Abstract

Control of quantum tunneling by external driving fields is a subject of major relevance in different linear and nonlinear dynamical systems. The driven double-well (bistable) potential has provided since more than one decade a simplified and paradigmatic model to investigate the dynamics underlying tunneling control in such diverse physical systems as cold atoms in optical traps, superconducting quantum interference devices, and multi-quantum dots. As for strong driving at a frequency close to the classical frequency at the bottom of each well one observes chaos-assisted tunneling enhancement, at lower frequencies and for certain ratios between frequency and amplitude of the driving field tunneling can be suppressed, as originally proposed in a famous work by Grossman, Hanggi and coworkers [1]. Such a phenomenon is nowadays referred to as "coherent destruction of tunneling" (CDT). In spite of the great amount of theoretical work devoted to CDT, up to date experimental evidences of CDT are few and rather indirect. In this contribution we report on a direct visualization of CDT using an optical realization of the quantum-mechanical driven double-well Hamiltonian based on two tunneling-coupled waveguides with a sinusoidally-curved axis. Our experimental implementation makes it possible for the first time to directly trace the wave function evolution in the driven double-well potential by exploiting the fluorescence pattern observed in an active erbium-ytterbium:glass waveguide. The optical structure designed and fabricated to realize CDT [see Fig. 1(a)] consists of a set of two parallel channel waveguides, whose axis is sinusoidally bent along the propagation distance z . The curvature plays here the same role as the external ac driving field in the quantum mechanical problem [2]. The waveguides have been manufactured by means of the ion-exchange technique in an active Er-Yb phosphate substrate and probed at 980 nm wavelength. The effective double-well potential of the structure, calculated from the measured 2D index profile, is shown in Fig. 1(b). CDT is obtained for the curved structures solely at prescribed values of the modulation period A and amplitude A corresponding to the crossing of the quasienergies of the periodic Hamiltonian, as shown in Fig. 1(c) by the solid curve. The experimental demonstration of CDT is shown in Fig. 2. In absence of the driving field, i.e. in the straight waveguides, photons periodically tunnel between the two waveguides, as visualized by the fluorescence pattern shown in Fig. 2(a). When the driving field is applied with the proper amplitude at the quasienergy crossing, CDT is clearly observed [Fig. 2(b) and (c)], but not when the amplitude does not correspond to quasienergy crossing [Fig. 2(d)].

© 2007 IEEE