Quantum‐optical analogies using photonic structures

Abstract

Engineered photonic waveguides have provided in the past decade an extremely rich laboratory tool to visualize with optical waves the classic analogues of a wide variety of coherent quantum phenomena encountered in atomic, molecular or condensed-matter physics. As compared to quantum systems, optics offers the rather unique advantage of a direct mapping of the wave function evolution in coordinate space by simple fluorescence imaging or scanning tunneling optical microscopy techniques. In this contribution recent theoretical and experimental advances in the field of quantum-optical analogies are reviewed. Special attention is devoted to some relevant optical analogies based on the use of curved photonic structures, including: coherent destruction of tunneling in driven bistable potentials; coherent population transfer and adiabatic passage in laser-driven multilevel atomic systems; quantum decay control and Zeno dynamics; electronic Bloch oscillations and Zener tunneling, Anderson localization and dynamic localization in crystalline potentials. Curvilinear Propagation distance (cm) u u ( m) m 8 6 4 2 0 0 20 40 60 Curvilinear Propagation distance (cm) u Beam Center of Mass n > > 0 2 4 6 8 0 2 4 6 8 10 u u 0 Input Beam R a Optical analogue of quantum particle bouncing on a lattice under the gravitational field. A light wave packet periodically bounces the edge of a circularly-curved waveguide array, showing collapses and revivals.

Guided modes in the plane array of optical waveguides

“…In particular, this concerns the plane periodic arrays of waveguides, which is a special kind of low-dimensional photonic crystals. The main feature of such systems is a band structure of the optical spectrum which defines its peculiar properties [1][2][3][4]. Low-dimensional photonic crystal composed of the parallel rods are of a special interest.…”

Quantum-mechanical analogy and supersymmetry of electromagnetic wave modes in planar waveguides

“…Vice versa, the propagation of light in waveguides can be used for experimental verification of many quantum-mechanical effects, such as quantum tunneling and time of tunneling, Bloch oscillations in periodic structures, quantum chaos. The reviews on this subject can be found in [5][6][7][8]. Note also recent papers [9,10], where the quantum-mechanical analogy was used for investigation of light confinement in waveguide structures and in microtube bottle resonators, respectively.…”

Bloch oscillations in plasmonic waveguide arrays

“…Despite the different natures of these waves, the corresponding equations that govern their evolution can have the same mathematical form and hence allow mapping of wave phenomena in different physical systems on each other. This is the key idea behind the emerging field of quantum simulators 1,2 , where the quantum dynamics of a system that is hardly accessible by experimental means is reproduced with other equivalent quantum or classical optical systems 3,4 , providing a much better experimental control over the relevant parameters. For example, Felix Bloch predicted in his seminal paper 5 that a crystal electron carries out an oscillatory motion under the influence of an external static electric field.…”