Avoided level crossings, diabolic points, and branch points in the complex plane in an open double quantum dot

Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip

Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states, or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.

Metamaterial, plasmonic and nanophotonic devices

The field of metamaterials has opened landscapes of possibilities in basic science, and a paradigm shift in the way we think about and design emergent material properties. In many scenarios, metamaterial concepts have helped overcome long-held scientific challenges, such as the absence of optical magnetism and the limits imposed by diffraction in optical imaging. As the potential of metamaterials, as well as their limitations, become clearer, these advances in basic science have started to make an impact on several applications in different areas, with far-reaching implications for many scientific and engineering fields. At optical frequencies, the alliance of metamaterials with the fields of plasmonics and nanophotonics can further advance the possibility of controlling light propagation, radiation, localization and scattering in unprecedented ways. In this review article, we discuss the recent progress in the field of metamaterials, with particular focus on how fundamental advances in this field are enabling a new generation of metamaterial, plasmonic and nanophotonic devices. Relevant examples include optical nanocircuits and nanoantennas, invisibility cloaks, superscatterers and superabsorbers, metasurfaces for wavefront shaping and wave-based analog computing, as well as active, nonreciprocal and topological devices. Throughout the paper, we highlight the fundamental limitations and practical challenges associated with the realization of advanced functionalities, and we suggest potential directions to go beyond these limits. Over the next few years, as new scientific breakthroughs are translated into technological advances, the fields of metamaterials, plasmonics and nanophotonics are expected to have a broad impact on a variety of applications in areas of scientific, industrial and societal significance.

Unification of the family of Garrison-Wright's phases

Inspired by Garrison and Wight's seminal work on complex-valued geometric phases, we generalize the concept of Pancharatnam's “in-phase” in interferometry and further develop a theoretical framework for unification of the abelian geometric phases for a biorthogonal quantum system modeled by a parameterized or time-dependent nonhermitian hamiltonian with a finite and nondegenerate instantaneous spectrum, that is, the family of Garrison-Wright's phases, which will no longer be confined in the adiabatic and nonadiabatic cyclic cases. Besides, we employ a typical example, Bethe-Lamb model, to illustrate how to apply our theory to obtain an explicit result for the Garrison-Wright's noncyclic geometric phase, and also to present its potential applications in quantum computation and information.

Width bifurcation and dynamical phase transitions in open quantum systems

The states of an open quantum system are coupled via the environment of scattering wave functions. The complex coupling coefficients ω between system and environment arise from the principal value integral and the residuum. At high-level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im(ω) and Re(ω) influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re(ω) in a similar manner as it is well known from discrete states. Im(ω), however, leads to width bifurcation and finally (when the system is coupled to one channel, i.e., to one common continuum of scattering wave functions), to a splitting of the system into two parts with different characteristic time scales. The role of observer states is discussed. Physically, the system is stabilized by this splitting since the lifetimes of some states are longer than before, while that of one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wave functions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for N=2,4, and 10 states coupled mostly to one channel.

Feshbach projection formalism for transmission through a time-periodic potential

The Feshbach projection formalism is applied to consider quantum transmission through a tight-binding wire subject to a time-periodic potential. The wire is coupled with two leads via the coupling constant v{C}. The periodicity of the potential implies an additional temporal dimension that reduces the problem to stationary transmission through an effectively two-dimensional lattice system. The non-Hermitian effective Hamiltonian is formulated. This allows us to trace the redistribution of resonance positions and resonance widths with the growth of v{C} from the weak-coupling to the strong-coupling regime.

Goos-Hänchen 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 [Wiersig, Phys. Rev. Lett. 97, 253901 (2006)]. For the case of a microdisk cavity with elliptical cross section, we use the Husimi function to analyze this localization in phase space. Moreover, we present a semiclassical explanation of this phenomenon in terms of the Goos-Hänchen 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.

Experimental umbilic diabolos in random optical fields

The intensity of a random optical field consists of bright speckle spots (maxima) separated from dark areas (minima and optical vortices) by saddle points. We show that hidden in this complicated landscape are umbilic points--singular points at which the eigenvalues Lambda (+/-) of the Hessian matrix that measure the curvature of the landscape become degenerate. Although not observed previously in random optical fields, umbilic points are the most numerous of all special points, outnumbering maxima, minima, saddle points, and vortices. We show experimentally that the directions of principal curvature, the eigenvectors Psi (+/-), rotate about intensity umbilic points with positive or negative half-integer winding number, in accord with theory, and that Lambda (+) and Lambda (-) generate a double cone known as a diabolo. At optical vortices the curvature of the amplitude is singular, and we show from both theory and experiment that for this landscape Psi (+/-) rotate about vortex centers with a positive integer winding number. Diabolos can be classified as elliptic or hyperbolic, and we present initial results for the measured fractions of these two different types of umbilic diabolos.

Phase rigidity and avoided level crossings in the complex energy plane

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)|phi(lambda))/<phi(lambda)|phi(lambda)> that characterizes the phase rigidity of the eigenfunctions phi(lambda). In the scenario with avoided level crossings, r(lambda) varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r(lambda) is an internal property of an open quantum system. In the literature, the phase rigidity rho of the scattering wave function Psi(C)(E) is considered. Since Psi(C)(E) can be represented in the interior of the system by the phi(lambda), the phase rigidity rho of the Psi(C)(E) is related to the r(lambda) and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity rho to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity rho and transmission numerically for small open cavities.

Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

The spectroscopic properties of an open large Bunimovich cavity are studied numerically in the framework of the effective Hamiltonian formalism. The cavity is opened by attaching two leads to it in four different ways. In some cases, the transmission takes place via standing waves with an intensity that closely follows the profile of the resonances. In other cases, short-lived and long-lived resonance states coexist. The short-lived states cause traveling waves in the transmission while the long-lived ones generate superposed fluctuations. The traveling waves oscillate as a function of energy. They are not localized in the interior of the large chaotic cavity. In all considered cases, the phase rigidity fluctuates with energy. It is mostly near to its maximum value and agrees well with the theoretical value for the two-channel case.