Observation ofPT-Symmetry Breaking in Complex Optical Potentials

Abstract

In 1998, Bender and Boettcher found that a wide class of Hamiltonians, even though non-Hermitian, can still exhibit entirely real spectra provided that they obey parity-time requirements or PT symmetry. Here we demonstrate experimentally passive PT-symmetry breaking within the realm of optics. This phase transition leads to a loss induced optical transparency in specially designed pseudo-Hermitian guiding potentials.

Constant-intensity waves and their modulation instability in non-Hermitian potentials

“…They also remain valid for any sign of Kerr nonlinearity and thus allow us to perform a modulational stability analysis for non-homogeneous potentials. The most appropriate context to study the MI of such solutions is that of PT -symmetric optics [6][7][8][9][10][11]14,[19][20][21][22]24 . We find that in the selffocusing regime, the waves are always unstable, whereas in the defocusing regime the instability appears for specific values of Bloch momenta.…”

“…Such non-Hermitian potential regions 4,5 , which serve as sources and sinks for waves, respectively, can give rise to novel wave effects that are impossible to realize with conventional, Hermitian potentials. Examples of this kind, which were meanwhile also realized in the experiment [6][7][8][9][10] , are the unidirectional invisibility of a gain-loss potential 11 , devices that can simultaneously act as laser and as a perfect absorber [12][13][14] and resonant structures with unusual features like non-reciprocal light transmission 10 or loss-induced lasing [15][16][17] . In particular, systems with a so-called parity-time (PT ) symmetry 18 , where gain and loss are carefully balanced, have recently attracted enormous interest in the context of nonHermitian photonics [19][20][21][22][23][24] .…”

PT symmetric Aubry–Andre model

“…The Equ. (1) with (2) can be called the PT symmetric Aubry-Andre model [25], which can now be engineered experimentally [1][2][3]. The most interesting result of the Hermitian Aubry-Andre model is that the states at the center of the lattice is localized (Anderson localization) for irrational values of β when V > 2.…”

“…Recent experimental realization of PT symmetric optical systems with balanced gain and loss has attracted a lot of attention [1][2][3]. The PT symmetric optical systems lead to interesting results such as unconventional beam refraction and power oscillation [4][5][6], nonreciprocal Bloch oscillations [7], unidirectional invisibility [8], an additional type of Fano resonance [9], and chaos [10].…”

A new non-Hermitian E2-quasi-exactly solvable model

“…The physical motivation results from the current interest in extending the study of solvable models [4,5,6,7, 1] to non-Hermitian quantum mechanical systems [8,9,10,11]. The E 2 -quasi-exactly solvable models are especially interesting in optical settings [12,13,14,15,16,17,18,19,20] where the fact is exploited that the Helmholtz equation results as a reduction from the Schrödinger equation. Solvable models are rare exceptions in the study of quantum mechanical systems and the model presented here should be added to that list.…”