Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization

Abstract

Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena, such as level crossings in nuclear and condensed matter physics, and unusual phenomena in optics, such as loss-induced lasing and unidirectional transmission, can be understood by considering a simple 2 × 2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge, and as the system parameters vary, these EPs can collide and merge, leading to higher-order singularities and topological characteristics much richer than those seen in two-state systems. The new physics obtained is not limited to the acoustic systems demonstrated here. It also applies to other systems as well, such as coupled photonic cavities and waveguides.

General theory of spontaneous emission near exceptional points

“…Motivated by recent interest in higher-order EPs [72][73][74][75], we generalize our results from the previous section to nth order degeneracies (i.e., EPs that form when n degenerate eigenvectors merge). In this case, we define the enhancement factor as the ratio of the LDOS peak at the EP and at a reference point with n non-degenerate resonances (generalizing our earlier definition for M EP /M ∞ ).…”

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

“…EPs of this kind may be studied experimentally, and there is a rapidly increasing number of studies related to fundamental science and technology. For example, there are studies with pump-induced lasers [7,8], microwave cavities and wires [9][10][11][12][13][14][15][16][17], LRC circuits [18], exciton-polariton billiards [19], and more [20,21].…”

Nonperturbative emergence of the Dirac fermion in a strongly correlated composite Fermi liquid

“…Besides this nice property, other non-hermitian systems have been studied theoretically and experimentally 42 . Therefore we believe the non-hermitian Hamiltonian under consideration is not an obstacle as long as we remain in the real energy region.…”