Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

We study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially {equilibrated} Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part{, that actually corresponds to adiabatic switching on the disorder,} and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. {We also present an appropriate generalization to inhomogeneous trapped condensates.} Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

Robust optical physical unclonable function using disordered photonic integrated circuits

Physical unclonable function (PUF) has emerged as a promising and important security primitive for use in modern systems and devices, due to their increasingly embedded, distributed, unsupervised, and physically exposed nature. However, optical PUFs based on speckle patterns, chaos, or ‘strong’ disorder are so far notoriously sensitive to probing and/or environmental variations. Here we report an optical PUF designed for robustness against fluctuations in optical angular/spatial alignment, polarization, and temperature. This is achieved using an integrated quasicrystal interferometer (QCI) which sensitively probes disorder while: (1) ensuring all modes are engineered to exhibit approximately the same confinement factor in the predominant thermo-optic medium (e. g. silicon), and (2) constraining the transverse spatial-mode and polarization degrees of freedom. This demonstration unveils a new means for amplifying and harnessing the effects of ‘weak’ disorder in photonics and is an important and enabling step toward new generations of optics-enabled hardware and information security devices.