Impact of Phonons on Dephasing of Individual Excitons in Deterministic Quantum Dot Microlenses

Abstract

Optimized light-matter coupling in semiconductor nanostructures is a key to understand their optical properties and can be enabled by advanced fabrication techniques. Using in situ electron beam lithography combined with a low-temperature cathodoluminescence imaging, we deterministically fabricate microlenses above selected InAs quantum dots (QDs), achieving their efficient coupling to the external light field. This enables performing four-wave mixing microspectroscopy of single QD excitons, revealing the exciton population and coherence dynamics. We infer the temperature dependence of the dephasing in order to address the impact of phonons on the decoherence of confined excitons. The loss of the coherence over the first picoseconds is associated with the emission of a phonon wave packet, also governing the phonon background in photoluminescence (PL) spectra. Using theory based on the independent boson model, we consistently explain the initial coherence decay, the zero-phonon line fraction, and the line shape of the phonon-assisted PL using realistic quantum dot geometries.

Keywords: coherent nonlinear spectroscopy; electron beam lithography; excitons; four-wave mixing; phonons; quantum dots.

Figure 1

(a) Spectrally resolved FWM amplitude generated by a few QD excitons embedded in a lens structure. The selected QD trion (GX^±) is labeled with the green ★. The horizontal bar indicates a neutral exciton–biexciton system (GXB) in a QD located at the lens periphery. Inset: Calculated distribution of the near-field intensity for the QD-lens structure. The semiconductor–air interface is shown by the solid black line, and the distributed Bragg reflector starts below the dashed line. (b) Spectrally integrated FWM amplitude of a trion in the target QD as a function of the pulse area of . The blue line shows the fit to the expected |sin(θ₁/2)| amplitude dependence of the FWM.

Figure 2

(Top) Three-pulse sequence employed to measure the trion population dynamics. and , having a delay of τ₁₂ = 20 ps, create the trion population and are jointly advanced in time, such that the FWM triggered by probes the population decay via the τ₂₃ dependence. (Bottom) Measurement yielding the exciton lifetime T₁ = 347 ± 12 ps. The noise level is indicated by open circles.

Figure 3

(a) (Top) Two-pulse sequence applied to probe the echo profile. (Bottom) Integrated FWM amplitude versus τ_2R at 5 K revealing the Gaussian echo with a temporal width yielding σ; the theoretical fit is given by the solid line. Inset: Inhomogeneous broadening retrieved from the echo temporal width for different temperatures. (b) (Top) Two-pulse sequence applied to probe the trion dephasing. (Bottom) Measured FWM amplitude as a function of the delay τ₁₂, yielding coherence dynamics for different temperatures; theoretical fits as solid lines. Inset: Dephasing time T₂ as a function of temperature.

Figure 4

(a) Cartoon depicting propagation of a phonon packet from a QD after its excitation with a short, femtosecond pulse. (b) Two-pulse time-integrated FWM amplitudes for initial delays τ₁₂. The FWM amplitudes at different temperatures (see legend) are normalized at τ₁₂ = 0 to show the phonon-induced dephasing. (c) PL spectra for different temperatures. Solid lines: experimental data; dashed lines: theoretical curves. (d) Final FWM values after the initial decay (red cirles) as a function of temperature along with the theoretical calculation (blue line) (cf. panel b). Additional temperatures for (b) and (c) are shown in Supporting Information Figure S2. Z² estimated from temperature-dependent PL spectra are given by gold crosses.