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Register a new userSwitch between the types of the symmetry breaking bifurcation in optically induced photorefractive rotational double-well potential
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We study the possibility of switching the types of symmetry breaking bifurcation (SBB) in the cylinder shell waveguide with helical double-well potential along propagation direction. This model is described by the one-dimensional nonlinear Schr{o}dinger (NLS) equation. The symmetry- and antisymmetry-breakings can be caused by increasing the applied voltage onto the waveguide in the self-focusing and -defocusing cases, respectively. In the self-focusing case, the type of SBB can be switched from supercritical to subcritical. While in the self-defocusing case, the type of SBB can not be switched because only one type of SBB is found.
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Thawatchai Mayteevarunyoo (Department of Telecommunicationn Engineering
, Mahanakorn University of Technology
, Bangkok
2008
We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta-functions, a fully analytical solution is obtained for symmetric, antisymmetric and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta-functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.
Optical nonlinearities in solids reveal information about both the in-plane rotational and out-of-plane inversion symmetries of a crystal. In the van der Waals material hexagonal boron nitride (hBN) both these symmetries and the linear vibrational properties have led to the rich physics of mid-infrared phonon-polaritons. However, the role of strong electron-phonon nonlinearities requires further study. In this work, we investigate both theoretically and experimentally the rich interplay of phonon anharmonicity and symmetry in phonon-polariton mediated nonlinear optics. We show that large enhancements (>30x) of third-harmonic generation occur for incident femtosecond pulses that are resonant with the hBN transverse optical phonons. In addition, we predict and observe large transient sub-picosecond duration second-harmonic signals during resonant excitation, which in equilibrium is forbidden by symmetry. This surprising result indicates that instantaneous crystal inversion symmetry breaking can be optically induced and controlled via phonon interactions by both the power and polarization of the pump laser.
We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and BEC. The order in which the SSB and self-trapping transitions take place with the growth of the nonlinearity strength depends on the height of the central barrier of the DWP: the SSB happens first if the barrier is relatively high, while self-trapping comes first if the barrier is lower. The SSB of the leaky modes is characterized by specific asymmetry of their radiation tails, which, in addition, feature a resonant dependence on the relation between the total size of the system and radiation wavelength. As a result of the SSB, the instability of symmetric modes initiates spontaneous Josephson oscillations. Collisions of freely moving solitons with the DWP structure admit trapping of an incident soliton into a state of persistent shuttle motion, due to emission of radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.
We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.
We report results of the analysis of the spontaneous symmetry breaking (SSB) in the basic (actually, simplest) model which is capable to produce the SSB phenomenology in the one-dimensional setting. It is based on the Gross-Pitaevskii - nonlinear Schroedinger equation with the cubic self-attractive term and a double-well-potential built as an infinitely deep potential box split by a narrow (delta-functional) barrier. The barriers strength, epsilon, is the single free parameter of the scaled form of the model. It may be implemented in atomic Bose-Einstein condensates and nonlinear optics. The SSB bifurcation of the symmetric ground state (GS) is predicted analytically in two limit cases, viz., for deep or weak splitting of the potential box by the barrier. For the generic case, a variational approximation (VA) is elaborated. The analytical findings are presented along with systematic numerical results. Stability of stationary states is studied through the calculation of eigenvalues for small perturbations, and by means of direct simulations. The GS always undergoes the SSB bifurcation of the supercritical type, as predicted by the VA at moderate values of epsilon, although the VA fails at small epsilon, due to inapplicability of the underlying ansatz in that case. However, the latter case is correctly treated by the approximation based on a soliton ansatz. On top of the GS, the first and second excited states are studied too. The antisymmetric mode (the first excited state) is destabilized at a critical value of its norm. The second excited state undergoes the SSB bifurcation, like the GS, but, unlike it, the bifurcation produces an unstable asymmetric mode. All unstable modes tend to spontaneously reshape into the asymmetric GS.
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