Stefano Longhi Dipartimento di Fisica and Istituto di Fotonica e Nanotecnologie del CNR, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano, Italy Optical analogue of population trapping in the continuum: classical and quantum interference effects A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For classical light, the photonic system realizes an optical analogue of coherent population trapping in the continuum encountered in atomic physics, where destructive interference between different light leakage channels leads to the appearance of a trapped state embedded in the continuum. For nonclassical light, two-photon interference effects are predicted, such as the tendency of photon pairs to bunch when decaying into the continuum. PACS numbers: 42.82.Et, 42.50.Dv, 72.20.Ht It is well established that quantum mechanics of a non- relativistic particle and paraxial wave optics in dielectric media shear strong formal similarities (see, for instance, [1–3]). Owing to such similarities, the temporal evolution of a quantum particle (e.g. an electron in an atom or in a crystal) can be mimicked by means of light propaga- tion in suitably-designed photonic structures. Quantum- optical analogies have seen in recent years a renewed and increasing interest, both theoretically and experi- mentally, mainly motivated by the possibility offered by optics to visualize at a macroscopic level certain coherent phenomena, originally proposed for quantum systems, which may be of difficult access or of controversial in- terpretation in the quantum context (see, e.g., [4, 5] and references therein). In particular, recent works theoreti- cally proposed and experimentally demonstrated the op- tical analogues of some important coherent phenomena encountered in atomic and molecular physics, such as coherent population transfer [6, 7], electromagnetically- induced transparency [8], and population trapping in the continuum [9–11]. The latter effect has been extensively investigated in atomic physics in connection, for instance, with the problem of autoionization of an atom by ultra- violet radiation or in laser-induced continuum structures (see [12, 13] and references therein). In the simplest case, population trapping in the continuum describes decay suppression of two discrete states coupled to a common and unstructured continuum: as a single bound state coupled to the continuum decays in an irreversible way and population is transferred into the continuum, un- der certain conditions coupling of the continuum with the additional other bound state may partially or totally suppress the decay of states owing to a destructive inter- ference effect which was first studied by Fano for radiative transitions to autoionizing states in atoms [14]. Fano-like resonances in photonic systems have been considered in several recent works as well [15, 16], with a main focus on the scattering (transmission) properties of the struc- tures. These previous studies in optics have mostly con- sidered propagation of classical light in coupled guiding structures, disregarding the quantum nature of light. For classical light, destructive interference among different tunneling paths is responsible for the existence of bound states in the continuum, similarly to Fano interference in atomic physics. However, when few photons or nonclas- sical beams are used to excite the photonic structures, light propagation may show interference effects of quan- tum nature. Since long time, coupled waveguides are known to behave similarly to beam splitters (see, for in- stance, [17]) and to show strictly quantum features when nonclassical light propagates through them, such as two- photon Hong-Ou-Mandel quantum interference originally demonstrated for beam splitters [18]. Like beam splitters [19], coupled waveguides offer the possibility to transfer nonclassical properties of light and to generate entan- gled states [17, 20]. With recent technological advances in the realization of high-quality low-loss integrated pho- tonic structures and nonclassical light sources, such pos- sibilities are nowadays realities. High-fidelity Hong-Ou- Mandel quantum interference and integrated optical re- alizations of other key quantum photonic circuits have been recently demonstrated in silicon-based waveguide couplers [21]. In another recent experiment, Bromberg et al. [22] showed nontrivial photon correlations in coupled waveguide arrays and observed them using classical in- tensity correlation measurements. The possibility offered by experimentalists to test quantum aspects of light in integrated optic networks motivates to extend previous studies of quantum-optical analogies from the classical to the quantum level, highlighting interference effects of purely quantum nature. For instance, a recent theoretical study of optical Bloch oscillations and Zener tunneling in optical lattices [23] showed that propagation of nonclas- sical light in the lattice may reveal certain particle-like aspects of light and quantum interference phenomena. In this work we investigate classical and quantum inter- ference effects of light in an optical analogue of coher- ent population trapping, based on two optical channel waveguides side coupled to a common slab waveguide re- cently proposed in Ref.[9]. For classical light (coherent arXiv:1001.1000v1 [quant-ph] 6 Jan 2010 I. INTRODUCTION