Fluctuation properties of acoustic phonons generated by ultrafast optical excitation of a quantum dot

Abstract

We study theoretically the fluctuation properties of acoustic phonons created in a semiconductor quantum dot after ultrafast optical excitation. An excitation with a single ultrafast pulse creates an exciton confined to the quantum dot, which is coupled to longitudinal acoustic phonons. This leads to the formation of a polaron in the quantum dot accompanied by the emission of a phonon wave packet. We show that the fluctuations of the lattice displacement associated with the wave packet after a single laser pulse excitation in resonance with the exciton transition are always larger than their respective vacuum values. Manipulating the exciton with a second pulse can result in a reduction of the fluctuations below their vacuum limit, which means that the phonons are squeezed. We show that the squeezing properties of the wave packet strongly depend on the relative phase and the time delay between the two laser pulses.

Ultrafast atomic-scale visualization of acoustic phonons generated by optically excited quantum dots

“…We found that the excited electronic distribution efficiently couples to acoustic phonons through the deformation potential (DP) mechanism. In agreement with previous theoretical calculations, 43–45 we interpret our observations as a result of a nonequilibrium phonon population composed of two parts: one localized within the dots, as detected from the Bragg reflections, and one traveling at the speed of sound in the surrounding region as a phonon wavepacket (WP), as retrieved from the dynamics of surface wave resonance (SWR) features.…”

“…This is contrary to our experimental observations, where a time constant of 2.5–4 ps is measured and can rather be interpreted according to the following scenario. It has been theoretically predicted 43–45 that the deformation potential mechanism responsible for the excitation of acoustic phonons within the dots is associated to the buildup of a nonequilibrium phonon distribution consisting of two parts: a localized one that remains within the dots and reflects the polaronic nature of the excited state, as discussed above, and another part that, because of the spatial dispersion of the acoustic phonons, leaves the dot and propagates in the surrounding regions as a phonon wavepacket (WP) travelling at the speed of sound. In this scenario, the time necessary for the travelling wave to leave the dot and propagate in the surrounding substrate can be estimated as ${\tau }_{WP}=h/v_A,$where $h$ is the dot height and $v_A$ is the acoustic phonon speed.…”

Energy transport and coherence properties of acoustic phonons generated by optical excitation of a quantum dot

“…42,43 For this case, it has been found that by the impulsive excitation a lattice deformation in the region of the QD is created forming the acoustic polaron, which is accompanied by the emission of a phononic wave packet. [42][43][44][45][46] By excitation with a tailored series of pulses the fluctuations of the phonons can be modified such that squeezed phonon wave packets can be generated. 43 In the case of excitation by sufficiently slowly varying light fields, on the other hand, the polaron builds up adiabatically and no phonon wave packet is emitted.…”

“…[42][43][44][45][46] By excitation with a tailored series of pulses the fluctuations of the phonons can be modified such that squeezed phonon wave packets can be generated. 43 In the case of excitation by sufficiently slowly varying light fields, on the other hand, the polaron builds up adiabatically and no phonon wave packet is emitted.…”

“…43, where the exciton and phonon dynamics can be calculated analytically without any approximation. 42 In particular, it can be shown that the excitation by an ultrafast π-pulse indeed results in the generation of purely coherent phonons.…”