Simulating Floquet topological phases in static systems

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.

Disorder-aided pulse stabilization in dissipative synthetic photonic lattices

We consider a discrete time evolution of light in dissipative and disordered photonic lattice presenting a generalization of two popular non-Hermitian models in mathematical literature: Hatano-Nelson and random clock model and suggest a possible experimental implementation using coupled fiber loops. We show that if the model is treated as non-unitary Floquet operator rather than the effective Hamiltonian the combination of controlled photon loss and static phase disorder leads to pulse stabilization in the ring topology. We have also studied the topological invariant associated with the system and found additional evidence for the absence of Anderson transition.

Quantum Energy Expectation in Periodic Time-Dependent Hamiltonians via Green Functions

LetUFbe the Floquet operator of a time periodic HamiltonianH(t). For each positive and discrete observableA(which we call aprobe energy), we derive a formula for the Laplace time average of its expectation value up to timeTin terms of its eigenvalues and Green functions at the circle of radiuse1/T. Some simple applications are provided which support its usefulness.

QUANTUM PARAMETRIC RESONANCE: ANALYTICAL STUDIES

The quantum version of parametric resonance of the harmonic oscillator is studied in terms of Feynman's propagator method and a discrete map. The eigenfunctions and eigenvalues of the Floquet operator are derived explicitly. The solutions follow the general laws: In the regions of parametric resonance the spectrum of the Floquet operator becomes continuous, while it is pointlike in the stable regimes. The Gaussian wave packet undergoes spreading exponentially and linearly in the two regimes, respectively.

On the absolutely continuous subspaces of Floquet operators

The purpose of this paper is to describe various subspaces that are closely related to the absolutely continuous subspace of a Floquet operator. This paper generalises and extends several known results.