Synthetic Non-Hermitian Photonic Structures: Recent Results and Future Challenges

The prospect of judiciously utilizing both optical gain and loss has been recently suggested as a means to control the flow of light. This proposition makes use of some newly developed concepts based on non-Hermiticity and parity-time (PT) symmetry-ideas first conceived within quantum field theories. By harnessing such notions, recent works indicate that novel synthetic structures and devices with counter-intuitive properties can be realized, potentially enabling new possibilities in the field of optics and integrated photonics. Non-Hermitian degeneracies, also known as exceptional points (EPs), have also emerged as a new paradigm for engineering the response of optical systems. In this talk, we provide an overview of recent developments in this newly emerging field. The use of other type symmetries in photonics will be also discussed.

Time is basically continuous, but can be effectively discretized by establishing long-range correlations as we do by coupling pairs of dissimilar optical fiber loops. Light pulses propagating in our set-up behave like interacting with a so-called photonic mesh lattices with one or two transverse dimensions. Due to the inherent stability of our set-up based on telecommunication equipment we can transfer typical effects of spatial discreteness to the temporal domain. We also have excess to completely new phenomena requiring a precise control of gain and loss, extremely long propagation distances or strong nonlinear effects. By playing with gain, loss, phase modulation and nonlinearity we realize different parity time (PT) symmetric configurations, observe unidirectional invisibility, PT-Bloch oscillations and solitons in one- and two-dimensional lattices.

Exceptional points (EPs) are non-Hermitian degeneracies that feature the coalescence of the eigenvalues and the corresponding eigenstates when the parameters of a dissipative system are tuned appropriately. EPs universally occur in all open physical systems and dramatically affect their behaviour, leading to counterintuitive phenomena such as loss-induced lasing, unidirectional invisibility and enhanced sensors. In this talk, I will discuss the recent exploration of phenomena associated with non-Hermitian physics in my group, such as parity-time symmetry (PT-symmetry) and light-matter interactions around an exceptional point (EP), in high-quality WGM resonators, which can be used to achieve a new generation of optical systems enabling unconventional control of light flow. Non-Hermitian physics will be presented as an alternative guideline to design resonator structures with new physical behaviour and innovative functionality. Specifically, I will talk about nonreciprocal light transmission in a PT-symmetric resonator system. An interesting mechanism triggered by EPs to achieve a loss-induced revival of lasing will be reviewed. I will also explain how to enable chiral modes and directional lasing by operating a laser resonator around an EP. Of special note, sensing is an intriguing application that will benefit from a unique feature associated with EPs in non-Hermitian resonators. A non-Hermitian phonon laser tuned in the vicinity of EPs will be discussed briefly. In the end, I will present a new generic and hand-held microresonator platform that was transformed from a table-top setup, which may help release the power of high-Q WGM resonator technologies.

One of the frontiers of modern photonics is the engineering of the complex refractive index to create new synthetic systems with novel functionalitiesapplications in lasers and integrated guided optics. In the context of PT-symmetric and more generally of non-Hermitian optics, we will examine the power dynamics and amplification of light close to exceptional points of second and higher order.

Electronic circuit analysis originated with the study of non-Hermitian elements: the resistor. It is therefore not surprising that oscillatory non-Hermitian phenomena are most intuitively analyzed in this same context. Lumped circuits provide not only a simple analytical framework for modeling more complex systems, but also enabled the experimental demonstration of several fundamental non-Hermitian phenomena, including a Floquet PT-symmetric system. General principles will be discussed and recent experimental results will be presented with emphasis on the creation and manipulation of exceptional points.

We present theoretical and experimental results demonstrating manipulation of classical and quantum states of light in non-Hermitian photonic structures. We establish that parity-time symmetric structures can perform reversible purification of spatially incoherent light states, and experimentally realize the manipulation and detection of optical coherence using a specially designed waveguide coupler fabricated by direct femtosecond laser writing in glass. We also introduce a new conceptual approach for implementing arbitrary complex birefringence with polarization-dependent transmission using ultra-thin all-dielectric metasurfaces. The experimental characterization of fabricated metasurfaces demonstrates new regimes of polarisation control for enhanced measurements and unconventional interference for classical and quantum light.

In its simplest configuration, a ring resonator coupled to a single channel is an all-pass filter in the linear regime. Such devices and their generalizations have been investigated both experimentally and theoretically in the nonlinear regime, where either spontaneous four-wave mixing or spontaneous parametric down-conversion can be used to create sources and processors of nonclassical light. Applications include the generation of entangled photon pairs, the development of heralding sources and devices for quantum frequency conversion, and the generation of squeezed light. It is essential to consider scattering losses in all these applications. While at one level such structures are examples of general input/output theory, they have their own interesting features and are an example of systems that can be worked out in detail to reveal the physics of some of these features. We discuss some of our recent work in this area.

The prospect of judiciously utilizing both optical gain and loss has been recently suggested as a means to control the flow of light. This proposition makes use of some newly developed concepts based on non-Hermiticity and parity-time (PT) symmetry-ideas first conceived within quantum field theories. By harnessing such notions, recent works indicate that novel synthetic structures and devices with counter-intuitive properties can be realized, potentially enabling new possibilities in the field of optics and integrated photonics. Non-Hermitian degeneracies, also known as exceptional points (EPs), have also emerged as a new paradigm for engineering the response of optical systems. In this talk, we provide an overview of recent developments in this newly emerging field. The use of other type symmetries in photonics will be also discussed.

I will talk about some of the practical applications of non-Hermiticity and exceptional points, which can lead to novel lasers and ultrasensitive sensors.

In this talk, I will discuss the formation of exceptional points in whispering-gallery microcavities. We distinguish three different mechanisms based on weak deformation or perturbation of the cavity's boundary: asymmetric backscattering of counterpropagating waves, interaction of modes with different angular momentum, and coupling of internal and external modes. Finally, we discuss sensors for single-particle detection based on exceptional points in optical microcavities.

We experimentally demonstrate silicon-photonic waveguide devices that function as a broadband asymmetric transmission mode converter while dynamically encircling an EP (EEP) in the optical domain. The silicon device consists of two coupled channel waveguides with complex propagation-index profiles configured such that excited photonic modes undergo time-asymmetric EEP parametric evolutions. Real and imaginary propagation-index profiles required for the EEP evolution are realized by tuning waveguide width and photonic tunnel-gap size, respectively. We explain the underlying design principle, theoretical analyses, fabrication, and measurement of the proposed photonic EEP device. Comprehensive theoretical and experimental analyses show robust time-asymmetry in the optical transmission over a broad spectral domain from 1,250 nm to 1,650 nm. We may establish robust EEP device in the optical domain and an important step toward realization of on-chip optical isolators taking advantages of the unique non-Hermitian wave dynamics. [1] Y. Choi, C. Hahn, J. W. Yoon, S. H. Song and P. Berini, “Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points,” Nat. Commun. 8, 14154 (2017). [2] J. W. Yoon, Y. Choi, C. Hahn, G. Kim, S. H. Song, K.-Y. Yang, J. Y. Lee, Y. Kim, C. S. Lee, J. K. Shin, H.-S. Lee, and P. Berini, “Broadband time-asymmetry of light through a topological loop around an exceptional point,” submitted (Feb. 2018).

I this talk I will describe the transport of energy through a network of coupled harmonic oscillators with active gain and loss sites. Despite it simplicity such a network exhibits a range of anomalous transport phenomena, which arise from the competition between coherent and incoherent processes in combination with non-linear saturation effects. These phenomena become in particular interesting for microscopic networks, where the presence of thermal and quantum noise leads to a transition between a chaotic and a noiseless transport regime. This transition is closely related to PT symmetry breaking in balanced gain-loss systems, but occurs more generally and therefore has important consequences for energy transport at the microscopic level.

Exciton polaritons, the hybrid quasi-particles formed from strong coupling of photons to semiconductor excitons, have emerged as promising candidates for implementing novel photonic devices such as ultrafast optical information processors [1-3], sources of quantum light [4,5] and nonlinear optical simulators based on arrays of coupled micro-resonators [6]. Polaritons can propagate like photons but their excitonic component allows for giant effective third order nonlinearity, gain, and sensitivity to real magnetic fields. These properties are advantageous for incorporation of strong nonlinearity into devices with non-trivial topological features [7,8] or PT symmetry [9,10]. In this talk I will review our experimental results on low power bright [11] and dark [12] solitons and continuum generation in polariton waveguides as well as spontaneous pattern formation [13] in Fabry-Perot microcavities. I will also discuss polariton lasing in a Lieb-lattice of coupled optical micro-resonators [14] and the role of spin-orbit coupling in Lieb and one-dimensional zig-zag lattices. [1] T. Espinosa-Ortega and T. C. H. Liew, Phys. Rev. B 87, 195305 (2013) [2] D. Ballarini et. al., Nat. Commun., 4, 1778 (2014) [3] A. Dreismann et., al. Nat. Materials, 15, 1074 (2016) [4] T. Boulier, et. al., Nat. Commum. 5, 3260 (2014) [5] A. Delteil, T. Fink, A. Schade, S. Höfling, C. Schneider, and A. Imamoğlu, arXiv:1805.04020 (2018) [6] A. Amo and J. Bloch, C. R. Physique 17, 934-945 (2016). [7] A. V. Nalitov, D. D. Solnyshkov, and G. Malpuech, Phys. Rev. Lett. 114, 116401 (2015) [8] T. Karzig, C. E. Bardyn, N. H. Lindner, and G. Refael, Phys. Rev. X, 5, 031001 (2015) [9] I. Yu. Chestnov, et. al., Sci. Rep. 6 19551 (2016) [10] S. V. Suchkov et. al., Laser Photon. Rev. 10 177-213 (2016) [11] P. M. Walker et. al., Nat. Commun. 6, 8317 (2015) [12] P. M. Walker et. al., Phys. Rev. Lett. 119, 097403 (2017) [13] C. E. Whittaker et. al. Phys. Rev. X 7, 031033 (2017) [14] C. E. Whittaker et. al., Phys. Rev. Lett. 120, 097401 (2018)

In the context of linear optics typical models for semiconductor lasers consist of a set of linear evolution equations for the optical fields, that is nonlinearly coupled to a nonlinear system of transport equations for the charge carriers in the active region of these lasers. The latter system is typically evolving along the recombination time scale, which is usually 3 orders of magnitude slower than the photon lifetime in semiconductor lasers. This special structure of the model motivates a spectral representation of the optical subsystem, which is non-hermitian by nature, because of radiating boundary conditions, as well as by the presence of gain and losses in the resonator. As a first consequence, the spectrum of the optical subsystem is complex, where the real part can be interpreted as the optical frequency of the corresponding mode, whereas the imaginary part is the (reverse) lifetime of the mode, such that the modes with the smallest imaginary part are favoured for lasing. As a second consequence, the modes are not power-orthogonal, but bi-orthogonal with respect to their adjoint partners. This implies counter-intuitive effects, as the appearance of Petermanns K-factor in the evolution of the optical fields, which measures the „non-hermiticity’’ of the optical resonator. As a third consequence, the modes can completely degenerate in so-called exceptional points, where the Petermann K-factor reaches infinity, with even more striking consequences. Several examples will show new types of instabilities and dynamic scenaria in semiconductor lasers that arise from these facts, and demonstrate their practical use in photonic technologies for high-speed applications.

to be announced

Moebius strip is a continuous one-sided surface formed from a rectangular strip by rotating one end 180 degrees and attaching to the other end. This marvelous structure with only one side and only one boundary is the epitome of the topologically non-trivial phenomenon and shows various curious properties due to its unorientability. Besides fundamental studies on topology, the unorientability enable the Moebius strip to be applicable to many useful applications in various field. Here, we investigate eigenfunctions in Moebius ladder lattice which can be considered as the prototype for eigenfunction analysis of real space Moebius strip. PT-symmetry is applied to the Moebius ladder lattices and then the PT-phase transitions in PT-symmetric Moebius ladder lattice appear at new transition points because of the combination between PT-symmetry and non-trivial topology of real space. Finally, we report the interface states are localized at the twisted interface and protected by PT-symmetry.

Kai Wang (1), Lukas J. Maczewsky (2), Alexander A. Dovgiy (1), Andrey E. Miroshnichenko (3), Alexander Moroz (4), Demetrios N. Christodoulides (5), Alexander Szameit (2), and Andrey A. Sukhorukov (1) (1) Nonlinear Physics Centre, The Australian National University, Canberra, Australia (2) Institute for Physics, Universität Rostock, Rostock, Germany (3) School of Engineering and Information Technology, University of New South Wales, Canberra, Australia (4) Wave-scattering.com (5) CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA Discrete lattices play an important role in fundamental physics, due to the universality of wave propagation and localization spanning from electrons in atomic potentials to light in periodic photonic structures. The latest research reveals unique benefits of two- and higher-dimensional structures for tailoring light confinement and emission [1], implementing imperfections-insensitive transmission [2], and even realization of optical neural networks [3]. Yet, it remains an open question on the potential for implementing multi-dimensional photonics on planar integrated all-optical platforms. Here, we introduce a new, general and practical approach for mapping arbitrary multi-dimensional tight-binding lattices to a planar (1D) lattice, where the photon dynamics remains exactly equivalent, and theoretically demonstrate an application in ultra-sensitive optical detection and low-threshold nonlinear switching. Our mapping procedure is based on Lanczos matrix tridiagonalization. Whereas this algorithm was traditionally formulated in an abstract form for linear matrices, we find that it is applicable to coupled-mode discrete Schrödinger equation describing completely the nonstationary light dynamics. Our approach allows multi-dimensional structures to be mapped to a 1D semi-infinite lattice with only nearest-neighbour couplings. Importantly, Lanczos algorithm allows us to map any initial multi-dimensional excitation to the first site of the equivalent planar lattice. It is also possible to add defect to the excitation site, where the wave dynamics in that site is exactly the same as in the defect site of the multi-dimensional lattice. Our concept can enable fundamental advances in optical switching and sensing. Specifically, we find that the excitation efficiency, i.e. the amount of light remaining trapped at the defect, exhibits unique features in high-dimensional space. In directly accessible dimensions of N = 1,2,3, the excitation efficiency grows gradually as the defect strength is increased. However, only for high-dimensional (N = 4,5,...) lattices, the excitation suddenly jumps from zero to a finite value as the defect strength crosses a critical threshold. This effect was absent in previous studies of linear optical lattices, and it corresponds to an ultra-high sensitivity to extremely small changes in defect strength. Although photonic lattices with N= 4, 5, . . . are out of reach for direct experimental realizations, we successfully applied our approach to mapping the multi-dimensional lattice into a planar (1D) structure, where the special variation of couplings can be achieved by engineering the separations between the waveguides [4]. Moreover, we introduce Kerr-nonlinearity to the defect waveguide and numerically demonstrate a low-threshold switching controlled by the input power. In conclusion, we introduced a powerful approach for designing practical synthetic photonic structures behaving as complicated multi-dimensional structures. As an important application, we predicted a sharp switching from zero to strong localization at critical surface defect strength in four and higher-dimensional synthetic lattices, demonstrating the potential for optical detection with fundamentally enhanced sensitivity and optical switching with ultra-low threshold in both linear and nonlinear regimes. By proper use of loss and gain, our concept may also be generalized to the synthesis of non-Hermitian high-dimensional lattices. References [1] J. D. Joannopoulos, R. D. Meade, et al., Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, Princeton, 2008). [2] M. C. Rechtsman, J. M. Zeuner, et al., Nature 496, 196 (2013). [3] P. R. Prucnal and B. J. Shastri, Neuromorphic Photonics (CRC Press, 2017). [4] M. Heinrich, M. A. Miri, et al., Nat. Commun. 5, 3698 (2014).

Abstract: In my talk I will present results from three recent projects centered around non-Hermitian physics. In the first project we managed to show that the line-width of a phonon laser broadens significantly when approaching an exceptional point [1]. In the second project we provide a first experimental demonstration of a random anti-laser - a disordered system that perfectly absorbs a suitably shaped incoming wave state [2]. In the third project we implemented our theoretical prediction on scattering states in disordered media with constant intensity and perfect transmission [3] in an acoustic setup. Using several loudspeakers with gain and loss allows us to steer an incoming sound wave across a strongly disordered waveguide without any reflection or variation in its pressure [4]. [1] J. Zhang, B. Peng, S. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y. -X. Liu, S. Rotter, and L. Yang (Nature Photonics, in print) [2] K. Pichler, M. Kühmayer, J. Böhm, A. Brandstötter, P. Ambichl, U. Kuhl, and S. Rotter (in preparation) [3] K. G. Makris, A. Brandstötter, P. Ambichl, Z. H. Musslimani, and S. Rotter, Light Sci. Appl. 6, e17035 (2017) [4] E. Rivet, A. Brandstötter, K. G. Makris, H. Lissek, S. Rotter, and R. Fleury, arXiv:1804.02363 (Nature Physics, in print)

In this talk I will first show the existence of a novel non-Hermitian symmetry, which we termed complex mirror symmetry. I will then discuss a process that generates high-order non-Hermitian degeneracies based on this symmetry, which can potentially increase the spontaneous emission rate and sensing sensitivity of optical devices by orders of magnitude.

I will present experimental microwave results showing topological features like topological protected states, flat bands, winding number etc. The experiment is based on evanescently coupled dielectric resonators [1] realizing a system which can be described by tight binding theory. The SSH chain, here weakly coupled dimers with strong intra dimer couplings, exhibits a state at 'zero energy' which is topologically protected. We have experimentally exploited the structures and stability of this state [2]. In the two-dimensional version, the Lieb lattice, the same type of state can be realized, but it is hidden within the flat bands created due to the two dimensional structures. This degeneracy is lifted due to next-nearest neighbor coupling which we realize experimentally [3]. In a proof of principle experiment we have used the SSH chain to implement a reflective dimer [4] by changing the absorption or the 'eigenenergy' of the defect. Depending on the parameter the structure at the defect energy is transparent or reflective without creating large absorption within the system, thus gaining a large dynamical range of the limiter, given by the difference between the limiting threshold and the limiters damage threshold [5]. [1] M. Bellec, U. Kuhl, G. Montambaux, and F. Mortessagne, "Tight-binding couplings in microwave artificial graphene," Phys. Rev. B 88, 115437 (2013). [2] C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, "Selective enhancement of topologically induced interface states in a dielectric resonator chain," Nature Communicatios 6, 6710 (2015). [3] C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, "Partial chiral symmetry-breaking as a route to spectrally isolated topological defect states in twodimensional artificial materials," 2D Mater. 4, 025008 (2017). [4] E. Makri, H. Ramezani, T. Kottos, and I. Vitebskiy, "Concept of a reflective power limiter based on nonlinear localized modes," Phys. Rev. A 89, 031802(R) (2014). [5] U. Kuhl, F. Mortessagne, E. Makri, I. Vitebskiy, and T. Kottos, "Waveguide photonic limiters based on topologically protected resonant modes," Phys. Rev. B 95, 121409(R) (2017).

The investigation of the propagation of light in mesoscopic systems is a rich subject ranging from billiards for light to new schemes for realizing directional emission from microcavity lasers. The concept of quantum-classical, here wave-ray, correspondence, proves to be as useful as for the originally studied electronic mesoscopic systems such as quantum dots, including the insight from semiclassical corrections to the naive ray picture. The propagation of electromagnetic waves in realistic, three-dimensional optical microcavities requires to pay attention to the evolution of the light's polarization as a new degree of freedom. In systems like dielectric Möbius strips or cone-shaped microtube cavities, the polarization state of resonant whispering gallery-type modes may differ strongly from the reference case of homogeneous cylinders. Whereas we find that the polarization of the electromagnetic field follows the wall orientation in thin Möbius strips, thereby reflecting the accumulated geometric phase, we observe that light ignores the Möbius topology when the strip's thickness is increased. Breaking of symmetries further influences the morphology of resonances and can induce a transition from linear to elliptical polarization. In an outlook we will discuss the potential for applications like sensors based on the principles of mesoscopic optics.

The recent development of topological insulator states for photons1–3 has led to an exciting new field of “topological photonics,” which has as a central goal the development of extremely robust photonic devices4. Topological insulator physics has been studied extensively in condensed matter5 and cold atoms6. However, photonic systems offer the possibility of non-Hermitian effects through the engineering of optical gain and loss, which opens an entire new field of physics. In this talk, we will discuss our recent experimental work on non-Hermitian topological phenomena in coupled lattice systems, in particular the first demonstration of non-hermitian PT-symmetric topological interface state. References [1] Haldane, F. D. M. & Raghu, S., Phys. Rev. Lett. 100, 013904 (2008) [2] Wang, Z. et al., Nature 461, 772–775 (2009) [3] Rechtsman, M. C. et al., Nature 496, 196–200 (2013) [4] Hafezi et al., Nature Physics 7, 907-912 (2011) [5] Hasan, M. Z. & Kane, C. L., Rev. Mod. Phys. 82, 3045–3067 (2010) [6] Jotzu, G. et al., Nature 515, 237–240 (2014)

Optical supersymmetry (SUSY) has recently been proposed as a versatile design strategy for multimoded optical systems. Supersymmetric partners are characterized by the fact that they share all of their effective indices with their progenitor structure. The crucial exception is the fundamental mode, which is absent from the spectrum of the partner waveguide. We demonstrate experimentally how this global phase-matching property can be exploited for efficient mode conversion. Multimode structures and their superpartners are experimentally realized in coupled networks of femtosecond laser-written waveguides, and the corresponding light dynamics are directly observed by means of fluorescence microscopy. We show that SUSY transformations can readily facilitate the removal of the fundamental mode from multimode optical structures. In turn, hierarchical sequences of such SUSY partners naturally implement the conversion between modes of adjacent order. Our experiments illustrate just one of the many possibilities of how SUSY may serve as a building block for integrated mode-division multiplexing arrangements. Venturing beyond the Hermitian realm, supersymmetric methods give rise to extended families of non-PT-symmetric configurations that nevertheless exhibit fully real spectra of eigenvalues. We also show how SUSY optical transformations can be utilized to “heal” systems with spontaneously broken PT symmetry, i.e. to surgically remove the complex conjugate pairs of eigenstates without affecting the remaining bulk of real eigenvalues. Overall, supersymmetric notions may enrich and expand integrated photonics by versatile and readily scalable optical components and desirable, yet previously unattainable, multimode functionalities.

Communication and computing, two of the largest industries in the world, are one the verge of being transformed by quantum information science. Light is our best medium for sending information over long distances, because it moves at nature’s speed limit, and doesn’t degrade for hundreds of kilometres. But to send quantum information, we require quantum light. Sources of quantum light based on nonlinear optical processes, which mediate interactions between photons, are becoming an established standard for generating single photons and other important quantum states of light. While existing sources were sufficient for proof-of-principle experiments, and to demonstrate the feasibility of optics for quantum technologies, significant progress in the field will require a much higher degree of control over quantum light. In this talk, I will discuss theoretical work on expanding the capabilities of nonlinear optics in the quantum regime, with the ultimate goal of developing an arbitrary quantum light generator. In particular, I will introduce novel techniques—such as customized poling, Moire gratings, and engineered loss—for shaping the properties of quantum light at the source.

Photonic quantum walk systems can be considered as a standard model to describe the dynamics of quantum particles in a discretized environment and serve as a simulator for complex quantum systems, which are not as readily accessible. However, their experimental realization requires setups with increasing complexity in terms of number of modes and control of the system parameters. Here, we employ an optical feedback loop, which provides high homogeneity, precise control of the system parameters and optimal resource efficiency. In this time-multiplexing scheme the walker's position is mapped into the time domain ensuring the requisite interference properties. Fast electro-optic modulators serving as dynamic coin operations enable us to study topological effects in single- and multi-step quantum walk protocols. By additionally applying a deterministic in- and outcoupling controlled local sinks are introduced in the walker's dynamics by which we investigate measurement induced effects via recurrence probabilities. References: 1. A. Schreiber et al. “Photons Walking the Line: A Quantum Walk with Adjustable Coin Oper- ations,” PRL 104, 050502 (2010). 2. A. Schreiber et al. “A 2D Quantum Walk Simulation of Two-Particle Dynamics,” Science 336/6077, 55–58 (2012). 3. S. Barkhofen et al. „Supersymmetric polarization anomaly in photonic discrete-time quantum walks“ arXiv:1804.09496 4. S. Barkhofen et al. "Measuring topological invariants in disordered discrete-time quantum walks“ PRA 96 033846 (2017) 5. T. Nitsche et al. “Probing Measurement Induced Effects in Quantum Walks via Recurrence,” Sci. Adv. 2018;4:eaar6444.

(Joint work with S. Franke, M. Richter, A. Knorr, M. Dezfouli, S. Hughes, P. Kristensen.) A novel quantization scheme for the electromagnetic field in dissipative and open systems using quasi-normal [1,2] modes is presented. Contrary to many “modes-of-the-universe” approaches that utilize the microscopic Maxwell equations together with a set of uncontrolled approximations, this scheme is based on the macroscopic Maxwell equations and thus leads to the correct classical limit [3]. Applications for certain leaky and hybrid cavity-QED systems/effects including cavity enhanced spontaneous emission rates are developed [1] and shown to agree well with corresponding semi-classical results [4]. [1] P.T. Leung et al., Phys. Rev. A 49, 3057 (1994). [2] P.T. Kristensen and S. Hughes, ACS Photonics 1, 2, (2014). [3] S. Franke et al., in preparation (2018). [4] M.K. Dezfouli et al., Phys. Rev. A 95, 013846 (2017).

We develop a theoretical framework that lays out the fundamental rules under which a periodic (Floquet) driving scheme can induce non-reciprocal transport. Our approach utilizes an extended Hilbert space where a Floquet network with an extra (frequency) dimension naturally arises. The properties of this network (its on-site potential and the intersite couplings) are in one-to-one correspondence with the initial driving scheme. Its proper design allows for a control of the multipath scattering processes and the associated interferences. We harness this degree of freedom to realize driving schemes with narrow or broad-band non-reciprocal transport.

In this talk, we focus on the applications of parity-time-symmetric (PT-symmetric) photonic structures for designing novel, robust and compact integrated optical devices. In the first part of this talk, by exploiting the emerging non-Hermitian photonics design at an exceptional point, we demonstrate a microring laser generating a single-mode OAM vortex lasing with the ability to precisely define the topological charge of the OAM mode. We show that the polarization associated with OAM lasing can be further manipulated on demand, creating a radially polarized vortex emission. Our OAM microlaser could find applications in the next generation of integrated optoelectronic devices for optical communications. In the second part of the talk, we focus on the advantages offered by the PT-symmetric photonics in the design of one of the most widely used integrated optics devices – a directional coupler. Despite the benefits which the directional couplers based on PT-symmetric systems may offer to the field of integrated optics, the realization of such couplers relies on rather strict design constraints on the waveguide parameters. We investigate directional couplers built of dissimilar waveguides that do not fulfill the PT symmetry. Nevertheless, we demonstrate that for properly designed parameters, at least one mode of such couplers shows a behavior similar to the one observed in PT-symmetric systems. Finally, we discuss a nonlinearly triggered transition from a full to a broken PT-symmetric regime in finite-size systems described by smooth permittivity profiles and, in particular, in a conventional discrete waveguide directional coupler configuration with a rectangular profile.