Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point

Abstract

Complex potential and non-Hermitian hopping amplitude are building blocks of a non-Hermitian quantum network. Appropriate configuration, such as PT -symmetric distribution, can lead to a full real spectrum. To investigate the underlying mechanism of this phenomenon, we study the phase diagrams of a semi-infinite non-Hermitian systems. They consist of finite non-Hermitian clusters and semi-infinite leads. Based on the analysis of the solutions of the concrete systems, it is shown that they can have full real spectra without any requirements on the symmetry and the wave function within the leads becomes unidirectional plane waves at the exceptional point. This universal dynamical behavior is demonstrated as the persistent emission and reflectionless absorption of wave packets in the typical non-Hermitian systems containing the complex on-site potentials and non-Hermitian hopping amplitudes.

Non-Hermitian interferometer: Unidirectional amplification without distortion

“…(14), The divergence of r k and t k indicates the existence of spectral singularity, which has been pointed out in Ref. [48]. We note that it occurs only at the point µν = −1 for states with k = ±π/2.…”

Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system

“…Extra imaginary potentials induce many unusual features even in certain simple or trivial systems, which include quantum phase transition occurred in a finite system [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], unidirectional propagation and anomalous transport [4,[21][22][23][24][25][26][27][28], invisible defects [29][30][31], coherent absorption [32] and self sustained emission [33][34][35][36][37], lossinduced revival of lasing [38], as well as laser-mode selection [39,40]. Most of these phenomena are related to the critical behaviours near exceptional or spectral singularity points.…”

Non-Hermitian tight-binding network engineering

“…For example, in optics non-Hermitian tight-binding networks with complex on-site potentials are readily implemented by evanescent coupling of light modes trapped in optical waveguides or resonators with optical gain and loss in them, while the realization of controllable non-Hermitian coupling constants is a much less trivial task. However, complex hopping amplitudes play an important role for the observation of a wide variety of phenomena that have been disclosed in recent works [24,[29][30][31][32][33][34]. These include incoherent control of non-Hermitian Bose-Hubbard dimers [24], self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point [29], optical simulation of PT -symmetric quantum field theories in the ghost regime [30,31], invisible defects in tight-binding lattices [32], non-Hermitian bound states in the continuum [33], and Bloch oscillations with trajectories in complex plane [34].…”

“…To check the fidelity of the synthesized Hamiltonian, in Fig.3(e) we compare the numerically-computed evolution of the occupation probability P (t) = |c 0 (t)| 2 with the initial condition c n (0) = δ n,0 , as obtained by the exact Lee Hamiltonian with complex coupling [Eq. (29)] and by the synthesized effective Hamiltonian [Eq. (33)].…”