Stefano Longhi
The spectral and localization properties of PT-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure the unbroken PT phase are derived. The analysis is applied to the case of superlattices describing a complex (PT-symmetric) extension of the Harper Hamiltonian in the rational case.
http://arxiv.org/abs/1402.3165
Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
S.Bittner, B.Dietz, H.L.Harney, M.Miski-Oglu, A.Richter, F. Schäfer
Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
http://arxiv.org/abs/1402.3537
Chaotic Dynamics (nlin.CD)
A. Demirkaya, M. Stanislavova, A. Stefanov, T. Kapitula, P.G. Kevrekidis
In the present work we consider the introduction of PT-symmetric terms in the context of classical Klein-Gordon field theories. We explore the implication of such terms on the spectral stability of coherent structures, namely kinks. We find that the conclusion critically depends on the location of the kink center relative to the center of the PT-symmetric term. The main result is that if these two points coincide, the kink’s spectrum remains on the imaginary axis and the wave is spectrally stable. If the kink is centered on the “lossy side” of the medium, then it becomes stabilized. On the other hand, if it becomes centered on the “gain side” of the medium, then it is destabilized. The consequences of these two possibilities on the linearization (point and essential) spectrum are discussed in some detail.
http://arxiv.org/abs/1402.2942
Pattern Formation and Solitons (nlin.PS); Mathematical Physics (math-ph)
C. Yuce
PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of disorder for small number of lattice sites. We obtain the Hofstadter Butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserves the total intensity.
http://arxiv.org/abs/1402.2749
Quantum Physics (quant-ph)
Charles Liang, Derek D. Scott, Yogesh N. Joglekar
In systems with “balanced loss and gain”, the PT-symmetry is broken by increasing the non-hermiticity or the loss-gain strength. We show that finite lattices with oscillatory, PT-symmetric potentials exhibit a new class of PT-symmetry breaking and restoration. We obtain the PT phase diagram as a function of potential periodicity, which also controls the location complex eigenvalues in the lattice spectrum. We show that the sum of PT-potentials with nearby periodicities leads to PT-symmetry restoration, where the system goes from a PT-broken state to a PT-symmetric state as the average loss-gain strength is increased. We discuss the implications of this novel transition for the propagation of a light in an array of coupled waveguides.
http://arxiv.org/abs/1402.2544
Quantum Physics (quant-ph); Optics (physics.optics)
Atushi Tanaka, Sang Wook Kim, Taksu Cheon
The correspondence between exotic quantum holonomy that occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expressions of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, are obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher order EP, which is broken into lower order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.
http://arxiv.org/abs/1402.1634
Quantum Physics (quant-ph)
D. Krejcirik, P. Siegl, M. Tater, J. Viola
We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.
http://arxiv.org/abs/1402.1082
Spectral Theory (math.SP); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
F. Bagarello, S. Triolo
We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the Hilbert space, and we apply the procedure to coherent states. We conclude the paper considering a simple application of our construction to pseudo-hermitian quantum mechanics.
http://arxiv.org/abs/1402.0425
Mathematical Physics (math-ph)
Li Ge, A. Douglas Stone
We consider the role of degeneracy in Parity-Time (PT) symmetry breaking for non-hermitian wave equations beyond one dimension. We show that if the spectrum is degenerate in the absence of T-breaking, and T is broken in a generic manner (without preserving other discrete symmetries), then the standard PT-symmetry breaking transition does not occur, meaning that the spectrum is complex even for infinitesimal strength of gain and loss. However the reality of the entire spectrum can be preserved over a finite interval if additional discrete symmetries X are imposed when T is broken, if X decouple all degenerate modes. When this is true only for a subset of the degenerate spectrum, there can be a partial PT transition in which this subset remains real over a finite interval of T-breaking. If the spectrum has odd-degeneracy, a fraction of the degenerate spectrum can remain in the symmetric phase even without imposing additional discrete symmetries, and they are analogous to dark states in atomic physics. These results are illustrated by the example of different T-breaking perturbations of a uniform dielectric disk and sphere. Finally, we show that multimode coupling is capable of restoring the PT-symmetric phase at finite T-breaking. We also analyze these questions when the parity operator is replaced by another spatial symmetry operator and find that the behavior can be qualitatively different.
http://arxiv.org/abs/1402.0428
Quantum Physics (quant-ph); Optics (physics.optics)
Vladimir V. Konotop, Dmitry A. Zezyulin
We introduce a stochastic PT-symmetric coupler, which is based on dual-core waveguides with fluctuating parameters, such that the gain and the losses are exactly balanced in average. We consider different parametric regimes which correspond to the broken and unbroken PT symmetry, as well as to the exceptional point of the underlying deterministic system. We demonstrate that in all the cases the statistically averaged intensity of the field grows. This result holds for either linear or nonlinear coupler and is independent on the type of fluctuations.
http://arxiv.org/abs/1401.6352
Optics (physics.optics)