Observation of Dynamic Localization in Periodically Curved Waveguide Arrays

Abstract

We report on a direct experimental observation of dynamic localization (DL) of light in sinusoidallycurved Lithium-Niobate waveguide arrays which provides the optical analog of DL for electrons in periodic potentials subjected to ac electric fields as originally proposed by Dunlap and Kenkre [D.H. Dunlap and V.M. Kenkre, Phys. Rev. B 34, 3625 (1986)]. The theoretical condition for DL in a sinusoidal field is experimentally demonstrated.PACS numbers: 42.82. Et, 63.20.Pw, 42.25.Bs The quantum motion of an electron in a periodic potential subjected to an external field has provided since a long time a paradigmatic model to study fascinating and rather universal coherent dynamical phenomena. These include the long-predicted Bloch oscillations (BO) for dc fields [1], i.e. an oscillatory motion of the wave packet related to the existence of a Wannier-Stark ladder energy spectrum, and the more recently-predicted dynamic localization (DL) for ac fields [2], in which a localized particle periodically returns to its initial state following the periodic change of the field. In recent years, BO have been experimentally observed in a wide variety of systems including semiconductor superlattices [3], atoms in accelerated optical lattices [4], and optical waveguide arrays with a transverse refractive index gradient [5,6,7]. DL is a phenomenon similar to BO which occurs when the electron is subjected to an ac field. The condition for DL, as originally predicted by Dunlap and Kenkre [2] in the nearest-neighbor tight-binding (NNTB) approximation and for a sinusoidal driving field E(t) = F sin(ωt), is that J 0 (Γ) = 0, where Γ = eaF/ ω and a is the lattice period. DL has been shown to be related to the collapse of the quasienergy minibands [8], and the general conditions for DL beyond the NNTB approximation and for generalized ac fields have been identified [9]; DL under the action of both ac and dc fields has been also studied [10], and the influence of excitonic and many-body effects on DL in semiconductor superlattices has been considered (see, e

Tight-binding lattices with an oscillating imaginary gauge field

“…The application of oscillating electric or magnetic fields on a particle hopping on a lattice introduces Peierls' phases that can be tailored to realize such important effects as hopping rate renormalization, coherent destruction of tunneling, dynamic localization, and quantum Hall physics [17][18][19][20]. While great attention has been devoted so far to study Peierls' phase in driven Hermitian systems and the related broad fields of artificial gauge fields and novel phases of matter, the effects of an oscillating imaginary gauge field have been so far overlooked.…”

“…For a time-periodic gauge field with period T = 2π/ω, i.e. h(t + T ) = h(t), according to Floquet theory the N quasi energies of the time-periodic Hamiltonian (20) are given by E l = (i/T )ln(µ l ), where µ l (l = 1, 2, ..., N ) are the N eigenvalues of the matrix U(T ), i.e. of the propagator over one oscillation period T .…”

“…However, it is well known that in ordinary tight-binding Hermitian quantum models oscillating electric and/or magnetic fields can deeply change the hopping dynamics via Peierls' substitution with important applications to coherent quantum state storage, dynamic decoupling and decoherence control (see, for instance, [16] and references * stefano.longhi@polimi.it therein). In one-dimensional lattices, oscillating fields renormalize the effective hopping rates and can result in coherent destruction of tunneling and dynamic localization [17,18], which have been observed in matter wave and optical systems [19,20]. In two-dimensional lattices, gauge fields are responsible for many important phenomena related to quantum Hall physics, topological insulators and new phases of matter [21].…”

Self-collimation in PT -symmetric crystals

“…Such self-collimation effect is accounted by the appearance of flat segments in the dispersion curves of propagating modes (the Bloch modes), for certain ranges of frequencies and propagation directions. The quantum mechanical analog of self-collimation is the so-called dynamical localization, which is known to occur in modulated lattices [2][3][4][5]. In addition, self-collimation has also been demonstrated in acoustics [6,7], and exciton-polariton condensates [8], though the study of the phenomenon is more advanced in the field of optics.…”

Band-specific phase engineering for curving and focusing light in waveguide arrays

“…This simple physical mechanism, called discrete diffraction, has profound implications on the macroscopic behaviour of a WGA as an optical medium, enabling a diversity of linear and nonlinear phenomena that are absent in continuous media. Among them are discrete solitons [3,4], Bloch-momentum dependent diffraction [5], Bloch oscillations [6] and surface Bloch oscillations [7,8], Rabi oscillations [9], Zener tunnelling [10], perfect or fractional revivals [11], discrete Talbot effect [12], and dynamic localization [13]. The peculiar behaviour of light inside waveguide lattices is owed to the photonic band structure that is associated with the periodic effective-index "potential".…”