Experimental measurement of the reappearance of Rabi rotations in semiconductor quantum dots

TL;DR

This work tackles phonon-induced decoherence in resonantly driven solid-state quantum emitters by demonstrating the non-monotonic reappearance of Rabi rotations in a single GaAs quantum dot and linking the effect to the phonon spectral density $J(\omega)$ and the instantaneous Rabi energy $\Omega(t)$. The authors combine a controlled, few-ps pulsed excitation with high-fidelity resonance fluorescence and a numerically exact PT-MPO theory for a two-level system coupled to longitudinal acoustic phonons, achieving quantitative agreement across temperatures and pulse parameters. A key finding is the experimental observation of Rabi reappearance up to large pulse areas, consistent with theory, and extending the understanding of electron-phonon interactions to practical state preparation in solid-state quantum devices. These results have implications for designing robust, high-fidelity quantum-dot photon sources and for generalizing phonon-aware control strategies to other localized solid-state emitters.

Abstract

Phonons in solid-state quantum emitters play a crucial role in their performance as photon sources in quantum technology. For resonant driving, phonons dampen the Rabi oscillations resulting in reduced preparation fidelities. The phonon spectral density, which quantifies the strength of the carrier-phonon interaction, is non-monotonous as a function of energy. As one of the most prominent consequences, this leads to the reappearance of Rabi rotations for increasing pulse power, which was theoretically predicted in Phys. Rev. Lett. 98, 227403 (2007). In this paper we present the experimental demonstration of the reappearance of Rabi rotations.

Figures (9)

• Figure 1: (a) Calculated Rabi oscillations for different pulse areas, varied by adjusting the pulse intensity. The lower damping of the population evolution for small (blue lines) and large (red lines) pulse areas results in a higher contrast of the final state population compared to intermediate pulse areas (green lines). (b) Rabi rotation obtained for a pulse duration of $\tau = 9.0ps$ at $T = 6.1K$. The damping of the oscillation reaches its maximum for a pulse area of $\sim 9 \pi$. Further increasing the pulse area leads to a clear reappearance of the Rabi rotation. The theoretical model is in excellent agreement with the experimental data. The experimental data is shifted to the average of the oscillation to emphasize the envelope.
• Figure 2: (a) Energy level scheme of a two-level system consisting of the ground $\ket{g}$ and excited state $\ket{x}$ coupled to a resonant laser field. In the rotating frame, dressed states are formed. Their degeneracy is lifted and the splitting $\hbar\Omega_0$ is proportional to the amplitude of the laser pulse as indicated in the bottom. Between the dressed states, phonons can induce transitions, but for low temperatures only phonon emission is allowed. (b) Instantaneous Rabi energy as a function of time. The colored background shows the phonon spectral density $J(\omega)$. When the Rabi frequency and the phonon spectral density agree, an efficient coupling to the phonons takes place.
• Figure 3: (a) Gate voltage dependent photoluminescence measurement for non-resonant excitation exhibits distinct charge plateaus of the neutral X$^0$ and negatively charged X$^-$ exciton. The blue dashed line indicates the applied gate voltage $V = 0.85V$ chosen for resonant excitation. (b) The gated quantum dot structure facilitates the acquisition of spectra under identical conditions with the trion transition tuned in (blue) and out of resonance (dashed orange) with the excitation laser energy. This allows the subtraction of remaining unsuppressed laser to clear the spectrum from unwanted background laser signal (green).
• Figure 4: Rabi rotations of the negative trion transition driven by a $9.0ps$ long laser pulse for varying sample temperature from $6.1K$ to $50K$. The single data sets are offset along the y-axis for more clarity. Clear indication of the reappearance of the Rabi rotation is even found for elevated temperatures.
• Figure 5: Sketch of the folded 4f-pulse shaper setup used to adjust wavelength and duration of the excitation pulse. The width of the slit determines the duration of the carved out pulse while the position in the Fourier plane selects the center wavelength. The pulses are fiber coupled to a confocal, cryogenic $\mu$PL setup. The back scattered laser light is suppressed in the detection path by cross-polarized filtering, realized with thin-film polarizers, a polarizing beam splitter and a quarter wave plate. In addition, spatial filtering of the detection path is done by fiber coupling into a single mode fiber.