The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra. The concept has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc. The inclusion of nonlinearity has led to a number of new phenomena for which no counterparts exist in traditional dissipative systems. Several examples of nonlinear parity-time symmetric systems in different physical disciplines are presented and their implications discussed.

Nonlinear waves in PT -symmetric systems

When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Ei…

Bose-Einstein condensation

Nonreciprocal electromagnetic devices play a crucial role in modern microwave and optical technologies. Conventional methods for realizing such systems are incompatible with integrated circuits. With recent advances in integrated photonics, the need for efficient on-chip magnetless nonreciprocal devices has become more pressing than ever. This paper leverages space-time engineered asymmetric photonic band gaps to generate optical isolation. It shows that a properly designed space-time modulated slab is highly reflective/transparent for opposite directions of propagation. The corresponding design is magnetless, accommodates low modulation frequencies, and can achieve very high isolation levels. An experimental proof of concept at microwave frequencies is provided.

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Optical isolation based on space-time engineered asymmetric photonic band gaps

We report the existence and properties of localized modes described by a nonlinear Schr\"odinger equation with a complex $\mathcal{PT}$-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one-dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters, although the corresponding linear Schr\"odinger eigenvalue problem possesses unbroken $\mathcal{PT}$ symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power-flow density associated with these localized modes has also been examined.

Nonlinear localized modes in PT -symmetric Rosen-Morse potential wells

Hetero-Bäcklund transformation and similarity reduction of an extended (2+1)-dimensional coupled Burgers system in fluid mechanics

Solitons in PT-symmetric potential with competing nonlinearity

U. Al Khawaja,1 S. M. Al-Marzoug,2,3 H. Bahlouli,2,3 and Yuri S. Kivshar4 1Physics Department, United Arab Emirates University, P. O. Box 15551, Al-Ain, United Arab Emirates 2Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3Saudi Center for Theoretical Physics, Dhahran 31261, Saudi Arabia 4Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia (Received 30 May 2013; revised manuscript received 11 July 2013; published 19 August 2013)

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Unidirectional soliton flows in PT-symmetric potentials

Saudi Center for Theoretical Physics, Dhahran 31261, Saudi Arabia(Dated: June 3, 2015)The interaction between two bright solitons in a dipolar Bose-Einstein condensate (BEC) hasbeen investigated aiming at ﬁnding the regimes when they form a stable bound state, known assoliton molecule. To study soliton interactions in BEC we employed a method similar to that usedin experimental investigation of the interaction between solitons in optical ﬁbers. The idea consistsin creating two solitons at some spatial separation from each other at initial time t

Interaction of solitons in one-dimensional dipolar Bose-Einstein condensates and formation of soliton molecules

Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross-Pitaevskii equation and good qualitative agreement between them is demonstrated.

S.M. Al-Marzoug

Papers

Solitons in PT-symmetric potential with competing nonlinearity

Unidirectional soliton flows in PT-symmetric potentials

Interaction of solitons in one-dimensional dipolar Bose-Einstein condensates and formation of soliton molecules

Weakly bound solitons and two-soliton molecules in dipolar Bose–Einstein condensates

Unidirectional flow of discrete solitons in optical waveguide arrays with nonlinearity management