arXiv subjects

Stefan Rotter

Publications and source records attributed to Stefan Rotter.

At least 127 records · Page 7Linked to original sources

arXiv2014

Route from spontaneous decay to complex multimode dynamics in cavity QED

We study the non-Markovian quantum dynamics of an emitter inside an open multimode cavity, focusing on the case where the emitter is resonant with high-frequency cavity modes. Based on a Green's function 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 strong coupling regime (iii) gives rise to quantum revivals of the atomic inversion on a time scale associated with the cavity round-trip 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.

quant-ph↗

arXiv2013

Breaking of PT-symmetry in bounded and unbounded scattering systems

PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry breaking points of such an unbounded scattering system to those of 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.

physics.optics↗

arXiv2013

Pump-Controlled Directional Light Emission from Random Lasers

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 optimization-based approach which shapes extended lasing modes in the weakly scattering regime according to any predetermined emission pattern.

physics.optics↗

arXiv2013

Impact of intrinsic biophysical diversity on the activity of spiking neurons

We study the effect of intrinsic heterogeneity on the activity of a population of leaky integrate-and-fire neurons. By rescaling the dynamical equation, we derive mathematical relations between multiple neuronal parameters and a fluctuating input noise. To this end, common input to heterogeneous neurons is conceived as an identical noise with neuron-specific mean and variance. As a consequence, the neuronal output rates can differ considerably, and their relative spike timing becomes desynchronized. This theory can quantitatively explain some recent experimental findings.

q-bio.NC↗

arXiv2012

Recurrent Interactions in Spiking Networks with Arbitrary Topology

The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations emerges in sparsely connected networks. We apply linear response theory to evaluate the influence of detailed network structure on neuron dynamics. It turns out that pairwise correlations induced by direct and indirect network connections can be related to the matrix of direct linear interactions. Furthermore, we study the influence of characteristics of the neuron model. Interpreting the reset as self-inhibition we examine its influence, via the spectrum of single neuron activity, on network autocorrelation functions and the overall correlation level. The neuron model also affects the form of interaction kernels and consequently the time-dependent correlation functions. We finally find that a linear instability of networks with Erdős-Rényi topology coincides with a global transition to a highly correlated network state. Our work shows that recurrent interactions have a profound impact on spike train statistics and provides tools to study effects of specific network topologies.

q-bio.NC↗

arXiv2011

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models.

physics.soc-ph↗

arXiv2011

Cavity QED with magnetically coupled collective spin states

We report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to 13C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time T1 of the NV center at millikelvin temperatures in a non-destructive way.

cond-mat.mes-hall↗

arXiv2011

Generating particle-like scattering states in wave transport

We introduce a procedure to generate scattering states which display trajectory-like wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates to the Wigner-Smith time-delay matrix and to the transmission matrix with classical (noiseless) transmission eigenvalues close to 0 or 1. Our procedure to create such beam-like states is based solely on the scattering matrix and successfully tested numerically for regular, chaotic and disordered cavities. These results pave the way for the experimental realization of highly collimated wave fronts in transport through complex media with possible applications like secure and low-power communication.

cond-mat.mes-hall↗

arXiv2010

The perfect integrator driven by Poisson input and its approximation in the diffusion limit

In this note we consider the perfect integrator driven by Poisson process input. We derive its equilibrium and response properties and contrast them to the approximations obtained by applying the diffusion approximation. In particular, the probability density in the vicinity of the threshold differs, which leads to altered response properties of the system in equilibrium.

q-bio.NC↗

arXiv2010

Probing decoherence through Fano resonances

We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex plane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.

cond-mat.mes-hall↗

arXiv2010

Non-equilibrium dynamics of stochastic point processes with refractoriness

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze non-stationary renewal processes.

math.PR↗

arXiv2009

Multiplicatively interacting point processes and applications to neural modeling

We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for recurrent networks of spiking neurons with exponential transfer functions. The expected rates of all neurons in the network are approximated by a first-order differential system. We study the stability of the solutions of this equation, and use the new formalism to implement a winner-takes-all network that operates robustly for a wide range of parameters. Finally, we discuss relations with the generalised linear model that is widely used for the analysis of spike trains.

math.PR↗

arXiv2009

Transport through open quantum dots: making semiclassics quantitative

We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual energy and magnetic field dependent elements of the scattering matrix. Two key ingredients are essential: (i) inclusion of pseudo-paths which have the topology of linked classical paths resulting from diffraction in addition to classical paths and (ii) a high-level approximation to diffractive scattering. Within this framework of the pseudo-path semiclassical approximation (PSCA), typical shortcomings of semiclassical theories such as violation of the anti-correlation between reflection and transmission and the overestimation of conductance fluctuations are overcome. Beyond its predictive capabilities the PSCA provides deeper insights into the quantum-to-classical crossover.

cond-mat.mes-hall↗

arXiv2009

The strong-coupling limit of a Kondo spin coupled to a mesoscopic quantum dot: effective Hamiltonian in the presence of exchange correlations

We consider a Kondo spin that is coupled antiferromagnetically to a large chaotic quantum dot. Such a dot is described by the so-called universal Hamiltonian and its electrons are interacting via a ferromagnetic exchange interaction. We derive an effective Hamiltonian in the limit of strong Kondo coupling, where the screened Kondo spin effectively removes one electron from the dot. We find that the exchange coupling constant in this reduced dot (with one less electron) is renormalized and that new interaction terms appear beyond the conventional terms of the strong-coupling limit. The eigenenergies of this effective Hamiltonian are found to be in excellent agreement with exact numerical results of the original model in the limit of strong Kondo coupling.

cond-mat.mes-hall↗

arXiv2009

Ab initio self-consistent laser theory and random lasers

We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by fully time-dependent numerical simulations or by using major approximations which neglect non-linear modal interactions and/or the openness of the laser system. We have found a time-independent technique for determining these stationary solutions which can treat lasers of arbitrary complexity and degree of openness. Our method has been shown to agree with time-dependent numerical solutions to high accuracy and has been applied to find the electric field patterns (lasing modes) of random lasers, which lack a laser cavity and are so strongly damped that the linear system has no detectable resonances. Our work provides a link between an important non-linear wave system and the field of quantum/wave chaos in linear systems.

physics.optics↗

arXiv2008

Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems

Quantum systems with discrete symmetries can usually be desymmetrized, but this strategy fails when considering transport in open systems with a symmetry that maps different openings onto each other. We investigate the joint probability density of transmission eigenvalues for such systems in random-matrix theory. In the orthogonal symmetry class we show that the eigenvalue statistics manifests level repulsion between only every second transmission eigenvalue. This finds its natural statistical interpretation as a staggeredsuperposition of two eigenvalue sequences. For a large number of channels, the statistics for a system with a lead-transposing symmetry approaches that of a superposition of two uncorrelated sets of eigenvalues as in systems with a lead-preserving symmetry (which can be desymmetrized). These predictions are confirmed by numerical computations of the transmission-eigenvalue spacing distribution for quantum billiards and for the open kicked rotator.

cond-mat.mes-hall↗

arXiv2008

Strong Interactions in Multimode Random Lasers

Unlike conventional lasers, diffusive random lasers (DRLs) have no resonator to trap light and no high-Q resonances to support lasing. Due to this lack of sharp resonances the DRL has presented a challenge to conventional laser theory. We present a theory able to treat the DRL rigorously, and provide results on the lasing spectra, internal fields and output intensities of DRLs. Typically DRLs are highly multimode lasers, emitting light at a number of wavelengths. We show that the modal interactions through the gain medium in such lasers are extremely strong and lead to a uniformly spaced frequency spectrum, in agreement with recent experimental observations.

physics.optics↗

arXiv2008

Diffractive paths for weak localization in quantum billiards

We study the weak localization effect in quantum transport through a clean ballistic cavity with regular classical dynamics. We address the question which paths account for the suppression of conductance through a system where disorder and chaos are absent. By exploiting both quantum and semiclassical methods, we unambiguously identify paths that are diffractively backscattered into the cavity (when approaching the lead mouths from the cavity interior) to play a key role. Diffractive scattering couples transmitted and reflected paths and is thus essential to reproduce the weak-localization peak in reflection and the corresponding anti-peak in transmission. A comparison of semiclassical calculations featuring these diffractive paths yields good agreement with full quantum calculations and experimental data. Our theory provides system-specific predictions for the quantum regime of few open lead modes and can be expected to be relevant also for mixed as well as chaotic systems.

cond-mat.mes-hall↗