Xiao-Dong Cui, Yujun Zheng
We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two states, biorthogonal or not, are generally derived by employing the generalized interference method. The counterpart of Manini-Pistolesi non-diagonal geometric phase in the non-Hermitian setting is taken as a typical example.
Quantum Physics (quant-ph)
IV Barashenkov, L Baker, NV Alexeeva
We consider parity-time (PT) symmetric arrays formed by N optical waveguides with gain and N waveguides with loss. When the gain-loss coefficient exceeds a critical value γc, the PT-symmetry becomes spontaneously broken. We calculate γc(N) and prove that γc→0 as N→∞. In the symmetric phase, the periodic array is shown to support 2N solitons with different frequencies and polarisations.
Optics (physics.optics); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)
Gennadiy Burlak, Boris A. Malomed
We introduce one- and two-dimensional (1D and 2D) models of parity-time PT-symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical waveguides, in the spatiotemporal and spatial domains, respectively. Stationary solutions for PT-symmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry breaking with the increase of the energy (norm), and retrieve the stability at still larger energies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable, is found by means of an analytical approximation, based on the CW (zero-dimensional) counterpart of the system. The approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numerical results for the stability limits of the 2D solitons are obtained by means of the computation of eigenvalues for small perturbations, and verified in direct simulations. Although large parts of the solitons families are unstable, the instability is quite weak. Collisions between 2D solitons in the PT-symmetric coupler are studied by means of simulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.
Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)
Yaroslav V. Kartashov, Vladimir V. Konotop, Fatkhulla Kh. Abdullaev
We report a diversity of stable gap solitons in a spin-orbit coupled Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is shown that the solitons, can be classified by the main physical symmetries they obey, i.e. symmetries with respect to parity (P), time (T), and internal degree of freedom, i.e. spin, (C) inversions. The conventional gap and gap-stripe solitons are obtained in lattices with different parameters. It is shown that solitons of the same type but obeying different symmetries can exist in the same lattice at different spatial locations. PT and CPT symmetric solitons have anti-ferromagnetic structure and are characterized respectively by nonzero and zero total magnetizations.
Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS)
In natural light harvesting systems, the sequential quantum events of photon absorption by specialized biological antenna complexes, charge separation, exciton formation and energy transfer to localized reaction centers culminates in the conversion of solar to chemical energy. A notable feature in these processes is the exceptionally high efficiencies (> 95 %) at which excitation is transferred from the illuminated protein complex site to the reaction centers. Such high exciton propagation rates within a system of interwoven biomolecular network structures, is yet to be replicated in artificial light harvesting complexes. A clue to unraveling the quantum puzzles of nature may lie in the observation of long lived coherences lasting several picoseconds in the electronic spectra of photosynthetic complexes, even in noisy environmental baths. A number of experimental and theoretical studies have been devoted to unlocking the links between quantum processes and information protocols, in the hope of finding answers to nature’s puzzling mode of energy propagation. This review presents developments in quantum theories, and links information-theoretic aspects with photosynthetic light-harvesting processes in biomolecular systems. There is examination of various attempts to pinpoint the processes that underpin coherence features arising from the light harvesting activities of biomolecular systems, with particular emphasis on the effects that factors such non-Markovianity, zeno mechanisms, teleportation, quantum predictability and the role of multipartite states have on the quantum dynamics of biomolecular systems. A discussion of how quantum thermodynamical principles and agent-based modeling and simulation approaches can improve our understanding of natural photosynthetic systems is included.
Quantum Physics (quant-ph); Biological Physics (physics.bio-ph); Chemical Physics (physics.chem-ph)
Xuele Liu, Subhasish Dutta Gupta, G.S. Agarwal
Spectral singularities are ubiquitous with PT-symmetry leading to infinite transmission and reflection coefficients. Such infinities imply the divergence of the fields in the medium thereby breaking the very assumption of the linearity of the medium used to obtain such singularities. We identify saturable nonlinearity retaining contributions from all orders of the field to limit the infinite growth and regularize the spectral singularity. We present explicit numerical results to demonstrate regularization. The all order nonlinear PT-symmetric device is shown to exhibit very effective isolation or optical diode action, since transmission through such a system is nonreciprocal. In contrast, a linear system or a system with Kerr nonlinearity is known to have only reciprocal transmission. Further we demonstrate optical bistability for such a system with high contrast.
Ilario Giordanelli, Gian Michele Graf
We give a partially alternate proof of the reality of the spectrum of the imaginary cubic oscillator in quantum mechanics.
Mathematical Physics (math-ph)
Mohammed F. Saleh, Andrea Marini, Fabio Biancalana
We have investigated the interaction between a strong soliton and a weak probe with certain configurations that allow optical trapping in gas-filled hollow-core photonic crystal fibers in the presence of the shock effect. We have shown theoretically and numerically that the shock term can lead to an unbroken parity-time (PT) symmetry potential in these kinds of fibers. Reciprocity breaking, a remarkable feature of the PT symmetry, is also demonstrated numerically. Our results will open different configurations and avenues for observing PT-symmetry breaking in optical fibers, without the need to resort to cumbersome dissipative structures.
Ananya Ghatak, Raka Dona Ray Mandal, Bhabani Prasad Mandal (BHU)
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes imaginary. For one PT-symmetric case we have entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from left (or right) at certain discrete energies. The penetrating states in the other PT-symmetric configuration are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. Presence of MSS and reflectionlessness are also discussed for the free states in the later case.
Quantum Physics (quant-ph)
H.Xu, P.G.Kevrekidis, Q.Zhou, D.J.Frantzeskakis, V.Achilleos, R.Carretero-Gonzalez
We study the nonlinear Schrodinger equation with a PT-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized Duffing equation. This way, we can obtain exact soliton solutions existing in the presence of suitable PT-symmetric potentials, and study their stability and dynamics. We report interesting new features, including oscillatory instabilities of solitons and (nonlinear) PT-symmetry breaking transitions, for focusing and defocusing nonlinearities.
Pattern Formation and Solitons (nlin.PS)