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Conference on Lasers and Electro-Optics

Relativistic physics in waveguide arrays: The \textsl{Zitterbewegung}

Felix Dreisow, Matthias Heinrich, Robert Keil, Andreas Tünnermann, Stefan Nolte, Stefano Longhi, Alexander Szameit

Published May 22, 2011• 0 citations
OpenAlex

Abstract

We introduce binary waveguide arrays as an optical model system for studying relativistic quantum mechanics. The peculiar Zitterbewegung is observed in femtosecond laser inscribed lattices using waveguide fluorescence microscopy.

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Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the electron wave packet exhibits a trembling or oscillating behavior during its motion, caused by its interaction or coupling with the negative energy state. To directly observe ZB in electronic systems is difficult, due to the challenges associated with the small amplitude of the motion which is of the order of Compton wavelength. Photonic systems offer an alternative paradigm. We exploit the concept of pseudo parity-time (pseudo ) symmetry to study ZB in non-Hermitian quantum systems implemented as an experimentally feasible optical waveguide array. In particular, the non-Hermitian Hamiltonian is realized through evanescent coupling among the waveguides to form a one-dimensional lattice with periodic modulations in gain and loss along the guiding direction. As the modulation frequency is changed, we obtain a number of phenomena including periodically suppressed ZB trembling, spatial energy localization, and Hermitian-like ZB oscillations. We calculate phase diagrams indicating the emergence of different types of dynamical behaviors of the relativistic non-Hermitian quantum system in an experimentally justified parameter space. We provide numerical results and a physical analysis to explain the distinct dynamical behaviors revealed by the phase diagrams. Our findings provide a deeper understanding of both the relativistic ZB phenomenon and non-Hermitian pseudo- systems, with potential applications in controlling/harnessing light propagation in waveguide-based optical systems.
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.
Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.
Quantum simulators are getting to the level of real devices, constituted by a quantum system which can be controlled in its preparation, evolution and measurement and whose dynamics can implement that of the target quantum system we want to simulate. In this context, photonics quantum technologies are expected to play an instrumental role in the realization of controlled quantum systems capable, in their evolution, to simulate a given complex system. I will present some of the main results obtained in this field in our laboratory by using integrated waveguide optical circuits that represent the hardware of a quantum simulator. These systems are constituted by interferometer arrays of beam splitters and phase shifters fabricated on single integrated platforms by femtosecond laser writing technique and have the potential of speeding-up the evolution from lab systems to the next generation of quantum optical devices for real-world applications. Using the mobility of photons we are able to create arbitrary interconnections within these systems and to mimic the main features of quantum phenomena of increasing complexity.