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arXiv:2302.02480 · ACS Photonics

Temporal Sorting of Optical Multiwave-Mixing Processes in Semiconductor Quantum Dots

Stefan Grisard, Artur V. Trifonov, Hendrik Rose, Rilana Reichhardt, Matthias Reichelt, Christian Schneider, Martin Kamp, Sven Höfling, M. Bayer, T. Meier, Ilya A. Akimov

Published Sep 6, 2023• 2 citations
arXivHTMLPDF

Abstract

Interaction of light with atomic-like solid-state systems, such as semiconductor quantum dots (QDs) with discrete energy levels, is key for the implementation of high-speed quantum gates and information processing in semiconductor-based devices. Of particular interest are degenerate multiwave-mixing processes under resonant conditions that establish strong light–matter interactions beyond the limits of perturbative nonlinear optics. Here, we exploit a multitude of picosecond optical pulses to manipulate the unitary evolution of excitons in (In,Ga)As QDs and address the role of resonance detuning in an inhomogeneously broadened ensemble. In particular, we use the two-pulse photon echo sequence to uncover the coherent dynamics of charged excitons, whereas the areas of two additional control pulses serve as tuning knobs for adjusting the magnitude and timing of the coherent emission in a wide range up to several hundred of picoseconds. Furthermore, we make use of the spin degeneracy of the ground and excited states of charged QDs to control the polarization state of the emitted light. We reveal that control pulses, whose durations are comparable to the dephasing time of the ensemble, lead to a temporal sorting of optical multiwave-mixing processes, which is in accordance with the developed theoretical model. Lifting the temporal degeneracy allows us to smoothly trace the transition from the perturbative to the regime of Rabi rotations and opens up new possibilities for the optical investigation of complex energy-level structures in so far unexplored material systems.

DOI
10.1021/acsphotonics.3c00530

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Interaction of light with atomic-like solid-state systems, such as semiconductor quantum dots (QDs) with discrete energy levels, is key for the implementation of high-speed quantum gates and information processing in semiconductor-based devices. Of particular interest are degenerate multiwave-mixing processes under resonant conditions that establish strong light–matter interactions beyond the limits of perturbative nonlinear optics. Here, we exploit a multitude of picosecond optical pulses to manipulate the unitary evolution of excitons in (In,Ga)As QDs and address the role of resonance detuning in an inhomogeneously broadened ensemble. In particular, we use the two-pulse photon echo sequence to uncover the coherent dynamics of charged excitons, whereas the areas of two additional control pulses serve as tuning knobs for adjusting the magnitude and timing of the coherent emission in a wide range up to several hundred of picoseconds. Furthermore, we make use of the spin degeneracy of the ground and excited states of charged QDs to control the polarization state of the emitted light. We reveal that control pulses, whose durations are comparable to the dephasing time of the ensemble, lead to a temporal sorting of optical multiwave-mixing processes, which is in accordance with the developed theoretical model. Lifting the temporal degeneracy allows us to smoothly trace the transition from the perturbative to the regime of Rabi rotations and opens up new possibilities for the optical investigation of complex energy-level structures in so far unexplored material systems.
Semiconductor quantum dots are excellent candidates for ultrafast coherent manipulation of qubits by laser pulses on picosecond timescales or even faster. In inhomogeneous ensembles a macroscopic optical polarization decays rapidly due to dephasing, which, however, is reversible in photon echoes carrying complete information about the coherent ensemble dynamics. Control of the echo emission time is mandatory for applications. Here, we propose a novel concept to reach this goal. In a two-pulse photon echo sequence, we apply an additional resonant control pulse with multiple of 2pi area. Depending on its arrival time, the control slows down dephasing or rephasing of the exciton ensemble during its action. We demonstrate for self-assembled (In,Ga)As quantum dots that the photon echo emission time can be retarded or advanced by 5 ps relative to its nominal appearance time without control. This versatile protocol may be used to obtain significantly longer temporal shifts for suitably tailored control pulses.
Abstract Semiconductor quantum dots are excellent candidates for ultrafast coherent manipulation of qubits by laser pulses on picosecond timescales or even faster. In inhomogeneous ensembles a macroscopic optical polarization decays rapidly due to dephasing, which, however, is reversible in photon echoes carrying complete information about the coherent ensemble dynamics. Control of the echo emission time is mandatory for applications. Here, we propose a concept to reach this goal. In a two-pulse photon echo sequence, we apply an additional resonant control pulse with multiple of 2πarea. Depending on its arrival time, the control slows down dephasing or rephasing of the exciton ensemble during its action. We demonstrate for self-assembled (In,Ga)As quantum dots that the photon echo emission time can be retarded or advanced by up to 5 ps relative to its nominal appearance time without control. This versatile protocol may be used to obtain significantly longer temporal shifts for suitably tailored control pulses.
Controlling the quantum states of charge (excitons) or spin-polarized carriers in semiconductor quantum dots (QDs) has been the focus of a considerable research effort in recent years due to the strong promise of using this approach to develop solid state quantum computing hardware. The long-term scalability of this type of quantum computing architecture is enhanced by the use of QDs emitting in the telecom band, which would exploit the established photonic infrastructure. This thesis reports the use of all optical infrared experimental techniques to control exciton dynamics in two different QD samples consisting of InAs/GaAs QDs and InAs/InP QDs within a planar microcavity. An infrared quantum control apparatus was developed and used to apply optimized shaping masks to ultrafast pulses from an optical parametric oscillator. Pulse shaping protocols designed to execute a two-qubit controlled-rotation operation on an individual semiconductor QD were demonstrated and characterized. The quantum control apparatus was then implemented in simultaneous single qubit rotations using two uncoupled, distant InAs/GaAs QDs. These optimal control experiments demonstrated high fidelity optical manipulation of exciton states in the two QDs using a single broadband laser pulse, representing a step forward on the path to a scalable QD architecture and showcasing the power of pulse shaping techniques for quantum control on solid state qubits. As an alternative to single QDs, which have very low optical signals, subsets of QDs within an ensemble can be used in quantum computing applications. To investigate the mediation of inhomogeneities in a QD ensemble, pump-probe experiments were performed on InAs/InP QDs within a dielectric Bragg stack microcavity. Two different excitation geometries showed that the angle dependence of the microcavity transmission allowed for the spectral selection of QD subsets with transition energies resonant with the cavity mode. The microcavity mitigated inhomogeneities in the ensemble while providing a basis for addressing QD subsets which could be used as distinguishable quantum bits. This thesis work shows significant advances towards an optical computing architecture using quantum states in semiconductor QDs.
Following the ultrafast optical excitation of an inhomogeneously broadened ensemble, the macroscopic optical polarization decays rapidly due to dephasing. This destructive interference is, however, reversible in photon echo experiments. Here, we propose a concept in which a control pulse slows down either the dephasing or the rephasing of the exciton ensemble during its presence. We analyze and visualize this optical freezing process by showing and discussing results for different single and multiple sequences of control pulses using a simple model of inhomogeneously broadened two-level systems. This idea has been realized in experiments performed on self-assembled (In,Ga)As quantum dots where it was possible to retard or advance the photon echo emission time by several picoseconds. The measurements are in very good agreement with numerical simulations for a more realistic model which, in particular, takes the spatial shape of the laser pulses into account.
In this work, we study the resonant nonlinear optical response obtained when optical fields are used to excite charged semiconductor quantum dots (QDs). The basic physics of charged excitons (trions) created by optical excitation of charged QDs is of interest from the point of view of optically driven spin based quantum computing (QC). Stimulated Raman excitation, resonantly enhanced by the optical dipole coupling to the trion state, was used to optically generate electron spin coherence in the ground state of charged QDs. The evolution of the spin coherence was monitored through quantum beats in the phase-sensitively detected four wave mixing signal. The decay of the beats is a measure of the spin coherence time, which was found to be at least an order of magnitude greater than either the trion dipole coherence, or the Raman coherence time between excitons in a single neutral QD. A fascinating outcome of the experiment was the first observation of a contribution to the spin coherence induced by the vacuum field, which is also responsible for spontaneous emission from the trion state, known as spontaneously generated coherence (SGC). QC demands that coherent optical manipulations should be performed within the spin coherence time. We performed coherent optical control experiments, with a pair of phase-locked pump pulses, that showed the quantum nature of the coherence through interference of different quantum mechanical pathways. We showed both in experiment and theory that we can manipulate the spin coherence on the time scale of the Larmor frequency, as well as on an ultrafast femtosecond time scale, corresponding to the optical frequency of the trion state. Finally, resonant optical excitation of both the bright and nominally forbidden transitions from a single electron spin in a QD to the trion state were demonstrated. This allows for direct optical access to all the transitions required for optically driven QC with QD electron spins. We used frequency-domain nonlinear spectroscopy measurements on single QD trions to obtain the trion dipole decoherence and decay rates. Further, we demonstrated that the single electron spin coherence could be generated and detected optically, and found that the spin coherence time was significantly greater than in ensemble measurements at the same magnetic field.
The nonlinear optical response of an ensemble of semiconductor quantum dots is analyzed by wave-mixing processes, where we focus on four-wave mixing with two incident pulses. Wave-mixing experiments are often described with semiclassical models, where the light is modeled classically and the material quantum mechanically. Here, however, we use a fully quantized model, where the light is given by a quantum state of light. Quantum light involves more degrees of freedom than classical light as e.g., its photon statistics and quantum correlations, which is a promising resource for quantum devices, such as quantum memories. The light-matter interaction is treated with a Jaynes-Cummings type model and the quantum field is given by a single mode since the quantum dots are embedded in a microcavity. We present numerical simulations of the four-wave-mixing response of a homogeneous system for pulse sequences and find a significant dependence of the result on the photon statistics of the incident pulses. The model constitutes a problem with a large state space which arises from the frequency distribution of the transition energies of the inhomogeneously broadened quantum dot ensemble that is coupled with a quantum light mode. Here we approximate the dynamics by summing over individual quantum dot-microcavity systems. Photon echoes arising from the excitation with different quantum states of light are simulated and compared.