Publications Project 10 
Nonlinear Phenomena in Complex Photonic Structures
Project Leader: Stefan Rotter
In situ realization of particlelike scattering states in a microwave cavity
J. Böhm, A. Brandstötter, P. Ambichl, S. Rotter, and U. Kuhl 

We realize scattering states in a lossy and chaotic twodimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states, we measure the system's complex transmission matrix and apply an adapted WignerSmith timedelay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase and amplituderegulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wavebased communication systems.  
Published: 20170206 

NonHermitian physics and PT symmetry
R. ElGanainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter and D. N. Christodoulides 

In recent years, notions drawn from nonHermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore nonHermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments.  
Published: 20170105 

Unidirectional zero reflection as gauged paritytime symmetry
J. Gear, Y. Sun, S. Xiao, L. Zhang, R. Fitzgerald, S. Rotter, H. Chen and J. Li 

We introduce here the concept of establishing paritytime (PT)symmetry through a gauge transformation involving a shift of the mirror plane for the parity operation. The corresponding unitary transformation on the system's constitutive matrix allows us to generate and explore a family of equivalent PTsymmetric systems. We further derive that unidirectional zero reflection for a reciprocal twoport system can always be associated with a passively gauged PTsymmetry. We demonstrate this experimentally using a microstrip transmissionline with magnetoelectric coupling. This study allows us to use bianisotropy as a practical route to realise and explore exceptional point behaviour of PTsymmetric or generally nonHermitian systems.  
Published: 20171221 

Ultralong relaxation times in bistable hybrid quantum systems
A. Angerer, S. Putz, D. O. Krimer, T. Astner, M. Zens, R. Glattauer, K. Streltsov, W. J. Munro, K. Nemoto, S. Rotter, J. Schmiedmayer, J. Majer 

Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last 50 years. Recently, the ability to engineer quantum metamaterials through hybridization has allowed us to explore these nonlinear effects in systems with no natural analog. We investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogenvacancy centers. One of the exciting properties of this spin system is its long spin lifetime, which is many orders of magnitude longer than other relevant time scales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds—a time scale much longer than observed so far for this effect. Our results provide a foundation for future quantum technologies based on nonlinear phenomena.  
Published: 20171208 

Super and AntiPrincipalModes in Multimode Waveguides
P. Ambichl, W Xiong, Y. Bromberg, B. Redding, H. Cao and S. Rotter 

We introduce special states for light in multimode waveguides featuring strongly enhanced or reduced spectral correlations in the presence of strong mode coupling. Based on the experimentally measured multispectral transmission matrix of a multimode fiber, we generate a set of states that outperform the established “principal modes” in terms of the spectral stability of their output spatial field profiles. Inverting this concept also allows us to create states with a minimal spectral correlation width, whose output profiles are considerably more sensitive to a frequency change than typical input wave fronts. The resulting “superprincipalmodes” and “antiprincipalmodes” are made orthogonal to each other even in the presence of modedependent loss. By decomposing them in the principalmode basis, we show that the superprincipalmodes are formed via interference of principal modes with close delay times, whereas the antiprincipalmodes are a superposition of principal modes with the mostdifferent delay times available in the fiber. Such novel states are expected to have broad applications in fiber communication, imaging, and spectroscopy.  
Published: 20171130 

Observation of mean path length invariance in lightscattering media
R. Savo, R. Pierrat, U. Najar, R. Carminati, S. Rotter, S. Gigan 

The microstructure of a medium strongly influences how light propagates through it. The amount of disorder it contains determines whether the medium is transparent or opaque. Theory predicts that exciting such a medium homogeneously and isotropically makes some of its optical properties depend only on the medium’s outer geometry. Here, we report an optical experiment demonstrating that the mean path length of light is invariant with respect to the microstructure of the medium it scatters through. Using colloidal solutions with varying concentration and particle size, the invariance of the mean path length is observed over nearly two orders of magnitude in scattering strength. Our results can be extended to a wide range of systems—however ordered, correlated, or disordered—and apply to all wavescattering problems.  
Published: 20171110 

Optimal control of nonMarkovian dynamics in a singlemode cavity strongly coupled to an inhomogeneously broadened spin ensemble
D. O. Krimer, B. Hartl, F. Mintert and S. Rotter 

Ensembles of quantummechanical spins offer a promising platform for quantum memories, but proper functionality requires accurate control of unavoidable system imperfections. We present an efficient control scheme for a spin ensemble strongly coupled to a singlemode cavity based on a set of Volterra equations relying solely on weak classical control pulses. The viability of our approach is demonstrated in terms of explicit storage and readout sequences that will serve as a starting point towards the realization of more demanding full quantummechanical optimal control schemes.  
Published: 20171016 

Optical physics: A laser model for cosmology
S. Rotter 

Experiments reveal that the laws governing the immediate aftermath of the Big Bang also apply to the behaviour of coupled lasers. The findings could be used to solve complex computational problems.  
Published: 20170913 

Wave propagation through disordered media without backscattering and intensity variations
K. G Makris, A. Brandstötter, P. Ambichl, Z. H. Musslimani and S. Rotter 

A fundamental manifestation of wave scattering in a disordered medium is the highly complex intensity pattern the waves acquire due to multipath interference. Here we show that these intensity variations can be entirely suppressed by adding disorderspecific gain and loss components to the medium. The resulting constantintensity waves in such nonHermitian scattering landscapes are free of any backscattering and feature perfect transmission through the disorder. An experimental demonstration of these unique wave states is envisioned based on spatially modulated pump beams that can flexibly control the gain and loss components in an active medium.  
Published: 20170908 Press release TU Wien, 20170913 [55/2017] 

Focusing inside Disordered Media with the Generalized WignerSmith Operator
P. Ambichl, A. Brandstötter, J. Böhm, M. Kühmayer, U. Kuhl, and S. Rotter 

We introduce a wave front shaping protocol for focusing inside disordered media based on a generalization of the established WignerSmith timedelay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specific experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength—ranging from strongly focusing on the designated target to completely bypassing it. Our protocol works without optimization or phase conjugation and we expect it to be particularly attractive for optical imaging in disordered media.  
Published: 20170718 

Symmetry, stability, and computation of degenerate lasing modes
D. Liu, B. Zhen, L. Ge, F. Hernandez, A. Pick, S. Burkhardt, M. Liertzer, S. Rotter and S. G. Johnson 

We present a general method to obtain the stable lasing solutions for the steadystate ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closedform expressions for both circulating modes and other types of lasing solutions as well as for their linearized MaxwellBloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its “chiral” intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.  
Published: 20170223 

Principal modes in multimode fibers: exploring the crossover from weak to strong mode coupling
W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao 

We present experimental and numerical studies on principal modes in a multimode fiber with mode coupling. By applying external stress to the fiber and gradually adjusting the stress, we have realized a transition from weak to strong mode coupling, which corresponds to the transition from single scattering to multiple scattering in mode space. Our experiments show that principal modes have distinct spatial and spectral characteristic in the weak and strong mode coupling regimes. We also investigate the bandwidth of the principal modes, in particular, the dependence of the bandwidth on the delay time, and the effects of the modedependent loss. By analyzing the pathlength distributions, we discover two distinct mechanisms that are responsible for the bandwidth of principal modes in weak and strong mode coupling regimes. Their interplay leads to a nonmonotonic transition of the average principal mode bandwidth from weak to strong mode coupling. Taking into account the modedependent loss in the fiber, our numerical results are in qualitative agreement with our experimental observations. Our study paves the way for exploring potential applications of principal modes in communication, imaging and spectroscopy.  
Published: 20170206 

Spectral hole burning and its application in microwave photonics
S. Putz, A.s Angerer, D. O. Krimer, R. Glattauer, W. J. Munro, S. Rotter, J. Schmiedmayer & J. Majer 

Spectral hole burning, used in inhomogeneously broadened emitters, is a wellestablished optical technique, with applications from spectroscopy to slow light and frequency combs. In microwave photonics, electron spin ensembles are candidates for use as quantum memories with potentially long storage times. Here, we demonstrate longlived collective dark states by spectral hole burning in the microwave regime. The coherence time in our hybrid quantum system (nitrogen–vacancy centres strongly coupled to a superconducting microwave cavity) becomes longer than both the ensemble's freeinduction decay and the bare cavity dissipation rate. The hybrid quantum system thus performs better than its individual subcomponents. This opens the way for longlived quantum multimode memories, solidstate microwave frequency combs, spin squeezed states, opticaltomicrowave quantum transducers and novel metamaterials. Beyond these, new cavity quantum electrodynamics experiments will be possible where spin–spin interactions and manybody phenomena are directly accessible.  
Published: 20161121 

Sustained photon pulse revivals from inhomogeneously broadened spin ensembles
D. O. Krimer, M. Zens, S. Putz and S. Rotter 

A very promising recent trend in applied quantum physics is to combine the advantageous features of different quantum systems into what is called “hybrid quantum technology”. One of the key elements in this new field will have to be a quantum memory enabling to store quanta over extended periods of time. Systems that may fulfill the demands of such applications are combshaped spin ensembles coupled to a cavity. Due to the decoherence induced by the inhomogeneous ensemble broadening, the storage time of these quantum memories is, however, still rather limited. Here we demonstrate how to overcome this problem by burning wellplaced holes into the spectral spin density leading to spectacular performance in the multimode regime. Specifically, we show how an initial excitation of the ensemble leads to the emission of more than a hundred wellseparated photon pulses with a decay rate significantly below the fundamental limit of the recently proposed “cavity protection effect”.  
Published: 20161122 

Constant Intensity Supermodes in NonHermitian Lattices
K.G. Makris, Z.H. Musslimani, D.N. Christodoulides, S. Rotter 

We study the existence of a novel class of waves, with constant intensity (CI) in coupled nonHermitian photonic systems. These generalized plane waves exist only in optical structures that are composed of gain and loss (in both linear and nonlinear domains). In the framework of coupled mode theory, we examine the properties of such supermodes in finite waveguide lattices. In particular, CIsupermodes with periodic, localized, and disordered phases in finite chains of optical elements are considered in detail. Extensions to the nonlinear regime and the connection to the continuum limit are also studied.  
Published: 201609 

Random lasers for broadband directional emission
S. Schönhuber, M. Brandstetter, T. Hisch, C. Deutsch, M. Krall, H. Detz, A. M. Andrews, G. Strasser, S. Rotter, and K. Unterrainer 

Broadband coherent light sources are becoming increasingly important for sensing and spectroscopic applications, especially in the midinfrared and terahertz (THz) spectral regions, where the unique absorption characteristics of a whole host of molecules are located. The desire to miniaturize such light emitters has recently led to spectacular advances, with compact onchip lasers that cover both of these spectral regions. The long wavelength and small size of the sources result in a strongly diverging laser beam that is difficult to focus on the target that one aims to perform spectroscopy with. Here, we introduce an unconventional solution to this vexing problem, relying on a random laser to produce coherent broadband THz radiation as well as an almost diffractionlimited farfield emission profile. Our random lasers do not require any fine tuning and thus constitute a promising example of practical device applications for random lasing.  
Published: 20160921 

PTsymmetry breaking in the steady state of microscopic gain–loss systems
K. V. Kepesidis, T. J. Milburn, J. Huber, K. G. Makris, S. Rotter and P. Rabl 

The phenomenon of PT (parity and timereversal) symmetry breaking is conventionally associated with a change in the complex mode spectrum of a nonHermitian system that marks a transition from a purely oscillatory to an exponentially amplified dynamical regime. In this work we describe a new type of PTsymmetry breaking, which occurs in the steadystate energy distribution of open systems with balanced gain and loss. In particular, we show that the combination of nonlinear saturation effects and the presence of thermal or quantum noise in actual experiments results in unexpected behavior that differs significantly from the usual dynamical picture. We observe additional phases with preserved or 'weakly' broken PTsymmetry, and an unconventional transition from a highnoise thermal state to a lowamplitude lasing state with broken symmetry and strongly reduced fluctuations. We illustrate these effects here for the specific example of coupled mechanical resonators with optically induced loss and gain, but the described mechanisms will be essential for a general understanding of the steadystate properties of actual PTsymmetric systems operated at low amplitudes or close to the quantum regime.  
Published: 20160907 

Diffusive to quasiballistic random laser: incoherent and coherent models
W. Guerin, Y. D. Chong, Q. Baudouin, M. Liertzer, S. Rotter, and R. Kaiser 

We study the crossover between the diffusive and quasiballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasiballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.  
Published: 20160812 

Effective PTsymmetric metasurfaces for subwavelength amplified sensing
S. Xiao, J. Gear, S. Rotter and J. Li 

We propose a novel design principle for ultrathin metasurfaces to realize optically amplified sensing with a performance that exceeds those of passive coherent perfect absorbers by several orders of magnitude. Our strategy is based on a generalized condition of lasing, coherent perfect absorption and their coexistence in metamaterials that feature an effective PTsymmetry. The devices we introduce here can be operated in configurations that involve both a onesided or a twosided wave incidence, where the latter case allows us to tune the degree of amplified absorption through the coherent phase between the two input beams. We also discuss how the conditions on the material parameters can be relaxed, away from the ideal case, such that a substantial amplification of the sensing performance can easily be reached in practical applications.  
Published: 20160808 

Spatiotemporal Control of Light Transmission through a Multimode Fiber with Strong Mode Coupling
W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao 

We experimentally generate and characterize eigenstates of the WignerSmith timedelay matrix, called principal modes, in a multimode fiber with strong mode coupling. The unique spectral and temporal properties of principal modes enable global control of temporal dynamics of optical pulses transmitted through the fiber, despite random mode mixing. Our analysis reveals that welldefined delay times of the eigenstates are formed by multipath interference, which can be effectively manipulated by spatial degrees of freedom of input wave fronts. This study is essential to controlling dynamics of wave scattering, paving the way for coherent control of pulse propagation through complex media.  
Published: 20160725 

Particlelike wave packets in complex scattering systems
B. Gérardin, J. Laurent, P. Ambichl, C. Prada, S. Rotter, and A. Aubry 

A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging, or communication purposes. Controlling wave propagation through complex systems is thus of fundamental interest in many areas, ranging from optics or acoustics to medical imaging or telecommunications. Here, we study the propagation of elastic waves in a cavity and a disordered waveguide by means of laser interferometry. From the direct experimental access to the timedelay matrix of these systems, we demonstrate the existence of particlelike wave packets that remain focused in time and space throughout their complex trajectory. Due to their limited dispersion, their selective excitation will be crucially relevant for all applications involving selective wave focusing and efficient information transfer through complex media.  
Published: 20160725 

Modulational instability in a PTsymmetric vector nonlinear Schrödinger system
J.T. Cole, K.G. Makris, Z.H. Musslimani, D.N. Christodoulides, S. Rotter 

A class of exact multicomponent constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PTPTsymmetric complex potential is constructed. This type of uniform wave pattern displays a nontrivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constantintensity continuous waves are then used to perform a modulational instability analysis in the presence of both nonhermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier–Floquet–Bloch theory. In the selffocusing case, we identify an intensity threshold above which the constantintensity modes are modulationally unstable for any Floquet–Bloch momentum belonging to the first Brillouin zone. The picture in the selfdefocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.  
Published: 20160725 

Dynamically encircling an exceptional points for asymmetric mode switching
J. Doppler, A.A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T.J. Milburn, P. Rabl, N. Moiseyev, S. Rotter 

Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a stateflip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a twomode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.  
Published: 20160725 Press release TU Wien, 20160726 [46/2016] 

Chiral modes and directional lasing at exceptional pointsB. Peng, S.K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, L. Yang 

Controlling the emission and the flow of light in micro and nanostructures is crucial for onchip information processing. Here we show how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point (EP)—a degeneracy universally occurring in all open physical systems when two eigenvalues and the corresponding eigenstates coalesce. In our experiments with a fibercoupled whisperinggallerymode (WGM) resonator, we dynamically control the chirality of resonator modes and the emission direction of a WGM microlaser in the vicinity of an EP: Away from the EPs, the resonator modes are nonchiral and laser emission is bidirectional. As the system approaches an EP, the modes become chiral and allow unidirectional emission such that by transiting from one EP to another one the direction of emission can be completely reversed. Our results exemplify a very counterintuitive feature of nonHermitian physics that paves the way to chiral photonics on a chip.  
Published: 20160621 

Twofold PT symmetry in doubly exponential optical latticesJ.T. Cole, K.G. Makris, Z.H. Musslimani, D.N. Christodoulides, S. Rotter 

We introduce a family of nonHermitian optical potentials that are given in terms of doubleexponential periodic functions. The center of ΡΤ symmetry is not around zero and the potential satisfies a shifted ΡΤsymmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted ΡΤsymmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.  
Published: 20160104 

Interactioninduced mode switching in steadystate microlasersL. Ge, D. Liu, A. Cerjan, S. Rotter, H. Cao, S.G. Johnson, H.E. Türeci, A.D. Stone 

We demonstrate that due to strong modal interactions through crossgain saturation, the onset of a new lasing mode can switch off an existing mode via a negative power slope. In this process of interactioninduced mode switching (IMS) the two involved modes maintain their identities, i.e. they do not change their spatial field patterns or lasing frequencies. For a fixed pump profile, a simple analytic criterion for the occurrence of IMS is given in terms of their self and crossinteraction coefficients and noninteracting thresholds, which is verified for the example of a twodimensional microdisk laser. When the spatial pump profile is varied as the pump power is increased, IMS can be induced even when it would not occur with a fixed pump profile, as we show for two coupled laser cavities. Our findings apply to steadystate lasing and are hence different from dynamical mode switching or hopping. IMS may have potential applications in robust and flexible alloptical switching.  
Published: 20160104 

General description of quasiadiabatic dynamical phenomena near exceptional pointsT.J. Milburn, J. Doppler, C.A. Holmes, S. Portolan, S. Rotter, P. Rabl 

The appearance of socalled exceptional points in the complex spectra of nonHermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the stateexchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyze this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasistationarity interrupted by abrupt nonadiabatic transitions and we present a qualitative and quantitative description of this switching behavior by connecting the problem to the phenomenon of stability loss delay. This approach makes accurate predictions for the breakdown of the adiabatic theorem as well as the occurrence of chiral behavior observed previously in this context and provides a general framework to model and understand quasiadiabatic dynamical effects in nonHermitian systems.  
Published: 20151130 

Smooth Optimal Quantum Control for Robust SolidState Spin MagnetometryT. Nöbauer, A. Angerer, B. Bartels, M. Trupke, S. Rotter, J. Schmiedmayer, F. Minert, J. Majer 

We experimentally demonstrate a simple yet versatile optimal quantum control technique that achieves tailored robustness against qubit inhomogeneities and control errors while requiring minimal bandwidth. We apply the technique to nitrogenvacancy (NV) centers in diamond and verify its performance using quantum process tomography. In a widefield NV center magnetometry scenario, we achieve a homogeneous sensitivity across a 33% drop in control amplitude, and we improve the sensitivity by up to 2 orders of magnitude for a normalized detuning as large as 40%, achieving a value of 20 nT Hz^{1/2} μm^{3/2} in sensitivity times square root volume.  
Published: 20151106 

Analytical study of quantumfeedbackenhanced Rabi oscillationsJ. Kabuss, D.O. Krimer, S. Rotter, K. Stannigel, A. Knorr, A. Carmele 

We present an analytical solution of the singlephoton quantum feedback in a cavity quantum electrodynamics system based on a halfcavity setup coupled to a structured continuum. Our exact analytical expression constitutes an important benchmark for quantumfeedback models and allows us to unravel the necessary conditions for the previously reported numerical result that a singleemittercavity system, which is initially in the weakcoupling regime, can be driven into the strongcoupling regime via the proposed quantumfeedback mechanism [A. Carmele et al., Phys. Rev. Lett. 110, 013601 (2013)]. We specify the phase relations between the cavity mode and the delay time and state explicitly the theoretical limit for a feedback effect in the singlephoton regime. Via the photonpath representation, we prove that the stabilization phenomenon relies on a destructive interference effect and we discuss the stabilization time in the weak and strongcoupling limits.  
Published: 20151102 

Steadystate ab initio laser theory for fully or nearly degenerate cavity modesS. Burkhardt, M. Liertzer, D.O. Krimer, S. Rotter 

We investigate the range of validity of the recently developed steadystate ab initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring fully or nearly degenerate pairs of resonator modes above the lasing threshold. Here we demonstrate how SALT can indeed be extended to describe such cases as well, with the effect that we significantly broaden the theory’s scope. In particular, we show how to use SALT in conjunction with a linear stability analysis to obtain stable singlemode lasing solutions that involve a degenerate mode pair. Our flexible and efficient approach is tested on onedimensional ring lasers as well as on twodimensional microdisk lasers with broken symmetry.  
Published: 20150727 

Hybrid Quantum Systems with Collectively Coupled Spin States: Suppression of Decoherence through Spectral Hole BurningD.O. Krimer, B. Hartl, S. Rotter 

Spin ensemble based hybrid quantum systems suffer from a significant degree of decoherence resulting from the inhomogeneous broadening of the spin transition frequencies in the ensemble. We demonstrate that this strongly restrictive drawback can be overcome simply by burning two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Using this procedure we find an increase of the coherence time by more than an order of magnitude as compared to the case without hole burning. Our findings pave the way for the practical use of these hybrid quantum systems for the processing of quantum information.  
Published: 20150714 

Constantintensity waves and their modulation instability in nonHermitian potentialsK.G. Makris, Z.H. Musslimani, D.N. Christodoulides, S. Rotter 

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave’s constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with nonHermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on nonHermitian scattering that have recently been put forward.  
Published: 20150708 Press release TU Wien, 20150810 [80/2015] 

Paritytime symmetry from stacking purely dielectric and magnetic slabsJ. Gear, F. Liu, S.T. Chu, S. Rotter, J. Li 

We show that paritytime symmetry in matching electric permittivity to magnetic permeability can be established by considering an effective parity operator involving both mirror symmetry and coupling between electric and magnetic fields. This approach extends the discussion of paritytime symmetry to the situation with more than one material potential. We show that the band structure of a onedimensional photonic crystal with alternating purely dielectric and purelymagnetic slabs can undergo a phase transition between propagation modes and evanescent modes when the balanced gain or loss parameter is varied. The cross matching between different material potentials also allows exceptional points of the constitutive matrix to appear in the longwavelength limit where they can be used to construct ultrathin metamaterials with unidirectional reflection.  
Published: 20150320 

Invariance property of wave scattering through disordered mediaR. Pierrat, P. Ambichl, S. Gigan, A. Haber, R. Carminati, S. Rotter 

A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system’s boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.  
Published: 20141128 Press release TU Wien, 20141126 [117/2014] 

NonMarkovian dynamics of a singlemode cavity strongly coupled to an inhomogeneously broadened spin ensembleD.O. Krimer, S. Putz, J. Majer, S. Rotter 

We study the dynamics of a spin ensemble strongly coupled to a singlemode resonator driven by external pulses. When themean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spincavity dynamics. On this basis we show that coherent oscillations between the spin ensemble and the cavity can be enhanced by a few orders of magnitude, when driving the system with pulses that match special resonance conditions. Our theoretical approach is tested successfully with an experiment based on an ensemble of negatively charged nitrogenvacancy centers in diamond strongly coupled to a superconducting coplanar singlemode waveguide resonator.  
Published: 20141024 

Lossinduced suppression and revival of lasingB. Peng, S.K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C.M. Bender, F. Nori, L. Yang 

Controlling and reversing the effects of loss are major challenges in optical systems. For lasers, losses need to be overcome by a sufficient amount of gain to reach the lasing threshold. In this work, we show how to turn losses into gain by steering the parameters of a system to the vicinity of an exceptional point (EP), which occurs when the eigenvalues and the corresponding eigenstates of a system coalesce. In our system of coupled microresonators, EPs are manifested as the lossinduced suppression and revival of lasing. Below a critical value, adding loss annihilates an existing Raman laser. Beyond this critical threshold, lasing recovers despite the increasing loss, in stark contrast to what would be expected from conventional laser theory. Our results exemplify the counterintuitive features of EPs and present an innovative method for reversing the effect of loss.  
Published: 20141017 Press release TU Wien, 20141017 [103/2014] 

Protecting a spin ensemble against decoherence in the strongcoupling regime of cavity QEDS. Putz, D.O. Krimer, R. Amsüss, A. Valookaran, T. Nöbauer, J. Schmiedmayer, S. Rotter, J. Majer 

Hybrid quantum systems based on spin ensembles coupled to superconducting microwave cavities are promising candidates for robust experiments in cavity quantum electrodynamics (QED) and for future technologies employing quantum mechanical effects. At present, the main source of decoherence in these systems is inhomogeneous spin broadening, which limits their performance for the coherent transfer and storage of quantum information. Here we study the dynamics of a superconducting cavity strongly coupled to an ensemble of nitrogen–vacancy centres in diamond. We experimentally observe how decoherence induced by inhomogeneous broadening can be suppressed in the strongcoupling regime  a phenomenon known as ‘cavity protection’. To demonstrate the potential of this effect for coherentcontrol schemes, we show how appropriately chosen microwave pulses can increase the amplitude of coherent oscillations between the cavity and spin ensemble by two orders of magnitude.  
Published: 20140817 Press release TU Wien, 20140818 [87/2014] 

Reversing the pump dependence of a laser at an exceptional pointM. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H.E. Türeci, G. Strasser, K. Unterrainer, S. Rotter 

When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a socalled exceptional point occurs, which acts as a source of nontrivial physics in a diverse range of systems. Lasers provide a natural setting to study such nonHermitian degeneracies, as they feature resonant modes and a gain material as their basic constituents. Here we show that exceptional points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power.  
Published: 20140603 Press release TU Wien, 20140617 [63/2014] 

Reflection resonances in surfacedisordered waveguides: strong higherorder effects of the disorderJ. Doppler, J.A. MéndezBermúdez, J. Feist, O. Dietz, D.O. Krimer, N.M. Makarov, F.M. Izrailev, S. Rotter 

We study coherent wave scattering through waveguides with a steplike surface disorder and find distinct enhancements in the reflection coefficients at welldefined resonance values. Based on detailed numerical and analytical calculations, we can unambiguously identify the origin of these reflection resonances to be higherorder correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.  
Published: 20140509 

Random lasers: Playing pinball with lightS. Rotter


Without a welldefined cavity, there is no obvious way to control the resonant modes in a random laser. Experiments now show that shaping the optical pump allows for controlled singlemode operation at predetermined lasing wavelengths.  
Published: 20140420 

The singlechannel regime of transport through random mediaA. Pena, A. Girschik, F. Libisch, S. Rotter, A.A. Chabanov 

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi1D systems, the single dominant transmission eigenchannel is formed by an individual Andersonlocalized mode or by a ‘necklace state’. In this singlechannel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the singlechannel regime and pulsed excitations of the disordered samples allows us to identify longlived localized modes and shortlived necklace states at long and short time delays, respectively.  
Published: 20140324 

Route from spontaneous decay to complex multimode dynamics in cavity QEDD.O. Krimer, M. Liertzer, S. Rotter, H.E. Türeci 

We study the nonMarkovian quantum dynamics of an emitter inside an open multimode cavity, focusing on the case where the emitter is resonant with highfrequency cavity modes. Based on a Green’sfunction technique suited for open photonic structures, we study the crossovers between three distinct regimes as the coupling strength is gradually increased: (i) overdamped decay with a time scale given by the Purcell modified decay rate, (ii) underdamped oscillations with a time scale given by the effective vacuum Rabi frequency, and (iii) pulsed revivals. The final multimode strongcoupling regime (iii) gives rise to quantum revivals of the atomic inversion on a time scale associated with the cavity roundtrip time. We show that the crucial parameter to capture the crossovers between these regimes is the nonlinear Lamb shift, accounted for exactly in our formalism.  
Published: 20140311 

Breaking of ΡΤ Symmetry in Bounded and Unbounded Scattering SystemsP. Ambichl, K.G. Makris, L. Ge, Y. Chong, A.D. Stone, S. Rotter 

PTsymmetric scattering systems with balanced gain and loss can undergo a symmetrybreaking transition in which the eigenvalues of the nonunitary scattering matrix change their phase shifts from real to complex values. We relate the PTsymmetrybreaking points of such an unbounded scattering system to those of the underlying bounded systems. In particular, we show how the PT thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.  
Published: 20131218 

Doublelayered nanoparticle stacks for surface enhanced infrared absorption spectroscopyJ. Srajer, A. Schwaighofer, G. Ramer, S. Rotter, B. Guenay, A. Kriegner, W. Knoll, B. Lendl, C. Nowak 

We demonstrate that doublelayered stacks of gold and insulator nanoparticles arranged on a flat gold surface dramatically enhance the sensitivity in absorption infrared microscopy. Through morphological variations of the nanoparticles, the frequency of the plasmon resonances can be tuned to match the frequency of the molecular vibration in the midinfrared region. The results show that the nanostructures enhance the absorption signal of the molecules by a factor of up to ∼2.2 x 10^{6}, while preserving their characteristic lineshape remarkably well.  
Published: 20131022 

Domesticating random lasersM. Liertzer, S. Rotter 

When pumped with a spatially modulated light beam, random lasers can be tuned to emit into specific, predetermined directions.  
Published: 20130920 

PumpControlled Directional Light Emission from Random LasersT. Hisch, M. Liertzer, D. Pogany, F. Mintert, S. Rotter 

The angular emission pattern of a random laser is typically very irregular and difficult to tune. Here we show by detailed numerical calculations that one can overcome the lack of control over this emission pattern by actively shaping the spatial pump distribution. We demonstrate, in particular, how to obtain customized pump profiles to achieve highly directional emission. Going beyond the regime of strongly scattering media where localized modes with a given directionality can simply be selected by the pump, we present an optimizationbased approach which shapes extended lasing modes in the weakly scattering regime according to any predetermined emission pattern.  
Published: 20130712 
