arXiv subjects

Jan Wiersig

Publications and source records attributed to Jan Wiersig.

At least 37 records · Page 2Linked to original sources

arXiv2018

Spontaneous $\mathcal{T}$-symmetry breaking and exceptional points in cavity quantum electrodynamics systems

Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which an atomic ensemble interacts coherently with a single resonant cavity mode. The interacting system can be effectively described by two coupled oscillators with positive and negative mass when the two-level atoms are prepared in their excited states. The occurrence of symmetry breaking is controlled by the atomic detuning and the coupling to the cavity mode, which naturally divides the parameter space into the symmetry broken and symmetry unbroken phases. The two phases are separated by a spectral singularity, a so-called exceptional point, where the eigenstates of the Hamiltonian coalesce. When encircling the singularity in the parameter space, the quasi-adiabatic dynamics shows chiral mode switching which enables topological manipulation of quantum states.

quant-ph↗

arXiv2017

Exploring the Photon-Number Distribution of Bimodal Microlasers

A photon-number resolving transition edge sensor (TES) is used to measure the photon-number distribution of two microcavity lasers. The investigated devices are bimodal microlasers with similar emission intensity and photon statistics with respect to the photon auto-correlation. Both high-$β$ microlasers show partly thermal and partly coherent emission around the lasing threshold. For higher pump powers, the strong mode of microlaser A emits Poissonian distributed photons while the emission of the weak mode is thermal. In contrast, laser B shows a bistability resulting in overlayed thermal and Poissonian distributions. While a standard Hanbury Brown and Twiss experiment cannot distinguish between simple thermal emission of laser A and the mode switching of laser B, a TES allows us to measure the photon-number distribution which provides important insight into the underlying emission processes. Indeed, our experimental data and its theoretical description by a master equation approach show that TESs are capable of revealing subtle effects like temporal mode switching of bimodal microlasers. As such our studies clearly demonstrate the huge benefit and importance of investigating nanophotonic devices via photon-number resolving sensors.

cond-mat.mes-hall↗

arXiv2015

Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity

The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and two waveguide coupled to the cavity. Due to the evanescent field's scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, the effect of a Kerr nonlinearity on the doublets is numerically investigated in the more general context of the relationship between cubic nonlinearity and dynamical tunneling. Within the numerical realization of the model system, it is observed that the doublets shows a bistable transition in its transmission curve as the Kerr-nonlinearity in the cavity is increased. At the same time, one rotational mode gets dominant over the other one in the transmission, since the two states in the doublet have uneven linewidths. By using coupled mode theory, the underlying mode dynamics of the phenomena is theoretically modelled and clarified.

physics.optics↗

arXiv2015

Rotating optical microcavities with broken chiral symmetry

We demonstrate in open microcavities with broken chiral symmetry, quasi-degenerate pairs of co-propagating modes in a non-rotating cavity evolve to counter-propagating modes with rotation. The emission patterns change dramatically by rotation, due to distinct output directions of CW and CCW waves. By tuning the degree of spatial chirality, we maximize the sensitivity of microcavity emission to rotation. The rotation-induced change of emission is orders of magnitude larger than the Sagnac effect, pointing to a promising direction for ultrasmall optical gyroscopes.

physics.optics↗

arXiv2014

Nonhermitian transport effects in coupled-resonator optical waveguides

Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., nonhermitian degeneracies at which not only the frequencies and decay rates coalesce but also the eigenmodes themselves. The non-hermitian corrections to the group velocity are largest in the regions around the exceptional points.

physics.optics↗

arXiv2013

Multimode Coupling by Boundary Wave Scattering

We show that coupling among multiple resonances can be conveniently introduced and controlled by boundary wave scattering. We demonstrate this principle in optical microcavities of quasi-circular shape, where the couplings of multiple modes are determined by the scattering from different harmonic boundary deformations. We analyze these couplings using a perturbation theory, which gives an intuitive understanding of the first-order and higher-order scattering processes. Different scattering paths between two boundary waves can either enhance or reduce their coupling strength. The effect of controlled multimode coupling is most pronounced in the direction of output from an open cavity, which can cause a dramatic change of the external cavity field distribution.

physics.optics↗

arXiv2012

Local chirality of optical waves in ultrasmall resonators

The local chiral symmetry between clockwise (CW) and counter-clockwise (CCW) propagating light in a deformed microcavity can be broken by wave optics effects, which become significant as the cavity size approaches the wavelength. We show that the spatial separation of the CW and CCW ray orbits underlying the high quality factor resonant modes results in unidirectional emission in free space. In the presence of a waveguide, evanescent coupling also becomes directional, and the output direction can be varied by selecting the coupling position along the cavity boundary. Our results demonstrate that the local chirality can be utilized to control the output directionality and enhance the collection efficiency of emission from ultrasmall resonators.

physics.optics↗

arXiv2011

Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities

Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes which agrees well with the predictions from an effective non-Hermitian Hamiltonian. A comparison to ray-tracing simulations is given.

physics.optics↗

arXiv2010

Measurement of the Goos-Hänchen shift in a microwave cavity

We present measurements of the Goos-Hänchen shift in a two-dimensional dielectric microwave cavity. Microwave beams are generated by a suitable superposition of the spherical waves generated by an array of antennas; the resulting beams are then reflected at a planar interface. By measuring the electric field including its phase, Poynting vectors of the incoming and reflected beams can be extracted, which in turn are used to find the incoming angle and the positions where the beam hits the interface and where it is reflected. These positions directly yield the Goos-Hänchen shift. The results are compared to the classical Artmann result and a numerical calculation using Gaussian beams.

physics.optics↗

arXiv2010

Electromagnetic modes in cavities made of negative-index metamaterials

We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads to quasi-bound states with a negative quality factor. To ensure positive quality factors and a consistent physical interpretation of the quasi-bound states it is essential to include the frequency dispersion of the permittivity and the permeability, as required by positive field energy and causality. The basic mode equation and the boundary conditions including linear frequency dispersion are derived. As an example we consider a disk-like cavity with deformed cross sectional shape. The transition from the unphysical nondispersive case with negative quality factors to the dispersive case with positive quality factors is demonstrated numerically and in an analytical perturbative treatment.

physics.optics↗

arXiv2009

Marginally Unstable Periodic Orbits in Semiclassical Mushroom Billiards

Optical mushroom shaped billiards offer a unique opportunity to isolate and study non-dispersive, marginally unstable periodic orbits. Here we show that the openness of the cavity to external fields presents unanticipated consequences for the far-field distribution, including directional emission. This is mediated by interactions of marginally unstable periodic orbits with chaotic modes and is potentially relevant for the design of microcavity lasers. We also show that such orbits are robust against perturbations to the shape of the cavity, despite the non-generic character of the classical counterpart and the lack of structural stability of the corresponding classical orbits.

nlin.CD↗

arXiv2009

Ray-wave correspondence in limacon-shaped semiconductor microcavities

The limacon-shaped semiconductor microcavity is a ray-chaotic cavity sustaining low-loss modes with mostly unidirectional emission patterns. Investigating these modes systematically, we show that the modes correspond to ray description collectively, rather than individually. In addition, we present experimental data on multimode lasing emission patterns that show high unidirectionality and closely agree with the ray description. The origin of this agreement is well explained by the collective correspondence mechanism.

physics.optics↗

arXiv2009

Quality factors and dynamical tunneling in annular microcavities

The key characteristic of an optical mode in a microcavity is its quality factor describing the optical losses. The numerical computation of this quantity can be very demanding for present-day devices. Here we show for a certain class of whispering-gallery cavities that the quality factor is related to dynamical tunneling, a phenomenon studied in the field of quantum chaos. We extend a recently developed approach for determining dynamical tunneling rates to open cavities. This allows us to derive an analytical formula for the quality factor which is in very good agreement with full solutions of Maxwell's equations.

physics.optics↗

arXiv2008

Lifetime statistics in chaotic dielectric microresonators

We discuss the statistical properties of lifetimes of electromagnetic eigenmodes in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed random-matrix model very well describes the lifetime statistics of long-lived resonances, provided that two effective parameters are appropriately renormalized. This renormalization is linked to the formation of anomalously short-lived resonances, a mechanism also known from the fractal Weyl law and the resonance trapping phenomenon.

physics.optics↗

arXiv2008

Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals

Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the non-orthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly non-orthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.

physics.optics↗

arXiv2008

Goos-Haenchen shift and localization of optical modes in deformed microcavities

Recently, an interesting phenomenon of spatial localization of optical modes along periodic ray trajectories near avoided resonance crossings has been observed [J. Wiersig, Phys. Rev. Lett. 97, 253901 (2006)]. For the case of a microdisk cavity with elliptical cross section we use the Husimi function to analyse this localization in phase space. Moreover, we present a semiclassical explanation of this phenomenon in terms of the Goos-Haenchen shift which works very well even deep in the wave regime. This semiclassical correction to the ray dynamics modifies the phase space structure such that modes can localize either on stable islands or along unstable periodic ray trajectories.

nlin.CD↗

arXiv2007

Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.

nlin.CD↗

arXiv2007

Combining directional light output and ultralow loss in deformed microdisks

A drawback of high-quality modes in optical microdisks is their isotropic light emission characteristics. Here we report a novel, robust, and general mechanism that results in highly directional light emission from those modes. This surprising finding is explained by a combination of wave phenomena (wave localization along unstable periodic ray trajectories) and chaotic ray dynamics in open systems (escape along unstable manifolds). The emission properties originating in the chaotic ray dynamics permit directional light output even from microlasers operating in the common multi-mode regime. We demonstrate our novel mechanism for the limacon billiard family and find directional emission with narrow angular divergence for a significant range of geometries and material parameters.

cond-mat.other↗