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Register a new userVisualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
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The discovery of novel topological phase advances our knowledge of nature and stimulates the development of applications. In non-Hermitian topological systems, the topology of band touching exceptional points is very important. Here we propose a real-energy topological gapless phase arising from exceptional points in one dimension, which has identical topological invariants as the topological gapless phase arising from degeneracy points. We develop a graphic approach to characterize the topological phases, where the eigenstates of energy bands are mapped to the graphs on a torus. The topologies of different phases are visualized and distinguishable; and the topological gapless edge state with amplification appropriate for topological lasing exists in the nontrivial phase. These results are elucidated through a non-Hermitian Su-Schrieffer-Heeger ladder. Our findings open new way for identifying topology phase of matter from visualizing the eigenstates.
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Degeneracy (exceptional) points embedded in energy band are distinct by their topological features. We report different hybrid two-state coalescences (EP2s) formed through merging two EP2s with opposite chiralities that created from the type III Dirac points emerging from a flat band. The band touching hybrid EP2, which is isolated, is induced by the destructive interference at the proper match between non-Hermiticity and synthetic magnetic flux. The degeneracy points and different types of exceptional points are distinguishable by their topological features of global geometric phase associated with the scaling exponent of phase rigidity. Our findings not only pave the way of merging EPs but also shed light on the future investigations of non-Hermitian topological phases.
We engineer mechanical gain (loss) in system formed by two optomechanical cavities (OMCs), that are mechanically coupled. The gain (loss) is controlled by driving the resonator with laser that is blue (red) detuned. We predict analytically the existence of multiple exceptional points (EPs), a form of degeneracy where the eigenvalues of the system coalesce. At each EP, phase transition occurs, and the system switches from weak to strong coupling regimes and vice versa. In the weak coupling regime, the system locks on an intermediate frequency, resulting from coalescence at the EP. In strong coupling regime, however, two or several mechanical modes are excited depending on system parameters. The mechanical resonators exhibit Rabi-oscillations when two mechanical modes are involved, otherwise the interaction triggers chaos in strong coupling regime. This chaos is bounded by EPs, making it easily controllable by tuning these degeneracies. Moreover, this chaotic attractor shows up for low driving power, compared to what happens when the coupled OMCs are both drived in blue sidebands. This works opens up promising avenues to use EPs as a new tool to study collective phenomena (synchronization, locking effects) in nonlinear systems, and to control chaos.
The usual concepts of topological physics, such as the Berry curvature, cannot be applied directly to non-Hermitian systems. We show that another object, the quantum metric, which often plays a secondary role in Hermitian systems, becomes a crucial quantity near exceptional points in non-Hermitian systems, where it diverges in a way that fully controls the description of wavepacket trajectories. The quantum metric behaviour is responsible for a constant acceleration with a fixed direction, and for a non-vanishing constant velocity with a controllable direction. Both contributions are independent of the wavepacket size.
We theoretically explore the role of mesoscopic fluctuations and noise on the spectral and temporal properties of systems of $mathcal{PT}$-symmetric coupled gain-loss resonators operating near the exceptional point, where eigenvalues and eigenvectors coalesce. We show that the inevitable detuning in the frequencies of the uncoupled resonators leads to an unavoidable modification of the conditions for reaching the exceptional point, while, as this point is approached in ensembles of resonator pairs, statistical averaging significantly smears the spectral features. We also discuss how these fluctuations affect the sensitivity of sensors based on coupled $mathcal{PT}$-symmetric resonators. Finally, we show that temporal fluctuations in the detuning and gain of these sensors lead to a quadratic growth of the optical power in time, thus implying that maintaining operation at the exceptional point over a long period can be rather challenging. Our theoretical analysis clarifies issues central to the realization of $mathcal{PT}$-symmetric devices, and should facilitate future experimental work in the field.
We demonstrate that with appropriate quantum correlation function, a real-space network model can be constructed to study the phase transitions in quantum systems. For the three-dimensional bosonic system, the single-particle density matrix is adopted to construct the adjacency matrix. We show that the Bose-Einstein condensate transition can be interpreted as the transition into a small-world network, which is accurately captured by the small-world coefficient. For the one-dimensional disordered system, using the electron diffusion operator to build the adjacency matrix, we find that the Anderson localized states create many weakly-linked subgraphs, which significantly reduces the clustering coefficient and lengthens the shortest path. We show that the crossover from delocalized to localized regimes as a function of the disorder strength can be identified as the loss of global connection, which is revealed by the small-world coefficient as well as other independent measures like the robustness, the efficiency, and the algebraic connectivity. Our results suggest that the quantum phase transitions can be visualized in real space and characterized by the network analysis with suitable choices of quantum correlation functions.
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