July 2012
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Day July 10, 2012

Giant amplification of modes in PT-symmetric waveguides

Vladimir V. Konotop, Valery S. Shchesnovich, Dmitry A. Zezyulin

The combination of the interference with the amplification of modes in a waveguide with gain and losses can result in a giant amplification of the propagating beam, which propagates without distortion of its average amplitude. An increase of the gain-loss gradient by only a few times results in a magnification of the beam by a several orders of magnitude.

http://arxiv.org/abs/1207.1792
Optics (physics.optics)

Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential

Ananya Ghatak, Bhabani Prasad Mandal, Zafar Ahmed

We bring out the existence of at most one spectral singularity (SS) and deep multiple minima in the reflectivity of the non-Hermitian (complex) Ginocchio potential. We find a parameter dependent single spectral singularity in this potential provided the imaginary part is emissive (not absorptive). The reflectionlessness of the real Hermitian Ginocchio’s potential at discrete positive energies gives way to deep multiple minima in reflectivity when this potential is perturbed and made non-Hermitian (complex). A novel co-existence of a SS with deep minima in reflectivity is also revealed wherein the first reflectivity zero of the Hermitian case changes to become a SS for the non-Hermitian case.

http://arxiv.org/abs/1207.1979

Quantum Physics (quant-ph)

PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring

Derek D. Scott, Yogesh N. Joglekar

We study the properties of an N-site tight-binding ring with parity and time-reversal (PT) symmetric, Hermitian, site-dependent tunneling and a pair of non-Hermitian, PT-symmetric, loss and gain impurities \(\pm i\gamma\). The properties of such lattices with open boundary conditions have been intensely explored over the past two years. We numerically investigate the PT-symmetric phase in a ring with a position-dependent tunneling function \(t_\alpha(k)=[k(N-k)]^{\alpha/2}\) that, in an open lattice, leads to a strengthened PT-symmetric phase, and study the evolution of the PT-symmetric phase from the open chain to a ring. We show that, generally, periodic boundary conditions weaken the PT-symmetric phase, although for experimentally relevant lattice sizes \(N \sim 50\), it remains easily accessible. We show that the chirality, quantified by the (magnitude of the) average transverse momentum of a wave packet, shows a maximum at the PT-symmetric threshold. Our results show that although the wavepacket intensity increases monotonically across the PT-breaking threshold, the average momentum decays monotonically on both sides of the threshold.

http://arxiv.org/abs/1207.1945
Quantum Physics (quant-ph); Optics (physics.optics)

Nonlinear Schrödinger equation for a PT symmetric delta-functions double well

Holger Cartarius, Daniel Haag, Dennis Dast, Günter Wunner

The time-independent nonlinear Schrodinger equation is solved for two attractive delta-function shaped potential wells where an imaginary loss term is added in one well, and a gain term of the same size but with opposite sign in the other. We show that for vanishing nonlinearity the model captures all the features known from studies of PT symmetric optical wave guides, e.g., the coalescence of modes in an exceptional point at a critical value of the loss/gain parameter, and the breaking of PT symmetry beyond. With the nonlinearity present, the equation is a model for a Bose-Einstein condensate with loss and gain in a double well potential. We find that the nonlinear Hamiltonian picks as stationary eigenstates exactly such solutions which render the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and bifurcation scenarios different from those known from linear PT symmetric Hamiltonians.

http://arxiv.org/abs/1207.1669
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Chaotic Dynamics (nlin.CD)

From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators

Henning Schomerus

I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions which can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales which govern the spectral transition from real to complex eigenvalues. The possible presence of magneto-optical effects (a finite vector potential) in multichannel systems leads to a variant (termed PTT’ symmetry) which imposes the same spectral constraints as PT symmetry. I also provide multichannel versions of generalized flux-conservation laws.

http://arxiv.org/abs/1207.1454
Quantum Physics (quant-ph); Optics (physics.optics)