Exciton coherence propagation measured with non-local four-wave mixing micro-spectroscopy

TL;DR

This work tackles exciton coherence propagation in semiconductor nanostructures and demonstrates non-local coherent coupling via non-local four-wave mixing (FWM) micro-spectroscopy. Femtosecond pulses resonantly generate excitons within the light cone; scattered excitons populate in-plane momentum dark states, allowing diffusion over mesoscopic distances up to 10 μm, while coherence is probed by time-delayed non-local FWM with heterodyne detection. In a virtually disorder-free CdTe QW, they measure a diffusion velocity v_D ≈ 4×10^4 m/s and extract a diffusion coefficient D ≈ 16 cm^2/s from the density and coherence transport data. Coherence propagation is found to be ballistic with velocity v_c ≈ 1.25×10^3 km/s, two orders of magnitude larger than v_D, suggesting distinct transport mechanisms and enabling remote coherent interactions in excitonic circuits; the results point to non-local coherent control in semiconductor nanostructures and 2D heterostructures.

Abstract

Coherence transfer is a multi-disciplinary topic of interest, including chemistry, biology and physics. In quantum technologies, achieving non-local coherent coupling between solid-state qubits is of the utmost importance. Here, we demonstrate that excitons - i.e. electron-hole pairs bound by the Coulomb force within a quantum well - can act as a medium for mesoscopic optical coherence transfer in semiconductors. To this end, we use a femtosecond laser pulse to resonantly generate excitons within the light cone. These excitons can then either recombine radiatively or scatter out of the light cone, gaining an in-plane momentum in the process. In samples without disorder, such as the CdTe quantum wells used here, the resulting fast excitons can diffuse over mesoscopic distances before recombining radiatively. Using coherent nonlinear micro-spectroscopy, we carry out exciton time-of-flight measurements. Specifically, we monitor the spatio-temporal propagation of launched exciton wave packets, selectively observing their coherence or density on a scale of up to 10$\,μ$m. Our proof-of-principle experiment demonstrates that free excitons inherit a phase modulation from the optical pulsed excitation and can generate coherent links within excitonic circuits, offerring a higher level of miniaturisation and compactness than photonic or polaritonic architectures.

Figures (8)

• Figure 1: Linear and nonlinear optical response of the investigated CdTe quantum wells. a) Top: Sample layout, Bottom: Micro photoluminescence (blue) excited with a 532 nm CW diode, micro-reflectance (red) measured with a femto-second pulse centered 1610 meV, revealing the exciton-positive trion complex (X/X+). An increasing 532 nm excitation intensity encoded from the semi-transparent to solid lines. b) Time-resolved FWM of the exciton versus delay $\tau_{12}$, showing the free-induction decay. c) Time-integrated (TI) FWM amplitude versus delay $\tau_{12}$ yielding $(T_2,\,\gamma)$=(2 ps, 0.65 meV).
• Figure 2: Density diffusion of QW excitons measured with non-local four-wave mixing microscopy. a) Schematics of the QW excitons' dynamics, depicting an interplay of the direct radiative recombination of bright excitons and scattering towards the dark states, supplying large in-plane momenta and thus enabling a long-range spatial diffusion. b) Experimental configuration; Pumps ${\cal E}_{1,2}$ induce propagation of the exciton's density. The spatio-temporal dynamics of the diffusion process is inferred by measuring FWM amplitude as a function of ${\cal E}_{1,2}-{\cal E}_3$ distance and delay $\tau_{23}$, as illustrated in the pulse sequence. c) and d) Signatures of the exciton diffusion observed in the FWM ($\tau_{23},\,$r)-dependence, detected at the exciton X and trion X+, respectively. Note that the propagation signature appears to be more pronounced when monitoring X+. This is because X+ absorption, and thus FWM, are highly sensitive to the incoming exciton population. e) Time-of-flight analysis yielding the density propagation velocity of $v_{\rm D}=4\times10^4\,$m/s.
• Figure 3: Coherence propagation of QW excitons (X) measured with non-local four-wave mixing. a) Top: Pulse sequence employed to measure coherence dynamics. Bottom: FWM amplitude of X as a function of $\tau_{12}$. For increasing spatial separation of ${\cal E}_1$ and ${\cal E}_{2,3}$ a cross-over from an exponential decay toward delayed maximum of the FWM occurs due to coherence propagating from ${\cal E}_1$ to ${\cal E}_{2,3}$. The leftover FWM signal around $\tau_{12}$=0 is due to direct scattering of ${\cal E}_1$ onto ${\cal E}_{2,3}$. b) ${\cal E}_1$ intensity dependence of the coherence dynamics at the beam overlap. A considerable excitation induced dephasing is measured, as quantified in the inset.
• Figure S1: Four-wave mixing characterisation of the studied CdTe quantum well. a) Four-wave mixing amplitude spectra for different delays $\tau_{12}$ under spectrally broad excitation (25 meV pulse width centered at 1615 meV), showing neutral exciton (X), positive trion (X+) and biexciton (BX), and a light-hole neutral exciton (LH X) transitions. The pronounced quantum beating along the $\tau_{12}$ axis is due to the coherent coupling between the heavy-hole and light-hole exciton transitions. Fourier transforming along $\tau_{12}$ yields a two-dimensional FWM spectrum (see inset) with off-diagonal peaks that confirm the coherent coupling. The horizontally offset signal from X towards the low-energy side is due to the BX. b) As a) but under spectrally narrow excitation conditions (10 meV pulse width centered at 1610 meV; LH X is not excited). The FWM spectrum at $\tau_{12}=0\,$ps (black) directly shows the X/BX/X+ exciton complex. The FWM spectrum for longer delays ($\tau_{12}=8\,$ps, red) displays a spectral width of 0.6 meV (FWHM), which corresponds to the homogeneous line width measured via $\tau_{12}$-dependence of $T_2$=2.05 ps. The logarithmic colour scale covers 2 orders of magnitude from blue to white.
• Figure S2: Population dynamics measured at the beam overlap. a) FWM amplitude versus $\tau_{23}$ on X and X+ transitions measured at a pure CdTe quantum well as employed in the main manuscript. The initial decay on a 4 ps scale is followed by a re-population of bright exciton states occurring on a time scale of a few hundred ps. b) As in a) but measured on a CdTe quantum well doped with 0.17 % of Co$^{2+}$ ions. The cobalt ions act as efficient centres for non-radiative exciton recombination, preventing the formation of a long-lived exciton population. This allows us to measure the population lifetime of the initially injected cold excitons, $T_1$=1.22 ps, approaching the radiative limit $T_1$=$T_2$/2.