chapter  11
34 Pages

Quantum Breathers and Phonon Bound State in the Ferroelectric System

Approach ........................................................................ 262 11.3 Results and Discussion ............................................................... 263 11.3.1 Spectral Collocation Analysis ........................................ 264 11.3.2 Quantum Breathers ........................................................ 266

11.3.2.1 Two-Phonon Bound States ............................ 266 11.3.2.2 Lifetime of Quantum Breathers .................... 269

11.4 Conclusions ................................................................................ 271 Keywords .............................................................................................. 272 References ............................................................................................. 272

11.1 INTRODUCTION

11.1.1 FERROELECTRICITY

Lithium niobate and lithium tantalate are technologically very important ferroelectric materials with a low switching field that have several applications in the field of nonlinear photonics and memory switching devices. In a Hamiltonian system, such as dipolar system, the modal dynamics of such ferroelectrics can be well-modeled by a nonlinear Klein-Gordon (K-G) equation. Due to strong localization coupled with discreteness in a nonlinear K-G lattice, breathers and multi-breathers manifest in the localization peaks across the domains in polarization-space-time plot. Due to the presence of impurities in the structure, dissipative effects are observed. To probe the quantum states related to discrete breathers, the same K-G lattice is quantized to give rise to quantum breathers (QBs) that are explained by a periodic boundary condition (Bloch state). The gap between the localized and delocalized phonon-band is a function of impurity content that is again related to the effect of pinning of domains due to antisite defects, i.e., a point of easier switching, which is related to Landau coefficient (read, nonlinearity). Secondly, in a non-periodic boundary condition approach, the temporal evolution of quanta shows a ‘critical’ time of redistribution of quanta that is proportional to QB’s lifetime in femtosecond having a possibility for THz and other applications in quantum computation. Hence, the importance of both of the methods for characterizing quantum breathers is shown in these perspectives.