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Register a new userHow to Synthesize Exceptional Points with Three Resonators
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In non-Hermitian coulped-resonator networks, the eigenvectors of degenerate eigenmodes may become parallel due to the singularity at so-called Exceptional Points (EP). To exploit the parametric sensitivity at EPs, an important problem is, given an arbitrary set of coupled resonators, how to generate a desired EP by properly coupling them together. This paper provides the solution for the case of three resonators. We show that all physically admissible EPs can be realized with either weakly coupled linear networks or strongly coupled circular networks, and the latter type of EPs has not been reported in the literature. Each admissible EP eigenvalue can be realized by two and only two resonator networks, and the formulas for calculating the required coupling constants are provided. The characteristics of these EPs are illustrated by the change of transmission spectra near them, which verify the enhanced sensitivity induced by the singularity of EPs.
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Here we propose a new gravitational waves(GWs) detector in broad frequency band, which is operated at exceptional points(EPs) in micro cavities. The detected signal is an eigenfrequency split of the mechanical modes caused by the spatial strain. Due to the complex square root topology near the EP, the splitting is greatly enhanced for sufficiently small perturbations. Compared to current strategies, it can be achieved at the room temperature and has advantages in micro device scale, wide frequency band and higher sensitivity.
The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak $textit{blind}$ measurements (where the detectors readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements, and show that $textit{any}$ pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, while for low purity target states, it implies an oscillatory approach to the target state. The phase transition between these two regimes is characterized by a third-order exceptional point.
The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems over a decade, where the fidelity susceptibility density approaches $+infty$ in the thermodynamic limits. Here the fidelity susceptibility $chi$ is generalized to non-Hermitian quantum systems by taking the geometric structure of the Hilbert space into consideration. Instead of solving the metric equation of motion from scratch, we chose a gauge where the fidelities are composed of biorthogonal eigenstates and can be worked out algebraically or numerically when not on the exceptional point (EP). Due to the properties of the Hilbert space geometry at EP, we found that EP can be found when $chi$ approaches $-infty$. As examples, we investigate the simplest $mathcal{PT}$ symmetric $2times2$ Hamiltonian with a single tuning parameter and the non-Hermitian Su-Schriffer-Heeger model.
An example of exceptional points in the continuous spectrum of a real, pseudo-Hermitian Hamiltonian of von Neumann-Wigner type is presented and discussed. Remarkably, these exceptional points are associated with a double pole in the normalization factor of the Jost eigenfunctions normalized to unit flux at infinity. At the exceptional points, the two unnormalized Jost eigenfunctions are no longer linearly independent but coalesce to give rise to two Jordan cycles of generalized bound state eigenfunctions embedded in the continuum and a Jordan block representation of the Hamiltonian. The regular scattering eigenfunction vanishes at the exceptional point and the irregular scattering eigenfunction has a double pole at that point. In consequence, the time evolution of the regular scattering eigenfunction is unitary, while the time evolution of the irregular scattering eigenfunction is pseudounitary. The scattering matrix is a regular analytical function of the wave number $k$ for all $k$ including the exceptional points.
Attribute guided face image synthesis aims to manipulate attributes on a face image. Most existing methods for image-to-image translation can either perform a fixed translation between any two image domains using a single attribute or require training data with the attributes of interest for each subject. Therefore, these methods could only train one specific model for each pair of image domains, which limits their ability in dealing with more than two domains. Another disadvantage of these methods is that they often suffer from the common problem of mode collapse that degrades the quality of the generated images. To overcome these shortcomings, we propose attribute guided face image generation method using a single model, which is capable to synthesize multiple photo-realistic face images conditioned on the attributes of interest. In addition, we adopt the proposed model to increase the realism of the simulated face images while preserving the face characteristics. Compared to existing models, synthetic face images generated by our method present a good photorealistic quality on several face datasets. Finally, we demonstrate that generated facial images can be used for synthetic data augmentation, and improve the performance of the classifier used for facial expression recognition.
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