Alois Regensburger, Mohammad-Ali Miri, Christoph Bersch, Jakob Näger, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel
We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics.
http://arxiv.org/abs/1301.1455
Optics (physics.optics); Quantum Physics (quant-ph)
Henning Schomerus
One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Drawing on the concepts of band-structure topology, I here describe the formation of exponentially localized, topologically protected midgap states in photonic systems with spatially distributed gain and loss. When gain and loss are suitably arranged these states maintain their topological protection and then acquire a selectively tunable amplification rate. This finds applications in the beam dynamics along a photonic lattice and in the lasing of quasi-one-dimensional photonic crystals.
http://arxiv.org/abs/1301.0777
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Rajkumar Roychoudhury, Barnana Roy, Partha Pratim Dube
A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.
http://arxiv.org/abs/1301.0716
Mathematical Physics (math-ph); Quantum Physics (quant-ph)
The 11th Analytic and Algebraic Methods in Physics conference will be held at Villa Lanna, Prague, CZ between 30 October 2013 and 1 November 2013.
Details of the conference and registration may be found on:
http://gemma.ujf.cas.cz/~znojil/conf/micromeetingjedenact.html
O. Yesiltas
In this article, we have introduced a \(\mathcal{PT}\)-symmetric non-Hermitian Hamiltonian model which is given as \(\hat{\mathcal{H}}=\omega (\hat{b}^{\dagger}\hat{b}+1/2)+ \alpha (\hat{b}^{2}-(\hat{b}^{\dagger})^{2})\) where \(\omega\) and \(\alpha\) are real constants, \(\hat{b}\) and \(\hat{b^{\dagger}}\) are first order differential operators. The Hermitian form of the Hamiltonian \(\mathcal{\hat{H}}\) is obtained by suitable mappings and it is interrelated to the time independent one dimensional Dirac equation in the presence of position dependent mass. Then, Dirac equation is reduced to a Schr\”{o}dinger-like equation and two new complex non-\(\mathcal{PT}\)-symmetric vector potentials are generated. We have obtained real spectrum for these new complex vector potentials using shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.
http://arxiv.org/abs/1301.0205
Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Yan-Gang Miao, Zhen-Ming Xu
Real eigenvalues of some non-Hermitian (pseudo-Hermitian or PT-symmetric) Hamiltonians can be determined by solving operator quantum equations of motion rather than Schroedinger equations within the framework of quantum mechanics. This method is in particular applicable for the class of models which are closely related to the harmonic oscillator. In this way, a new application of quantum mechanics is thus given.
http://arxiv.org/abs/1212.6705
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)
Andrei G. Bytsko
An open \(U_q(sl_2)\)-invariant spin chain of spin S and length N with inhomogeneous coupling is investigated as an example of a non-Hermitian (quasi-Hermitian) model. For several particular cases of such a chain, the ranges of the deformation parameter gamma are determined for which the spectrum of the model is real. For a certain range of gamma, a universal metric operator is constructed and thus the quasi-Hermiticity of the model is established. The constructed metric operator is non-dynamical, its structure is determined only by the symmetry of the model. The results apply, in particular, to all known homogeneous \(U_q(sl_2)\)-invariant integrable spin chains with nearest-neighbour interaction. In addition, the most general form of a metric operator for a quasi-Hermitian operator in finite dimensional space is discussed.
http://arxiv.org/abs/0911.4476
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)
G. Najarbashi, M. A. Fasihi, M. Nakahara, F. Mirmasoudi, S. Mirzaei
In this paper the entanglement of multi-qubit fermionic pseudo Hermitian coherent states (FPHCS) described by anticommutative Grassmann numbers is studied. The pseudo-Hermitian versions of the well known maximally entangled pure states such as Bell and GHZ, W and biseparable states are introduced through integrating over the tensor products of FPHCSs with suitable choice of Grassmannian weight functions. Meanwhile as an illustration, the method is applied to tensor product of 2 and 3 qubit pseudo Hermitian systems. Then the measures of concurrence and average entropy are applied to quantify the entanglement of the pseudo two and three qubit states respectively.
http://arxiv.org/abs/1212.5675
Quantum Physics (quant-ph)
Yongyao Li, Jingfeng Liu, Wei Pang, Boris A. Malomed
We study effects of the spontaneous symmetry-breaking (SSB) in solitons built of the dipolar Bose-Einstein condensate (BEC), trapped in a dual-core system with the dipole-dipole interactions (DDIs) and hopping between the cores. Two realizations of such a matter-wave coupler are introduced, weakly- and strongly-coupled. The former one in based on two parallel pipe-shaped traps, while the latter one is represented by a single pipe sliced by an external field into parallel layers. The dipoles are oriented along axes of the pipes. In these systems, the dual-core solitons feature the SSB of the supercritical type and subcritical types, respectively. Stability regions are identified for symmetric and asymmetric solitons, and, in addition, for non-bifurcating antisymmetric ones, as well as for symmetric flat states, which may also be stable in the strongly-coupled system, due to competition between the attractive and repulsive intra- and inter-core DDIs. Effects of the contact interactions are considered too. Collisions between moving asymmetric solitons in the weakly-symmetric system feature elastic rebound, merger into a single breather, and passage accompanied by excitation of intrinsic vibrations of the solitons, for small, intermediate, and large collision velocities, respectively. A PT-symmetric version of the weakly-coupled system is briefly considered too, which may be relevant for matter-wave lasers. Stability boundaries for PT-symmetric and antisymmetric solitons are identified.
http://arxiv.org/abs/1212.5568
Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS)
Chao Hang, Guoxiang Huang, Vladimir V. Konotop
We show that a vapor of multilevel atoms driven by far-off resonant laser beams, with possibility of interference of two Raman resonances, is highly efficient for creating parity-time (PT) symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is anti-symmetric in space. The spatial modulation of the susceptibility is achieved by proper combination of standing-wave strong control fields and of Stark shifts induced by a far-off-resonance laser field. As particular examples we explore a mixture of isotopes of Rubidium atoms and design a PT-symmetric lattice and a parabolic refractive index with a linear imaginary part.
http://arxiv.org/abs/1212.5486
Optics (physics.optics)