation governs the dynamics of relativistic fermions. Several of its elusive predictions have been successfully investigated in classical optical simulators, for massive [1] as well as for massless [2] fermions. However, not only free particles can be described by this equation. There is also a direct correspondence to several magnetic solids, for instance chains of coupled spins with antiferromagnetic interaction, so-called spinPeierls (sP) systems. In particular, doping in such chains leads to defect spins with long-range correlations which are the physical origin for the unique magnetic and thermodynamic properties of such materials. These randomly positioned defects correspond to a spatial disorder of the mass-term in the Dirac equation [3]. So far, no simulator - quantum or classical - for sP systems or the random mass Dirac model in general has been implemented, only recently a simulator employing trapped Rydberg atoms has been proposed [4]. Here, we present an optical configuration implementing the 1D random mass Dirac model on a chip. We employ laser written waveguide arrays, arranged in a binary lattice and representing the mass by the index difference between the two waveguides of each unit cell (Fig. 1(a)-(c)). Disorder is introduced by randomly positioning domain walls, where the ordering within the unit cells is reversed. This corresponds to randomly located dopants in the sP-chain. We excite the defect states residing at these domain walls with a laser and observe long-range correlations in the ensemble average, decaying with a characteristic exponent of -3/2, in accordance with the Dirac model (Fig. 1(d))[5]. Our device allows the controlled investigation of the physics of Dirac fermions with random mass as well as sP-systems and other closely related materials. Moreover, our results suggest the occurrence of long-range correlations in integrated optical devices, being of potential interest for communication or sensing applications.