September 2011
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Month September 2011

Stability of solitons in PT-symmetric couplers

Rodislav Driben, Boris A. Malomed

Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the “supersymmetric” case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching (“management”).
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

Can Electroweak Theory Without A Higgs Particle Be Renormalizable?

J. W. Moffat

Whether there exists a massive electroweak (EW) theory, without a Higgs spontaneous symmetry breaking mechanism, that is gauge invariant and renormalizable is investigated. A Stueckelberg formalism for massive \(W\) and \(Z\) bosons is used to derive a gauge invariant EW theory. Negative energy scalar fields that emerge from the gauge invariance of the Lagrangian are removed by invoking an indefinite metric in Hilbert space. A unitary S-matrix and a positive energy spectrum can be obtained by using the PT symmetric formulation of the pseudo-Hermitian Hamiltonian. The theory predicts that if for a system of particles the scalar boson energy \(E_s < \lambda^{1/2}M_W\), where \(\lambda\) is a gauge parameter and \(M_W\) is the \(W\) boson mass, then as \(\lambda\rightarrow\infty\) the scalar boson mass \(\mu=\lambda^{1/2}M_W\) tends to infinity. The theory is perturbatively renormalizable and does not violate longitudinally polarized \(W_L W_L\rightarrow W_L W_L\) scattering in the energy range \(E < \lambda^{1/2}M_W\) for which the scalar bosons have an undetected mass. This means that with this scenario the EW theory can only be treated as an effective renomalizable theory and not as a UV complete theory.
High Energy Physics – Phenomenology (hep-ph); High Energy Physics – Theory (hep-th)

Non-hermitian dynamics of the photosynthetic exciton

A. Thilagam

The non-hermitian quantum dynamics of excitonic energy transfer in photosynthetic systems is investigated using a dissipative two-level dimer model which incorporates radiative terms. The approach is based on the Green’s function formalism which permits consideration of decoherence and intersite transfer processes on comparable terms. The results indicate a combination of coherent and incoherent behavior at higher temperatures with the possibility of exceptional points occuring at the coherent-incoherent crossover regime at critical temperatures. When each dimer site is coupled equally to the environmental sources of dissipation, the excitonic wavepacket evolves with time with a coherent component, which can be attributed to the indistinguishability of the sources of dissipation. The time evolution characteristics of the B850 Bchls dimer system is analysed using typical estimates in photosynthetic systems.
Quantum Physics (quant-ph)

Nonlocal gap solitons in parity-time symmetric optical lattices

Huagang Li, Xiujuan Jiang, Xing Zhu, Zhiwei Shi

We numerically study the nonlocal gap solitons in parity-time (PT) symmetric optical lattices built into a nonlocal self-focusing medium. We state the existence, stability, and propagation dynamics of such PT gap solitons in detail. Simulated results show that there exist stable gap soltions. The influences of the degree of nonlocality on the soliton power, the energy flow density and the stable region of the PT gap solitons are also examined.
Optics (physics.optics)

Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators

Gwangsu Yoo, H.-S. Sim, Henning Schomerus

PT-symmetric optical resonators combine absorbing regions with active, amplifying regions. The latter are the source of radiation generated via spontaneous and stimulated emission, which embodies quantum noise and can result in lasing. We calculate the frequency-resolved output radiation intensity of such systems and relate it to a suitable measure of excess noise and mode nonorthogonality. The lineshape differs depending on whether the emission lines are isolated (as for weakly amplifying, almost hermitian systems) or overlapping (as for the almost degenerate resonances in the vicinity of exceptional points associated to spontaneous PT-symmetry breaking). The calculations are carried out in the scattering input-output formalism, and are illustrated for a quasi one-dimensional resonator set-up. In our derivations we also allow for the more general case of a resonator in which the amplifying and absorbing regions are not related by symmetry.
Optics (physics.optics)

Topological properties of three interacting eigenmodes in a non-Hermitian Hamiltonian

Jung-Wan Ryu, Soo-Young Lee, Sang Wook Kim

We have investigated the topological properties associated with degeneracies of a non-Hermitian Hamiltonian, called as exceptional points (EPs), in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely determined when encircling more than two EPs once, we can recover the initial configuration of the modes by encircling two EPs three times or three EPs twice. The group theoretical consideration provides some hint on it. We confirm our expectation by numerically calculating the modes of an open quantum system, two dielectric microdisks.
Quantum Physics (quant-ph)

Exact Solution of Schrödinger Equation for Three Physical Potentials Using Nikiforov-Uvarov Method

B. J. Falaye, K. J. Oyewumi, M. Abbas

In this paper, we present the exact solution of one dimensional Schr\”odinger equation for Wood-Saxon plus Rosen-Morse plus symmetrical double well potential via Nikiforov-Uvarov mathematical method. The eigenvalues and eigenfunctions of this potential are obtained. The energy equations and the corresponding wave function for special cases of this potential are briefly discussed. The PT-symmetry and Hermiticity for this potential are also considered.
Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Spontaneous Generation of Photons in Transmission of Quantum Fields in PT Symmetric Optical Systems

G. S. Agarwal, Kenan Qu

We develop a rigorous mathematically consistent description of PT symmetric optical systems by using second quantization. We demonstrate the possibility of significant spontaneous generation of photons in PT symmetric systems. Further we show the emergence of Hanbury-Brown Twiss (HBT) correlations in spontaneous generation. We show that the spontaneous generation determines decisively the nonclassical nature of fields in PT symmetric systems. Our work can be applied to other systems like plasmonic structure where losses are compensated by gain mechanisms.
Quantum Physics (quant-ph)

Experimental Study of Active LRC Circuits with PT-Symmetries

Joseph Schindler, Ang Li, Mei C. Zheng, F. M. Ellis, Tsampikos Kottos

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain/loss mechanisms break the Hermiticity while preserving parity-time PT symmetry. For a value PT of the gain/loss strength parameter the eigen-frequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce acquiring a definite chirality. The consequences of the phase-transition in the spatiotemporal energy evolution are also presented.
Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)

Conserved Correlation in PT -symmetric Systems: Scattering and Bound States

Kumar Abhinav, Arun Jayannavar, P. K. Panigrahi

For one-dimensional PT -symmetric systems, it is observed that the non-local product obtained from the continuity equation can be interpreted as a conserved corre- lation function. This leads to physical conclusions, regarding both discrete and continuum states of such systems. Asymptotic states are shown to have necessarily broken PT -symmetry, leading to modified scattering and transfer matrices. This yields restricted boundary conditions, e.g., in- cidence from both sides, analogous to that of the proposed PT CPA laser. The interpretation of left and right states leads to a Hermitian S-matrix, resulting in the non-conservation of the flux. This further satisfies a duality condition, identical to the optical analogues. However, the non-local conserved scalar implements alternate boundary conditions in terms of in and out states, leading to the pseudo-Hermiticity condition in terms of the scattering matrix. Interestingly, when PT -symmetry is preserved, it leads to stationary states with real energy, naturally inter- pretable as bound states. The broken PT -symmetric phase is also captured by this correlation, with complex-conjugate pair of energies, interpreted as resonances.
Quantum Physics (quant-ph)