Henning Schomerus, Nicole Yunger Halpern
We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The spectral properties of the higher Landau levels are constrained by a generalized time-reversal symmetry. In the setting of two-dimensional photonic crystal lasers, the anomaly directly affects the mode selection and lasing threshold while in three-dimensional photonic lattices it can be probed via beam dynamics.
http://arxiv.org/abs/1208.2901
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics)
Alois Regensburger, Christoph Bersch, Mohammad-Ali Miri, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel
The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of ‘parity–time symmetry’ in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity–time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity–time symmetry to a new generation of multifunctional optical devices and networks.
http://dx.doi.org/10.1038/nature11298
Christopher Birchall, Henning Schomerus
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a PT or a PTT’ time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the hermitian limit of the considered models.
http://arxiv.org/abs/1208.2575
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Optics (physics.optics)
Christopher Birchall, Henning Schomerus
We find that in nonhermitian PT-symmetric systems (as realized in resonators with balanced absorption and amplification), a mechanism based on quantum-to-classical correspondence reduces the occurrence of strongly amplified states. The reduction arises from semiclassically emerging hierarchical phase-space structures that are associated with the coupling of the amplifying and absorbing regions (forward and backward-trapped sets and their complements), and amounts to a generalization of the fractal Weyl law, earlier proposed for ballistically open systems. In the context of the recently introduced class of PT-symmetric laser-absorbers, this phenomenon reduces the number of states participating in the mode competition.
http://arxiv.org/abs/1208.2259
Quantum Physics (quant-ph); Optics (physics.optics)
Petr Siegl, David Krejcirik
We show that the eigenvectors of the PT -symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic singularity reflected in the inevitable unboundedness of the inverse. Moreover, the existence of nontrivial pseudospectrum is observed. In other words, there is no quantum-mechanical Hamiltonian associated with it via bounded and boundedly invertible similarity transformations. These results open new directions in physical interpretation of PT -symmetric models with intrinsically singular metric, since their properties are essentially different with respect to self-adjoint Hamiltonians, for instance, due to spectral instabilities.
http://arxiv.org/abs/1208.1866
Quantum Physics (quant-ph); Mathematical Physics (math-ph)
Physical Review D 86, 121702 (2012)
Mohammad-Ali Miri, Alois Regensburger, Ulf Peschel, Demetrios N. Christodoulides
We investigate a new class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response is studied in both the passive and parity-time (PT) symmetric regime. The possibility of band merging and the emergence of exceptional points along with the associated optical dynamics are considered in detail both above and below the PT-symmetry breaking point. Finally unidirectional invisibility in PT-synthetic mesh lattices is also examined along with possible superluminal light transport dynamics.
http://arxiv.org/abs/1208.1722
Quantum Physics (quant-ph)
Zafar Ahmed
In non-relativistic quantum scattering, Hermiticity is necessary for both reciprocity and unitarity. Reciprocity means that both reflectivity (R) and transmitivity (T) are insensitive to the direction of incidence of a wave (particle) at a scatterer from left/right. Unitarity means that R+T=1. In scattering from non-Hermitian PT-symmetric structures the (left/right) handedness (non-reciprocity) of reflectivity is known to be essential and unitarity remains elusive so far. Here we present a surprising occurrence of both reciprocity and unitarity in scattering from a complex PT-symmetric potential. In special cases, we show that this potential can even become invisible (R=0, T=1) from both left and right sides. We also find that this optical potential can give rise to a perfect transmission (T=1) this time without both unitarity and reciprocity (of reflectivity).
http://arxiv.org/abs/1207.6896
Quantum Physics (quant-ph); Mathematical Physics (math-ph)
V. N. Rodionov
The quantum-field model described by non-Hermitian, but a \({\cal PT}\)-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value \(m \leq m_{max}= {m_1}^2/2m_2\) takes place for the case of a fermion field with a \(\gamma_5\)-dependent mass term (\(m\rightarrow m_1 +\gamma_5 m_2 \)). In the regions of unbroken \(\cal PT\) symmetry the Hamiltonian \(H\) has another symmetry represented by a linear operator \( \cal C\). We exactly construct this operator by using a non-perturbative method. In terms of \( \cal C\) operator we calculate a time-independent inner product with a positive-defined norm. As a consequence of finiteness mass spectrum we have the \(\cal PT\)-symmetric Hamiltonian in the areas \((m\leq m_{max})\), but beyond this limits \(\cal PT\)-symmetry is broken. Thus, we obtain that the basic results of the fermion field model with a \(\gamma_5\)-dependent mass term is equivalent to the Model with a Maximal Mass which for decades has been developed by V.Kadyshevsky and his colleagues. In their numerous papers the condition of finiteness of elementary particle mass spectrum was introduced in a purely geometric way, just as the velocity of light is a maximal velocity in the special relativity. The adequate geometrical realization of the limiting mass hypothesis is added up to the choice of (anti) de Sitter momentum space of the constant curvature.
http://arxiv.org/abs/1207.5463
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)
Raam Uzdin, Uwe Guenther, Saar Rahav, Nimrod Moiseyev
The evolution speed in projective Hilbert space is considered for Hermitian Hamiltonians and for non-Hermitian (NH) ones. Based on the Hilbert-Schmidt norm and the spectral norm of a Hamiltonian, resource-related upper bounds on the evolution speed are constructed. These bounds are valid also for NH Hamiltonians and they are illustrated for an optical NH Hamiltonian and for a non-Hermitian \(\mathcal{PT}\)-symmetric matrix Hamiltonian. Furthermore, the concept of quantum speed efficiency is introduced as measure of the system resources directly spent on the motion in the projective Hilbert space. A recipe for the construction of time-dependent Hamiltonians which ensure 100% speed efficiency is given. Generally these efficient Hamiltonians are NH but there is a Hermitian efficient Hamiltonian as well. Finally, the extremal case of a non-Hermitian non-diagonalizable Hamiltonian with vanishing energy difference is shown to produce a 100% efficient evolution with minimal resources consumption.
http://arxiv.org/abs/1207.5373
Quantum Physics (quant-ph)
Eva-Maria Graefe, Alexei A. Mailybaev, Nimrod Moiseyev
In atomic physics, adiabatic evolution is often used to achieve a robust and efficient population transfer. Many adiabatic schemes have also been implemented in optical waveguide structures. Recently there has been increasing interests in the influence of decay and absorption, and their engineering applications. Here it is shown that contrary to what is often assumed, even a small decay can significantly influence the dynamical behaviour of a system, above and beyond a mere change of the overall norm. In particular, a small decay can lead to a breakdown of adiabatic transfer schemes, even when both the spectrum and the eigenfunctions are only sightly modified. This is demonstrated for the decaying version of a STIRAP scheme that has recently been implemented in optical waveguide structures. It is found that the transfer property of the scheme breaks down at a sharp threshold, which can be estimated by simple analytical arguments.
http://arxiv.org/abs/1207.5235
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optics (physics.optics)