Abstract:
Spectral singularities are special points in the continuous spectra of some non-Hermitian linear operators which correspond to the real poles of the resolvent. Apart from the purely mathematical interest, spectral singularities admit simple and transparent physical meaning: they correspond to the situation when a localized non-Hermitian complex-valued potential operates as a laser or an antilaser. In this context, laser corresponds to a complex potential which emits stationary and coherent radiation with the fixed wavelength. Vice versa, a potential-antilaser operates as a coherent perfect absorber, i.e., absorbs the coherent bidirectional incident radiation at some fixed wavelength, with no reflection and no transmission. An especially interesting situation occurs when the complex potential satisfies the requirement of parity-time (PT) symmetry: in this case laser and antilaser coexist at the same wavelength. Spectral singularities are known for electromagnetic and acoustic waves, but can also be encountered in other waveguiding systems. In my talk, I will review some recent advances related to the physics of spectral singularities. I will show that spectral singularities and the associated laser-antilaser behavior can be extended conceptually and implemented experimentally for waves propagating in a nonlinear medium, which includes a Bose-Einstein condensate loaded in a periodic lattice with spatially localized dissipation [1] and an array of nonlinear optical waveguides where one waveguide is absorbing or emitting [2]. Additionally, I will discuss the mechanism of the PT-symmetry breaking (phase transition) through the splitting of a self-dual spectral singularity [3-4].
References:
[1] A. Müllers, B. Santra, C. Baals, J. Jiang, J. Benary, R. Labouvie, D. A. Zezyulin, V. V. Konotop, and H. Ott, Coherent perfect absorption of nonlinear matter waves, Science Advances 4, eaat6539 (2018).
[2] D. A. Zezyulin, H. Ott, and V. V. Konotop, Coherent perfect absorber and laser for nonlinear waves in optical waveguide arrays, Optics Letters 43, 5901 (2018).
[3] V. V. Konotop and D. A. Zezyulin, Phase transition through the splitting of self-dual spectral singularity in optical potentials, Optics Letters 42, 5206 (2017).
[4] V. V. Konotop and D. A. Zezyulin, Spectral singularities of odd-PT-symmetric potentials, Physical Review A 99, 013823 (2019).
Biography:
Dmitry Zezyulin (b. 1984) received the M.S. degree in applied mathematics from the Moscow Institute of Electronic Technology, Moscow, Russia, in 2006, and the Ph.D. degree in mathematical modeling from the Institute of Mathematical Modeling of Russian Academy of Sciences, Moscow, in 2009. Then he became a Postdoctoral Research Fellow at the University of Lisbon, Lisbon, Portugal. In 2017 he moved to the ITMO University in Saint-Petersburg, Russia. He studies wave phenomena in optics, Bose-Einstein condensates, and excitons-polaritons, with the particular focus on non-Hermitian and nonlinear behavior.
Seminar by the NYU-ECNU Institute of Physics at NYU Shanghai