Experimental observation of the topological structure of exceptional points

We report on a microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a complex interaction parameter, are encircled in the laboratory. The real and imaginary parts of an eigenvalue are given by the frequency and width of a resonance and the eigenvectors by the field distributions. Repulsion of eigenvalues--always associated with EPs--implies frequency anticrossing (crossing) whenever width crossing (anticrossing) is present. The eigenvalues and eigenvectors are interchanged while encircling an EP, but one of the eigenvectors undergoes a sign change which can be discerned in the field patterns.     

Exceptional points in multichannel resonance quantization

We derive from the quantization condition of a multichannel resonance problem the behaviour of resonance energies close to an exceptional point (EP) where two resonance energies coalesce. The formalism is applied to a one-dimensional model of the molecular ion H₂ ⁺. Although the approach does not use a matrix diagonalization procedure, all known results about exceptional points are present, including the transfer from one resonance to another when following a loop encircling the EP. We study how the resonance wave functions behave along loops around the EP, as well as the associated geometric phases.     

Anticrossing phenomena in a resonator with 2D electrons on liquid helium

We have investigated the details of the eigenmode for a resonator containing a two-dimensional electron system (2DES) formed on the surface of liquid helium. We show that anticrossing phenomena occur near the crossing point ω₀=ω_c, where ω₀ is the eigenmode of the resonator and ω_c is the cyclotron frequency. The structure of the coupling constant is established. It is a flexible parameter, i.e., sensitive especially to magnetic field and electron density. A finite coupling leads to a perturbation, δω, of the eigenmode of the resonator in presence of the 2DES. Corresponding calculations and measurements of δω are presented. The theory fits the experimental data. The influence of anticrossing on the cyclotron resonance absorption line shape is demonstrated.     

Improvement of the chirality near avoided resonance crossing in optical microcavity

Chirality is one of the important phenomena at the vicinity of exceptional point(EP). The conventional understanding is that the chirality is determined by asymmetrical scattering efficiency(?), which reaches to zero only when the resonance approaches EP. Here we study the possibility to enhance the chirality in open systems with a more robust mechanism. By combining chirality with avoided resonance crossing, we show that the chirality and ? can be dramatically modified. Taking a spiral shaped annular cavity as an example, we show that the chirality of optical resonances can be significantly improved when two sets of chiral states approach each other. The imbalance between counterclockwise(CCW) components and clockwise(CW) components has been enhanced by more than an order of magnitude. Our research provides a new route to tailor and control the chirality in open systems.     

Magnetic field effect on the electronic states and the intraband optical absorption spectrum of a laser dressed double quantum dot molecule

The simultaneous effects of intense terahertz (THz) laser, a homogeneous magnetic fields, and the modification of the structural parameters on the electronic states, and the intraband optical absorption spectrum in a two-dimensional double quantum dot molecule are theoretically investigated. The crossing and anticrossing are observed in the energy dependence on the magnetic field induction between the third and the fourth energy levels. Additionally, it is shown that an intense THz laser field always shifts the energy spectrum to higher values. The variation of the structural parameters leads to the change of the positions of the energy levels and the anticrossing point. Finally, we have found that the intraband optical absorption spectrum, particularly the absorption intensity and the peak position, can be effectively regulated by an intense THz laser and a magnetic fields, as well as by the variation of the structural parameters of the double quantum dot molecule.     

Photoluminescence of “dark” excitons in CdMnTe quantum well, embedded in a microcavity

A diluted magnetic semiconductor (DMS) quantum well (QW) microcavity operating in the limit of the strong coupling regime is studied by magnetoptical experiments. The interest of DMS QW relies on the possibility to vary the excitonic resonance over a wide range of energies by applying an external magnetic field, typically about 30 meV for 5 T in our sample. In particular, the anticrossing between the QW exciton and the cavity mode can be tuned by the external field. We observe the anticrossing and formation of exciton polaritons in magneto-reflectivity experiments. In contrast, magneto-luminescence exhibits purely excitonic character. Under resonant excitation conditions an additional emission line is observed at the energy of the dark exciton. The creation of dark excitons is made possible due to heavy hole–light hole mixing in the QW. The emission at this energy could be due to a combined spin flip of an electron and a bright exciton recombination.     

Accurate transport cross sections for the Lennard-Jones potential

It is well-known that in open quantum systems resonances can coalesce at an exceptional point, where both the energies and the wave functions coincide. In contrast to the usual behaviour of the scattering amplitude at one resonance, the coalescence of two resonances invokes a pole of second order in the Green’s function, in addition to the usual first order pole. We show that the interference due to the two pole terms of different order gives rise to patterns in the scattering cross section which closely resemble Fano-Feshbach resonances. We demonstrate this by extending previous work on the analogy of Fano-Feshbach resonances to classical resonances in a system of two driven coupled damped harmonic oscillators.     

Quantum metastability in time-periodic potentials

In this paper, we investigate quantum metastability of a particle trapped in between an infinite wall and a square barrier, with either a time-periodically oscillating barrier (Model A) or bottom of the well (Model B). Based on the Floquet theory, we derive in each case an equation which determines the stability of the metastable system. We study the influence on the stability of two Floquet states when their Floquet energies (real part) encounter a direct or an avoided crossing at resonance. The effect of the amplitude of oscillation on the nature of crossing of Floquet energies is also discussed. It is found that by adiabatically changing the frequency and amplitude of the oscillation field, one can manipulate the stability of states in the well. By means of a discrete transform, the two models are shown to have exactly the same Floquet energy spectrum at the same oscillating amplitude and frequency. The equivalence of the models is also demonstrated by means of the principle of gauge invariance.     

Controlled quantum interference of Mössbauer radiation in resonant scattering

Previously, our group described a quantum-interference effect (“valve effect”) to be expected in the resonant scattering of Mössbauer photons in the NMR mode. In the present study, it is shown that similar effects also occur in resonant-scattering spectra at the point of anticrossing of nuclear sublevels. Dynamical level anticrossing is also examined in this context.     

Giant Rabi splitting in metal/semiconductor nanohybrids

We present strong coupling regime between localized plasmon in lithographed nanoparticles and excitons in an organic semiconductor. The lithographed nanoparticles allow a very good control of the particle size and environment, thereby avoiding a large inhomogeneous broadening of the plasmonic resonances which could partially mask the plasmon/exciton hybridization. The nanoparticles diameter ranges from 100 to 200 nm. A giant Rabi splitting energy of 450 meV is obtained, and typical behaviors of mixed states, i.e. anticrossing of their energies and crossing of their linewidths, are observed. Three-dimensional finite-difference time-domain simulations and coupled oscillator calculations are used to analyze and corroborate the experimental results.     

Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid

We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.     

Laser control of magneto-polaron in transition metal dichalcogenides triangular quantum well

We study the dynamic of magneto-polaron condensate in monolayer two dimensional (2D) transition metal dichalcogenides (TMDs) materials of 2H types in triangular quantum well potential. Within both the quantum mechanical Schrödinger approach (QMSA) and the improved Wigner-Brillouin theory (IWBT), Landau energies levels (LELs) are derived. We have shown that the magneto-polaron condensation is enhanced in monolayer MoSe₂ compared to MoS₂, WS₂ and WSe₂. We derive various levels by increasing a magnetic field and laser parameter. We show that the quantum confinement lifts the degeneracy of the Landau levels (LLs) resulting in an anticrossing and crossing. The dephasing effect due to the quantum well potential's parameter plays an important role in the magneto-polaron energy corrections, which are also affected by the amplitude of the laser field. The system presents Stückelberg oscillations which is important for practical applications.     

Suppression of an acoustic mode by an elastic mode of a liquid-filled spherical shell resonator

The purpose of this paper is to report on the suppression of an approximately radial (radially symmetric) acoustic mode by an elastic mode of a water-filled, spherical shell resonator. The resonator, which has a 1-in. wall thickness and a 9.5-in. outer diameter, was externally driven by a small transducer bolted to the external wall. Experiments showed that for the range of drive frequencies (19.7-20.6 kHz) and sound speeds in water (1520-1570 m/s) considered in this paper, a nonradial (radially nonsymmetric) mode was also excited, in addition to the radial mode. Furthermore, as the sound speed in the liquid was changed, the resonance frequency of the nonradial mode crossed with that of the radial one and the amplitude of the latter was greatly reduced near the crossing point. The crossing of the eigenfrequency curves of these two modes was also predicted theoretically. Further calculations demonstrated that while the radial mode is an acoustic one associated with the interior fluid, the nonradial mode is an elastic one associated with the shell. Thus, the suppression of the radial acoustic mode is apparently caused by the overlapping with the nonradial elastic mode near the crossing point.     

Mode coupling between first- and second-order whispering-gallery modes in coupled microdisks

The mode characteristics for two coupled microdisks are investigated by the finite-difference time-domain technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first- and second-order WGMs can have a crossing point in some cases, which can induce anticrossing mode coupling between them and greatly reduce the mode Q factor of the coupled first-order WGMs. The time variation of mode field pattern shows the transformation between the coupled first- and second-order WGMs.     

Degeneracy of Resonances: Branch Point and Branch Cuts in Parameter Space

The rich phenomenology of crossings and anticrossings of energies and widths, observed in an isolated doublet of resonances when one control parameter is varied, is fully explained in terms of the topological properties of the energy hypersurfaces close to the degeneracy point. The hypersurface representing the complex resonance eigenvalues, as functions of the control parameters, has an algebraic branch point of rank one, and branch cuts in its real and imaginary parts, in parameter space. Associated with this singularity in parameter space, the scattering matrix, S _ℓ (E), and the Green’s function, G _ℓ ⁽⁺⁾(k; r,r'), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of any degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.     

Born-oppenheimer approximation near level crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.     

Quantum oscillations of the total spin in a heterometallic antiferromagnetic ring: evidence from neutron spectroscopy

Using inelastic neutron scattering and applied fields up to 11.4 T, we have studied the spin dynamics of the Cr7Ni antiferromagnetic ring in the energy window 0.05-1.6 meV. We demonstrate that the external magnetic field induces an avoided crossing (anticrossing) between energy levels with different total-spin quantum numbers. This corresponds to quantum oscillations of the total spin of each molecule. The inelastic character of the observed excitation and the field dependence of its linewidth indicate that molecular spins oscillate coherently for a significant number of cycles. Precise signatures of the anticrossing are also found at higher energy, where measured and calculated spectra match very well.     

Anomalous variation of the exciton Fano-resonance spectra in strongly biased Wannier-Stark ladder

Effects of the Wannier-Stark ladder (WSL) resonance on optical absorption spectra in strongly biased superlattices are theoretically investigated by solving the multichannel scattering problem relevant to the WSL-exciton Fano-resonance. When the bias of an electric field F is applied such that a WSL subband state is energetically aligned with adjacent ones, resulting in strong repulsion (anticrossing) due to Zener resonance, an onset of exciton absorption notably shifts toward the lower energy side. However, just a slight change of F away from the anticrossing leads to a peculiar suppression, lowering the absorption edge. According to a qualitative analytic model, such an anomalous variance is found ascribable to delocalization of WSL subband wave functions across several periods through a mixing of an exciton reduced mass in the region of the potential well with that in the region of the potential barrier.     

Crossing scenario for a nonlinear non-Hermitian two-level system

The diabolic crossing scenario of two-state quantum systems can be generalized to a non-Hermitian case as well as to a nonlinear one. In the non-Hermitian case two different crossing types appear, distinguished according to the crossing or anticrossing of real parts or imaginary parts of the eigenvalues. In the nonlinear case additional stationary states can emerge, leading to looped structures in the eigenvalues. Here we discuss the basic properties of the most general situation, the combined nonlinear and non-Hermitian system. It is shown that the eigenvalues and eigenstates can be achieved from the real roots of a quartic equation. The corresponding crossing scenario is quite intricate and can be understood as a hybrid of the ones for the nonlinear Hermitian and the linear non-Hermitian systems. In addition, the implications of combined nonlinearity and non-Hermiticity on the system dynamics is studied in terms of a generalized Landau—Zener probability.     

On the methylene hyperfine splitting in the anion radicals of 1,2-indandione, 4,4-dimethyl-1,2-tetralindione,and fluorene

A study has been made of nuclear magnetic resonance line-narrowing at temperatures approaching the melting point for several organic crystals in their plastic, rotator, phase. It was found that, whereas those solids with higher fusional entropies (>4·6 e.u.) yielded activation energies for the line narrowing process which were equivalent to those for self-diffusion as measured by radiotracer and plastic deformation techniques those with entropies of fusion <3·3 e.u. yielded energies which were much lower than those for self-diffusion. Solids with entropies in the intermediate region showed the former behaviour at low temperatures and the latter at high temperatures. It is proposed that this variation reflects a difference in the physical nature of the point defect in the various solids.