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)
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)
Carl M. Bender, Moshe Moshe, Sarben Sarkar
The conventional double-scaling limit of a quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian appears to define a quantum theory whose energy is complex. Worse yet, the functional integral for the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one approaches this correlated limit in a PT-symmetric fashion. The partition function is calculated explicitly in the double-scaling limit of an zero-dimensional O(N)-symmetric quartic model.
http://arxiv.org/abs/1206.4943
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Alexander Szameit, Mikael C. Rechtsman, Omri Bahat-Treidel, Mordechai Segev
We apply gain/loss to honeycomb photonic lattices and demonstrate that optical tachyons, a photonic version of particles that travel faster than the speed of light, can be generated by PT-symmetry breaking in this structure. We further show that the PT-symmetry can be restored via strain.
http://arxiv.org/abs/1103.3389
Optics (physics.optics)
Alexander Szameit, Mikael C. Rechtsman, Omri Bahat-Treidel, Mordechai Segev
We apply gain/loss to honeycomb photonic lattices and show that the dispersion relation is identical to tachyons – particles with imaginary mass that travel faster than the speed of light. This is accompanied by PT-symmetry breaking in this structure. We further show that the PT-symmetry can be restored by deforming the lattice.
http://arxiv.org/abs/1103.3389
Optics (physics.optics)
Joshua Feinberg
We briefly discuss construction of energy-dependent effective non-hermitian hamiltonians for studying resonances in open disordered systems
http://arxiv.org/abs/1011.5932
Disordered Systems and Neural Networks (cond-mat.dis-nn); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)