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Physical Review Letters

Decay Control via Discrete-to-Continuum Coupling Modulation in an Optical Waveguide System

Felix Dreisow, Alexander Szameit, Matthias Heinrich, Thomas Pertsch, Stefan Nolte, Andreas Tünnermann, Stefano Longhi

Published Oct 3, 2008• 80 citations
Publisher

Abstract

Control of optical tunneling via modulation of the coupling to the continuum is experimentally reported in femtosecond laser written waveguide arrays. The experiment demonstrates for optical tunneling in photonic lattices the universal mechanism of decay control recently proposed for quantum systems by Kofman and Kurizki [Phys. Rev. Lett. 87, 270405 (2001)]. In particular, we prove that the formation of a dressed discrete-continuum bound state in the regime of fractional decay can be suppressed by dynamic modulation of discrete-to-continuum coupling.

DOI
10.1103/physrevlett.101.143602

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Control of optical tunneling via modulation of the coupling to the continuum is experimentally reported in femtosecond laser written waveguide arrays. The experiment demonstrates for optical tunneling in photonic lattices the universal mechanism of decay control recently proposed for quantum systems by Kofman and Kurizki [Phys. Rev. Lett. 87, 270405 (2001)]. In particular, we prove that the formation of a dressed discrete-continuum bound state in the regime of fractional decay can be suppressed by dynamic modulation of discrete-to-continuum coupling.
Whereas classical physics generally predicts an exponential trend for the temporal decay of an unstable state, quantum mechanics provides a rather different description. The decay is initially quadratic, while at very large times it follows a power-law. Actually, the latter regime has never been observed experimentally. Here we employ arrays of femtosecond-laser-written optical waveguides to optically realize quantum systems where a discrete state is coupled to and can decay into a continuum. The transverse optical modes represent distinct quantum states of the photon and the temporal evolution of the system is mapped into the longitudinal propagation coordinate. By injecting laser light in the fabricated structures, and by imaging with high dynamic range the scattered light from above, we are able to observe experimentally different decay regimes, including the power-law tail. This process can be viewed as the quantum simulation of a quantum decay phenomenon.
This work shows that engineered waveguide-based systems can be designed to control photon tunneling decay, providing an experimentally accessible laboratory tool to test the universal features of dynamical control via parametric modulations, recently proposed for quantum mechanical decay. This study demonstrates the realization of quantum decay control and Zeno dynamics in photonic structures. By a proper design of the structure, acceleration or deceleration the tunneling decay rate, as well as suppression of fractional, can be achieved.
Controlling the decay dynamics of an unstable state coupled to a continuum is a longstanding problem of major interest in different areas of quantum and classical physics. Suppression of quan- tum mechanical decay and slow-down of the escape dynamics in macroscopic quantum and optical tunneling via dynamical decoupling methods have been proposed and experimentally demonstrated in different physical systems over the last two decades. So far most of dynamical decoupling schemes have been focused to Hermitian dynamics. In this work we consider the decay of an unstable state coupled to a continuum via a time-dependent non-Hermitian coupling with finite (albeit arbitrarily long) duration, and show rather generally that for a wide class of coupling temporal shapes, in which the real and imaginary parts of the coupling are related each other by a Hilbert transform, the metastable state returns to its initial condition after the interaction with the continuum. Re- markably, the absence of decay holds even beyond the weak-coupling (Markovian) limit and for arbitrarily slow (adiabatic) interactions. The method is illustrated by considering a paradigmatic example of decay dynamics of a metastable state coupled to a tight-binding continuum described by a Fano-Anderson model and realized by a semi-infinite tight-binding lattice. Non-Hermitian coupling can be implemented by fast modulation of the complex site energy of the edge site in the lattice.