Synthetic gauge fields for light beams in optical resonators

A method to realize artificial magnetic fields for light waves trapped in passive optical cavities with anamorphic optical elements is theoretically proposed. In particular, when a homogeneous magnetic field is realized, a highly-degenerate Landau level structure for the frequency spectrum of the transverse resonator modes is obtained, corresponding to a cyclotron motion of the optical cavity field. This can be probed by transient excitation of the passive optical resonator.Comment: 5 pages, 4 figure

Supersymmetric transparent optical intersections

Supersymmetric (SUSY) optical structures provide a versatile platform to manipulate the scattering and localization properties of light, with potential applications to mode conversion, spatial multiplexing and invisible devices. Here we show that SUSY can be exploited to realize broadband transparent intersections between guiding structures in optical networks for both continuous and discretized light. These include transparent crossing of high-contrast-index waveguides and directional couplers, as well as crossing of guiding channels in coupled resonator lattices.Comment: 5 pages, 5 figures, revised version to appear in Optics Letter

Non-Hermitian gauged topological laser arrays

Stable and phase-locked emission in an extended topological supermode of coupled laser arrays, based on concepts of non-Hermitian and topological photonics, is theoretically suggested. We consider a non-Hermitian Su-Schrieffer-Heeger chain of coupled microring resonators and show that application of a synthetic imaginary gauge field via auxiliary passive microrings leads to all supermodes of the chain, except one, to become edge states. The only extended supermode, that retains some topological protection, can stably oscillate suppressing all other non-topological edge supermodes. Numerical simulations based on a rate equation model of semiconductor laser arrays confirm stable anti-phase laser emission in the extended topological supermode and the role of the synthetic gauge field to enhance laser stability.Comment: 5 figure

Adiabatic quantum state transfer in tight-binding chains using periodic driving fields

A method for high-fidelity coherent adiabatic transport in a zig-zag tight-binding chain, based on application of two external periodic driving fields, is theoretically proposed. The method turns out to be robust against imperfections and disorder of the static lattice Hamiltonian, is tolerant to next-nearest neighborhood interactions, and enables coherent transport in long chains without the need for a local control and timing of the trapping potential.Comment: 6 pages, 4 figures, to appeer in EuroPhysics Letter

Localization, quantum resonances and ratchet acceleration in a periodically-kicked PT\mathcal{PT}-symmetric quantum rotator

We consider wave transport phenomena in a $\mathcal{PT}$-symmetric extension of the periodically-kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\mathcal{PT}$ phase. In the delocalized (quantum resonance) regime, $\mathcal{PT}$ symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically-kicked $\mathcal{PT}$-symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.Comment: 11 pages, 7 figure

Convective and absolute PT symmetry breaking in tight-binding lattices

We investigate the onset of parity-time ($\mathcal{PT}$) symmetry breaking in non-Hermitian tight-binding lattices with spatially-extended loss/gain regions in presence of an advective term. Similarly to the instability properties of hydrodynamic open flows, it is shown that $\mathcal{PT}$ symmetry breaking can be either absolute or convective. In the former case, an initially-localized wave packet shows a secular growth with time at any given spatial position, whereas in the latter case the growth is observed in a reference frame moving at some drift velocity while decay occurs at any fixed spatial position. In the convective unstable regime, $\mathcal{PT}$ symmetry is restored when the spatial region of gain/loss in the lattice is limited (rather than extended). We consider specifically a non-Hermitian extension of the Rice-Mele tight binding lattice model, and show the existence of a transition from absolute to convective symmetry breaking when the advective term is large enough. An extension of the analysis to ac-dc-driven lattices is also presented, and an optical implementation of the non-Hermitian Rice-Mele model is suggested, which is based on light transport in an array of evanescently-coupled optical waveguides with a periodically-bent axis and alternating regions of optical gain and loss.Comment: 13 pages, 7 figures (to appear in Phys. Rev. A

Effective magnetic fields for photons in waveguide and coupled resonator lattices

A method to realize effective magnetic fields for photons in square lattices of coupled optical waveguides or resonators is suggested, which is inspired by an optical analogue of photon-assisted tunneling of atom optics. It is shown that an artificial magnetic field can be achieved by application of an index gradient and periodic lumped phase shifts or modulation of the propagation constants/resonances, without the need to modulate the coupling strength.Comment: 5 pages, 2 figure

Zak phase of photons in optical waveguide lattices

Zak phase, i.e. the Berry phase acquired during an adiabatic motion of a Bloch particle across the Brillouin zone, provides a measure of the topological invariant of Bloch bands in one-dimensional crystalline potentials. Here a photonic structure, based on engineered lattices of evanescently-coupled optical waveguides, is proposed to detect Zak phase difference of photons undergoing Bloch oscillations in topologically distinct Bloch bands of dimerized superlattices.Comment: 4 figure

Bloch oscillations in non-Hermitian lattices with trajectories in complex plane

Bloch oscillations (BOs), i.e. the oscillatory motion of a quantum particle in a periodic potential, are one of the most striking effects of coherent quantum transport in the matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called 'acceleration' theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e. not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only {\it on average}, and that the periodic wave packet motion of the particle in the real space is described by a trajectory in {\it complex} plane, i.e. it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.Comment: 9 pages, 6 figures, to appear in Phys. Rev.

Exceptional points and photonic catastrophe

Exceptional points (EPs) with a global collapse of pairs of eigenfunctions are shown to arise in two locally-coupled and spatially-extended optical structures with balanced gain and loss. Global collapse at the EP deeply changes light propagation, which becomes very sensitive to small changes of initial conditions or system parameters, similarly to what happens in models of classical or quantum catastrophes. The implications of global collapse for light behavior are illustrated by considering discrete beam diffraction and Bloch oscillation catastrophe in coupled waveguide lattices.Comment: 5 pages, 4 figure