Distinguishing between spatial coherence and temporal coherence of phonons

Abstract

Coherent phonon transport is regarded as a promising strategy for controlling thermal properties in solids using the wave nature of phonons. However, no clear distinction between the spatial and temporal phonon coherence has been accounted for and a formalism that quantifies these two effects is still to be found. In this work, we propose a statistical approach for calculating the spatial and temporal coherence spectra using molecular dynamics simulations. We provide a microscopic assessment of these properties and we theoretically demonstrate that, while temporal and spatial coherence can be analytically related under specific conditions, they represent two characteristic lengths that set apart different physical effects. The former is associated with the phonon mean free path while the latter can be regarded as a measure of localization, representing the spatial extension of phonon wave packets. This provides a framework to engineer heat conduction in solids by quantitatively revealing the wave/particle nature of the vibrational modes.

Generalized decay law for particlelike and wavelike thermal phonons

“…Interestingly, wave packets follow a unimodal distribution as a function of coherence time, indicating the predominance and the limits in duration of a subpopulation centered at τ c ∼ 40 ps. The TAPND was not observed before, only its average on τ c obtained by other methods [8]. Previously, the founding work of Hardy [37] mentioned that the TAPND of a given mode k should be distributed along an ad hoc Gaussian function, i.e., D(k,…”

“…Previous studies also demonstrated that the particlelike and wavelike thermal phonons are coexisting at elevated temperature [4,4,[8][9][10]. In epitaxial oxide superlattices, Ravichandran et al [4] experimentally observed this mechanism and the predominant behavior depends on temperature and period.…”

Monitoring anharmonic phonon transport across interfaces in one-dimensional lattice chains

“…is calculated to present the composition of the phonon energy of a frequency ω occupying the total energy. This definition of y is similar to that provided by Latour and Chalopin [44], where they proposed to use the cross-spectral density function, m |χ j,i (ω)| k b T , to represent the composition of phonons. When atoms i and j are the same atom, the ratio y becomes proportional to the phonon density of states.…”

Controlling Light, Heat, and Vibrations in Plasmonics and Phononics

“…[200] More recently, Latour et al [201] proposed a microscopic theory of the phonon spatial coherence length based on correlation theory. In another work, Latour et al [221] used correlation theory to include spatial and temporal coherence, analyzing transport in a SL, defining coherent and incoherent transport regimes with relation to the phonon mean free path and the spatial coherence length.…”

“…[21,205,206,216] Although phonons can be generated from the heat source, [205] thermal phonons, as a result of the scattering processes required to reach equilibrium, are typically incoherent and controlling their phase relationship poses serious challenges. [221] In principle, non-equilibrium phonons can also be transferred across the interface between the heated and surrounding medium and this mechanism is still a subject of investigation. [180,222] These phonon excitation processes provide a potential ground to bridge plasmonics and phononics, as described in Section 4, where the focus will be on phonon generation in plasmonic (metallic) nanostructures.…”