Direct observation of the discrete character of intrinsic localized modes in an antiferromagnet

Abstract

In a strongly nonlinear discrete system, the spatial size of an excitation can become comparable to, and influenced by, the lattice spacing. Such intrinsic localized modes (ILMs)--also called 'discrete breathers' or 'lattice solitons'--are responsible for energy localization in the dynamics of discrete nonlinear lattices. Their energy profiles resemble those of localized modes of defects in a harmonic lattice but, like solitons, they can move (although, unlike solitons, some energy is exchanged during collisions between them). The manipulation of these localized energy 'hotspots' has been achieved in systems as diverse as annular arrays of coupled Josephson junctions, optical waveguide arrays, two-dimensional nonlinear photonic crystals and micromechanical cantilever arrays. There is also some evidence for the existence of localized excitations in atomic lattices, although individual ILMs have yet to be identified. Here we report the observation of countable localized excitations in an antiferromagnetic spin lattice by means of a nonlinear spectroscopic technique. This detection capability permits the properties of individual ILMs to be probed; the disappearance of each ILM registers as a step in the time-dependent signal, with the surprising result that the energy staircase of ILM excitations is uniquely defined.

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

“…Unlike the classical case where the localization is exponential, here we found algebraic localization. This is a long range behavior, which follows from the fact that the interaction γ induces a linear perturbation of the eigenstates which is local in real space, and also local in the matrix representation in (6). That induces a mean-field type interaction between the normal modes, and naturally leads to algebraic localization.…”

“…Their spatial profiles localize exponentially for short-range interaction. Recent experimental observations of breathers in various systems include such different cases as bond excitations in molecules, lattice vibrations and spin excitations in solids, electronic currents in coupled Josephson junctions, light propagation in interacting optical waveguides, cantilever vibrations in micromechanical arrays, cold atom dynamics in BoseEinstein condensates loaded on optical lattices, among others [5,6,7,8,9,10,11,12,13]. In many cases quantum dynamics is important.…”

Counting discrete emission steps from intrinsic localized modes in a quasi-one-dimensional antiferromagnetic lattice

“…12,27 In Ref. 20 and the experiments described here we apply the same locking idea to an antiferromagnet. First the AFMR mode is driven into the unstable amplitude range with a high power pump, next a lower power, cw driver is applied to lock a subset of the ILMs and finally the product spectrum is then probed with a third oscillator of variable frequency.…”

“…Recently we have identified a new ILM signature, namely, the discreteness associated with a small number of these excitations in an atomic lattice. 20 As individual ILMs become unlocked from a cw driver they are counted by means of a experimental approach. The discreteness appears in the timedependent emission spectra of a quasi-1D antiferromagnet when the system first is driven far from equilibrium and then is subjected to a four-wave mixing experiment at an ILM frequency, locked to a cw oscillator set below the lowest antiferromagnetic resonance ͑AFMR͒.…”

Asymptotic calculation of discrete non-linear wave interactions

“…[12] for a number of review papers on the topic. In this case, the applications refer to nonlinear waveguide arrays [13] and photorefractive crystals [14], to Bose-Einstein condensates in deep optical lattices [15], to the local denaturation of the DNA double strand [16], and to micro-mechanical cantilever arrays [17] among many others.…”