Loschmidt echo and fidelity decay near an exceptional point

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

Coherent tunneling by adiabatic passage in an optical waveguide system

We report on the first experimental demonstration of light transfer in an engineered triple-well optical waveguide structure which provides a classic analogue of Coherent Tunnelling by Adiabatic Passage (CTAP) recently proposed for coherent transport in space of neutral atoms or electrons among tunneling-coupled optical traps or quantum wells [A.D. Greentree et al., Phys. Rev. B 70, 235317 (2004); K. Eckert et al., Phys. Rev. A 70, 023606 (2004)]. The direct visualization of CTAP wavepacket dynamics enabled by our simple optical system clearly shows that in the counterintuitive passage scheme light waves tunnel between the two outer wells without appreciable excitation of the middle well.Comment: submitted for publicatio

Polarization coupling and pattern selection in a type-II optical parametric oscillator

We study the role of a direct intracavity polarization coupling in the dynamics of transverse pattern formation in type-II optical parametric oscillators. Transverse intensity patterns are predicted from a stability analysis, numerically observed, and described in terms of amplitude equations. Standing wave intensity patterns for the two polarization components of the field arise from the nonlinear competition between two concentric rings of unstable modes in the far field. Close to threshold a wavelength is selected leading to standing waves with the same wavelength for the two polarization components. Far from threshold the competition stabilizes patterns in which two different wavelengths coexist.Comment: 14 figure

Geometric potential and transport in photonic topological crystals

We report on the experimental realization of an optical analogue of a quantum geometric potential for light wave packets constrained on thin dielectric guiding layers fabricated in silica by the femtosecond laser writing technology. We further demonstrate the optical version of a topological crystal, with the observation of Bloch oscillations and Zener tunneling of purely geometric nature

Enantiomer discrimination in absorption spectroscopy and in voltammetry: highlighting fascinating similarities and connections

Absorption spectroscopy and voltammetry, of known analogies and connections, share even more fascinating similarities and connections at a higher complexity level, when "upgrading" them with the ability to discriminate between enantiomers by chiral selector implementation. In both techniques either "molecular" selectors or "electromagnetic" ones (L- versus Rcircularly polarized light components for spectroscopy, ccversus b-spin electrons for voltammetry) can be considered; moreover, external magnetic field application can replace a truly chiral actor. A tentative schematization is provided. Analogies and connections also concern molecular features of the enantiodiscrimination actors. In both techniques outstanding performances are obtained with inherently chiral molecules, in which a conjugated backbone with tailored torsion is source of chirality as well as spectroscopic and electrochemical activity, in an attractive three-fold interconnection. Their outstanding effects can be justified by a combination of chemical and electromagnetic properties (excellent potential molecular spin filters), a fascinating challenge for future developments

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO

Measurement of Superluminal optical tunneling times in double-barrier photonic bandgaps

Tunneling of optical pulses at 1.5 micron wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated. Tunneling time measurements as a function of barrier distance show that, far from the resonances of the structure, the transit time is paradoxically short, implying Superluminal propagation, and almost independent of the distance between the barriers. These results are in agreement with theoretical predictions based on phase time analysis and also provide an experimental evidence, in the optical context, of the analogous phenomenon expected in Quantum Mechanics for non-resonant superluminal tunneling of particles across two successive potential barriers. [Attention is called, in particular, to our last Figure]. PACS nos.: 42.50.Wm, 03.65.Xp, 42.70.Qs, 03.50.De, 03.65.-w, 73.40.GkComment: LaTeX file (8 pages), plus 5 figure

Novel Collective Effects in Integrated Photonics

Superradiance, the enhanced collective emission of energy from a coherent ensemble of quantum systems, has been typically studied in atomic ensembles. In this work we study theoretically the enhanced emission of energy from coherent ensembles of harmonic oscillators. We show that it should be possible to observe harmonic oscillator superradiance for the first time in waveguide arrays in integrated photonics. Furthermore, we describe how pairwise correlations within the ensemble can be measured with this architecture. These pairwise correlations are an integral part of the phenomenon of superradiance and have never been observed in experiments to date.Comment: 7 pages, 3 figure