Phase rigidity and avoided level crossings in the complex energy plane

Exceptional nexus with a hybrid topological invariant

Branch-point singularities known as exceptional points (EPs), which carry a nonzero topological charge, can emerge in non-Hermitian systems. We demonstrate with both theory and acoustic experiments an "exceptional nexus" (EX), which is not only a higher-order EP but also the cusp singularity of multiple exceptional arcs (EAs). Because the parameter space is segmented by the EAs, the EX possesses a hybrid topological invariant (HTI), which consists of distinct winding numbers associated with Berry phases accumulated by cyclic paths on different complex planes. The HTI is experimentally characterized by measuring the critical behaviors of the wave functions. Our findings constitute a major advance in the fundamental understanding of non-Hermitian systems and their topology, possibly opening new avenues for applications.

Tailoring exceptional points with one-dimensional graphene-embedded photonic crystals

We theoretically demonstrate that tunable exceptional points (EPs) can be realized by using graphene-embedded one-dimensional (1D) photonic crystals with optical pumping in the terahertz (THz) frequency range. By tuning the Fermi level of graphene sheet, the energy band are altered significantly and the EP appears. In particular, multiple EPs at different frequencies can be selectively produced via subtly adjusting the band structure. Furthermore, topological features of these EPs, such as crossing and anti-crossing of the real and imaginary parts of the eigenvalues, have been analyzed in detail. We expect that tunable EPs can provide an instructive method to design active optical devices based on photoexcited graphene sheets in the THz frequency range.

Locating Exceptional Points on Multidimensional Complex-Valued Potential Energy Surfaces

We present a method for locating non-Hermitian degeneracies, called exceptional points (EPs), and minimum-energy EPs between molecular resonances using the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method. EPs are the complex-valued analogue of conical intersections (CIs) and have a similar impact on nonadiabatic processes between resonances as CIs have on nonradiative transitions between bound states. We demonstrate that the CAP-EOM-CC method in the singles and doubles approximation (CAP-EOM-CCSD) yields crossings of the correct dimensionality. The use of analytic gradients enables applications to multidimensional problems. Results are presented for hydrogen cyanide and chloroethylene, for which the location of the crossings of anionic resonances is crucial for understanding the dissociative electron attachment process.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

A review of progress in the physics of open quantum systems: theory and experiment

This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantum systems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q   +   P   =   1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In addition to discussing experiments on mesoscopic quantum point contacts that provide evidence of the environmentally-mediated coupling of quantum states, we also review manifestations of DPTs in mesoscopic devices and other systems. These experiments include observations of resonance-trapping behavior in microwave cavities and open quantum dots, phase lapses in tunneling through single-electron transistors, and spin swapping in atomic ensembles. Other possible manifestations of this phenomenon are presented, including various superradiant phenomena in low-dimensional semiconductors. From these discussions a generic picture of OQSs emerges in which the environmentally-mediated coupling between different quantum states plays a critical role in governing the system behavior. The ability to control or manipulate this interaction may even lead to new applications in photonics and electronics.

Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations

The change of resonance widths in an open system under a perturbation of its interior has been recently introduced by Fyodorov and Savin [Phys. Rev. Lett. 108, 184101 (2012)] as a sensitive indicator of the nonorthogonality of resonance states. We experimentally study universal statistics of this quantity in weakly open two-dimensional microwave cavities and reverberation chambers realizing scalar and electromagnetic vector fields, respectively. We consider global as well as local perturbations, and also extend the theory to treat the latter case. The influence of the perturbation type on the width shift distribution is more pronounced for many-channel systems. We compare the theory to experimental results for one and two attached antennas and to numerical simulations with higher channel numbers, observing a good agreement in all cases.

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.

Statistics of resonance states in open chaotic systems: a perturbative approach

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (nonorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of weakly overlapping resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian orthogonal ensemble, we reveal and discuss the role of spectral fluctuations.