X. Q. Li, X. Z. Zhang, G. Zhang, Z. Song
We study the possibility of asymmetric transmission induced by a non-Hermitian scattering center embedded in a one-dimensional waveguide, motivated by the aim of realizing quantum diode in a non-Hermitian system. It is shown that a PT symmetric non-Hermitian scattering center always has symmetric transmission although the dynamics within the isolated center can be unidirectional, especially at its exceptional point. We propose a concrete scheme based on a flux-controlled non-Hermitian scattering center, which comprises a non-Hermitian triangular ring threaded by an Aharonov-Bohm flux. The analytical solution shows that such a complex scattering center acts as a diode at the resonant energy level of the spectral singularity, exhibiting perfect unidirectionality of the transmission. The connections between the phenomena of the asymmetric transmission and reflectionless absorption are also discussed.
http://arxiv.org/abs/1409.0420
Quantum Physics (quant-ph)
Sunkyu Yu, Hyun Sung Park, Xianji Piao, Bumki Min, Namkyoo Park
Chirality is a universal feature in nature, as observed in fermion interactions and DNA helicity. Much attention has been given to the chiral interactions of light, not only regarding its physical interpretation but also focusing on intriguing phenomena in excitation, absorption, generation, and refraction. Although recent progress in metamaterials and 3-dimensional writing technology has spurred artificial enhancements of optical chirality, most approaches are founded on the same principle of the mixing of electric and magnetic responses. However, due to the orthogonal form of electric and magnetic fields, intricate designs are commonly required for mixing. Here, we propose an alternative route to optical chirality, exploiting the nonmagnetic mixing of amplifying and decaying electric modes based on non-Hermitian theory. We show that a 1-dimensional helical eigenmode can exist singularly in a complex anisotropic material, in sharp contrast to the 2-dimensional eigenspaces employed in previous approaches. We demonstrate that exceptional interactions between propagating chiral waves result from this low-dimensionality, for example, one-way reflectionless chiral conversions and chirality reversal, each occurring for circular and linear polarization. Our proposal and experimental verification with complex polar meta-molecules not only provide a significant step for low-dimensional chirality, but also enable the dynamics of optical spin black hole.
http://arxiv.org/abs/1409.0180
Optics (physics.optics)
Altug Arda, Ramazan Sever
We investigate the approximate bound state solutions of the Schrodinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number \(\ell\).
http://arxiv.org/abs/1409.0518
Quantum Physics (quant-ph)
Amarendra K. Sarma, Balla Prannay
We have studied a three-level \(\Lambda\)-type atomic system with all the energy levels exhibiting decay. The system is described by a pseudo-Hermitian Hamiltonian and subject to certain conditions, the Hamiltonian shows parity-time (PT) symmetry. The probability amplitudes of various atomic levels both below and above the PT-theshold is worked out.
http://arxiv.org/abs/1408.6672
Quantum Physics (quant-ph); Optics (physics.optics)
Yaroslav V. Kartashov, Boris A. Malomed, Lluis Torner
We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a PT-symmetry in the form of a purely real spectrum of modes, we show that the PT-symmetry is never broken in the present system, and that the system always supports stable bright solitons, fundamental and multi-pole ones. Such phenomenon is connected to non-linearizability of the underlying evolution equation. The increase of the gain-losses strength results, in lieu of the PT-symmetry breaking, in merger of pairs of different soliton branches, such as fundamental and dipole, or tripole and quadrupole ones. The fundamental and dipole solitons remain stable for all values of the gain-loss coefficient.
http://arxiv.org/abs/1408.6174
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)
Rabin Banerjee, Pradip Mukherjee
We provide a reduction of a set of two coupled oscillators with balanced loss and gain in their elementary modes. A possible method of quantization based on these elementary modes, in the framework of PT symmetric quantum mechanics is indicated.
http://arxiv.org/abs/1408.5038
High Energy Physics – Theory (hep-th)
J. M. Lee, T. Kottos, B. Shapiro
We introduce the notion of PT-symmetry in magnetic nanostructures and show that they can support a new type of non-Hermitian dynamics. Using the simplest possible set-up consisting of two coupled ferromagnetic films, one with loss and another one with a balanced amount of gain, we demonstrate the existence of a spontaneous PT-symmetry breaking point where both the eigenfrequencies and eigenvectors are degenerate. Below this point the frequency spectrum is real indicating stable dynamics while above this point it is complex signaling unstable dynamics.
http://arxiv.org/abs/1408.3285
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD)
Changming Huang, Fangwei Ye, Yaroslav V. Kartashov, Boris A Malomed, Xianfeng Chen
The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schr\”odinger equation and the paraxial wave equation that governs the propagation of light in a guiding structure. We go beyond the bounds of the paraxial approximation and demonstrate, using the solution of the Maxwell’s equations for light beams propagating in deeply subwavelength waveguides and periodic lattices with “balanced” gain and loss, that the PT symmetry may stay unbroken in this setting. Moreover, the PT-symmetry in subwavelength optical structures may be restored after being initially broken upon the increase of gain and loss. Critical gain/loss levels, at which the breakup and subsequent restoration of the PT symmetry occur, strongly depend on the scale of the structure.
http://arxiv.org/abs/1408.2630
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)
Carl M. Bender, Daniel W. Hook, Nick E. Mavromatos, Sarben Sarkar
Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field \(\phi\). In Euclidean space the Lagrangian of such a theory, \(L=\frac{1}{2}(\nabla\phi)^2−ig\phi \exp(ia\phi)\), is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics) the energy spectrum is calculated in the semiclassical limit and the \(m\)th energy level in the \(n\)th sector is given by \(E_{m,n}∼(m+1/2)^2a^2/(16n^2)\).
http://arxiv.org/abs/1408.2432
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A. Szameit, D.N Christodoulides
We introduce a recursive bosonic quantization technique for generating classical PT photonic structures that possess hidden symmetries and higher order exceptional points. We study light transport in these geometries and we demonstrate that perfect state transfer is possible only for certain initial conditions. Moreover, we show that for the same propagation direction, left and right coherent transports are not symmetric with field amplitudes following two different trajectories. A general scheme for identifying the conservation laws in such PT-symmetric photonic networks is also presented.
http://arxiv.org/abs/1408.1561
Optics (physics.optics); Quantum Physics (quant-ph)