Coherent nonlinear optics using quantum emitters offers a powerful platform for investigating quantum phenomena. Ensembles of quantum emitters in solids often exhibit significant inhomogeneous broadening, leading to rapid dephasing of macroscopic polarization. However, this dephasing is often reversible, as evidenced by photon echoes (PEs), which retain complete information about coherent ensemble dynamics. Precise control over the PE emission time is crucial for applications in quantum technologies. Semiconductor quantum dots (QDs) are particularly attractive due to their discrete energy levels, high spectral selectivity, large oscillator strength, and long coherence times, enabling ultrafast initialization and coherent control with picosecond pulses. While Rabi oscillations and adiabatic rapid passage have been demonstrated in QDs, phase control in QD ensembles remains challenging due to inhomogeneous broadening. Photon echo protocols offer a solution by allowing for deterministic delayed emission of light. This work proposes and demonstrates a simple approach to control PE timing in self-assembled semiconductor QDs using resonant optical control pulses to freeze exciton dephasing and rephasing. This represents a significant advancement towards precise timing control in quantum systems.

The literature extensively covers coherent optical control of quantum emitters. Studies have shown the use of QDs for Rabi oscillations, adiabatic rapid passage, and even Ramsey fringes in single QDs. However, the challenge of controlling phase in QD ensembles due to inhomogeneous broadening has been a significant hurdle. Previous work has investigated dephasing inhibition in atoms and other systems, but the control of PE timing using resonant optical fields in semiconductor QDs remains largely unexplored. Other researchers have demonstrated deterministic control of PE timing in rare-earth nanophotonic crystals using detuned ac Stark pulses, but this method is significantly slower than the picosecond-scale control achieved in this study. The authors draw upon existing work on multi-wave mixing in two-level systems to inform their proposed method.

The study uses a two-pulse photon echo sequence on a sample of self-assembled (In,Ga)As QDs in a λ-microcavity. The first and second pulses have areas of π/2 and π respectively, and a third 'control' pulse with area 2πn (n being an integer) is added. The authors utilize the optical Bloch equations (OBEs) to model the system, considering the inhomogeneous broadening and finite spot size of the laser pulses. The experiments employ transient four-wave mixing (FWM) in reflection geometry, with the temporal profile of the FWM signal measured using heterodyne detection. The pulse areas and arrival times are varied to investigate the effect on the PE emission time. The theoretical model uses extended OBEs that take into account inhomogeneous broadening, finite spot size, and the temporal shapes of the laser pulses to simulate the experimental results. The simulations involved numerical solution of the extended OBEs considering the inhomogeneous broadening and finite spot size of the laser pulses. This process included simulating the macroscopic polarization, emitted electric field, interference with a reference pulse, spatial averaging, and ultimately obtaining the final signal Psignal(t) using temporal convolution. The parameters for the simulations were carefully chosen to match experimental conditions such as coherence time, exciton lifetime, and spectral characteristics. A Gaussian distribution of transition frequencies was used to represent the inhomogeneous broadening, with a total number of 1500 TLS. The spatial profile was treated using a radial coordinate system to simplify calculations.

The primary finding is the successful demonstration of resonant optical control over photon echo timing in self-assembled (In,Ga)As QDs. By applying a 2π control pulse, the researchers achieved a shift in the photon echo emission time of up to ±5 ps relative to the nominal time without the control pulse. This shift is achieved by applying the control pulse during either the dephasing or rephasing stage of the two-pulse sequence. Applying the control pulse during dephasing (pre-pulse) advances the echo, while applying it during rephasing (post-pulse) retards it. Importantly, the effect is robust, showing little dependence on the precise timing or phase of the control pulse within the respective time windows. Furthermore, the results show that the method works effectively even when the macroscopic polarization has decayed before the application of the control pulse. The experimental results were well-supported by simulations based on the optical Bloch equations (OBEs), incorporating the inhomogeneous broadening and finite laser spot size effects, demonstrating a good match between the theoretical model and experimental data. Simulations also confirmed that the effect is not limited to specific pulse intensities; the control pulse shifts the intensity-dependent transient effectively without causing dramatic changes in the pulse's shape. The authors further investigated the impact of varying control pulse area and observed oscillatory behaviour, confirming the effect of Rabi flopping. Experiments with multiple control pulses demonstrated the ability to increase the magnitude of the time shift, as expected.

The results demonstrate a significant advancement in the control of coherent phenomena in semiconductor quantum dots. The ability to accurately control the timing of photon echoes opens up new possibilities for applications in quantum information processing and quantum memory. The robustness of the method, its insensitivity to the precise timing and phase of the control pulse, and its compatibility with different excitation conditions makes it a practical and versatile tool. The agreement between experimental data and the theoretical model based on OBEs validates the underlying physical mechanisms and supports the potential for further improvements and generalizations. The technique's effectiveness on ultrafast timescales (picoseconds) makes it significantly faster than previous methods of PE timing control, potentially improving the performance of quantum memory protocols. Future research could explore the application of this technique to other quantum systems and investigate potential improvements to the accuracy and magnitude of the time shifts. The ability to control multiple pulses and potentially address different spin levels could enhance its capabilities.

This study successfully demonstrated a novel and robust method for controlling the timing of photon echoes in semiconductor quantum dots. The use of a resonant 2π control pulse allows for precise and bidirectional control of the emission time, paving the way for significant improvements in quantum memory and information processing technologies. Future research could explore the scalability of this technique and its application to more complex quantum systems, potentially opening up new possibilities in quantum information science.

The study primarily focuses on a specific type of QD (self-assembled (In,Ga)As QDs) and the results may not be directly transferable to all QD systems. The model utilizes a simplified representation of the complex interaction mechanisms in the system. While the agreement between simulations and experiment is good, some approximations may impact the accuracy of the theoretical predictions. The experimental setup uses a relatively large laser spot size, which might limit the precision of the time measurements. Further studies are needed to investigate the scaling of this method to larger ensembles of QDs and explore potential limitations at higher pulse repetition rates.