F. Nazari, N. Bender, H. Ramezani, M. K. Moravvej-Farshi, D. N. Christodoulides, T. Kottos
We introduce a new type of Fano resonances, realized in a photonic circuit which consists of two nonlinear PT-symmetric micro-resonators side-coupled to a waveguide, which have line-shape and resonance position that depends on the direction of the incident light. We utilize these features in order to induce asymmetric transport up to 47 dBs in the optical C-window. Our set-up requires low input power and does not compromise the power and frequency characteristics of the output signal.
http://arxiv.org/abs/1310.2313
Optics (physics.optics)
Ali Mostafazadeh
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrodinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, anti-lasing, and unidirectional invisibility.
http://arxiv.org/abs/1310.0592
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Optics (physics.optics)
F. Bagarello, M. Lattuca
We show how some recent models of PT-quantum mechanics perfectly fit into the settings of \(\cal D\) pseudo-bosons, as introduced by one of us. Among the others, we also consider a model of non-commutative quantum mechanics, and we show that this model too can be described in terms of \(\cal D\) pseudo-bosons.
http://arxiv.org/abs/1310.0359
Mathematical Physics (math-ph); Quantum Physics (quant-ph)
F. Kh. Abdullaev, V.A. Brazhnyi, M. Salerno
The resonant scattering of gap solitons (GS) of the periodic nonlinear Schr\”odinger equation with a localized defect which is symmetric under the parity and the time-reversal (PT) symmetry, is investigated. It is shown that for suitable amplitudes ratios of the real and imaginary parts of the defect potential the resonant transmission of the GS through the defect becomes possible. The resonances occur for potential parameters which allow the existence of localized defect modes with the same energy and norm of the incoming GS. Scattering properties of GSs of different band-gaps with effective masses of opposite sign are investigated. The possibility of unidirectional transmission and blockage of GSs by PT defect, as well as, amplification and destruction induced by multiple reflections from two PT defects, are also discussed.
http://arxiv.org/abs/1309.7655
Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Optics (physics.optics)
O. Vazquez-Candanedo, J. C. Hernandez-Herrejon, F. M. Izrailev, D. N. Christodoulides
We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of PT-symmetry in energy transport problems occurring in such PT-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples.
http://arxiv.org/abs/1309.6708
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
A. Grod, S. Kuzhel
Non-self-adjoint Schrodinger operators A which correspond to non-symmetric zero-range potentials are investigated. For a given A, the description of non-real eigenvalues, spectral singularities and exceptional points are obtained; the possibility of interpretation of A as a self-adjoint operator in a Krein space is studied, the problem of similarity of A to a self-adjoint operator in a Hilbert space is solved.
http://arxiv.org/abs/1309.5482
Mathematical Physics (math-ph); Spectral Theory (math.SP); Quantum Physics (quant-ph)
Carlos A. Margalli, J. David Vergara
The quantization of higher order time derivative theories including interactions is unclear. In this paper in order to solve this problem, we propose to consider a complex version of the higher order derivative theory and map this theory to a real first order theory. To achieve this relationship, the higher order derivative formulation must be complex since there is not a real canonical transformation from this theory to a real first order theory with stable interactions. In this manner, we work with a non-Hermitian higher order time derivative theory. To quantize this complex theory, we introduce reality conditions that allow us to map the complex higher order theory to a real one, and we show that the resulting theory is regularizable and renormalizable for a class of interactions.
http://arxiv.org/abs/1309.2928
High Energy Physics – Theory (hep-th)
Chao Hang, Dmitry A. Zezyulin, Vladimir V. Konotop, Guoxiang Huang
We propose a scheme of creating a tunable highly nonlinear defect in a one-dimensional photonic crystal. The defect consists of an atomic cell filled in with two isotopes of three-level atoms. The probe-field refractive index of the defect can be made parity-time (PT) symmetric, which is achieved by proper combination of a control field and of Stark shifts induced by a far-off-resonance field. In the PT-symmetric system families of stable nonlinear defect modes can be formed by the probe field.
http://arxiv.org/abs/1309.2839
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)
Jianke Yang
For the one-dimensional nonlinear Schroedinger equations with parity-time (PT) symmetric potentials, it is shown that when a real symmetric potential is perturbed by weak PT-symmetric perturbations, continuous families of asymmetric solitary waves in the real potential are destroyed. It is also shown that in the same model with a general PT-symmetric potential, symmetry breaking of PT-symmetric solitary waves do not occur. Based on these findings, it is conjectured that one-dimensional PT-symmetric potentials cannot support continuous families of non-PT-symmetric solitary waves.
http://arxiv.org/abs/1309.1652
Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)
Francisco M. Fernández, Javier Garcia
We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. We show that PT-symmetric Hamiltonians with point-group symmetry \(C_{2v}\) exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit.
http://arxiv.org/abs/1309.0808
Quantum Physics (quant-ph)