Heterodyne spectral interferometry is employed to perform four-wave mixing spectroscopy on a strongly-coupled system of an exciton confined in a single quantum dot and a photon mode of a pillar microcavtity. The coherent dynamics of one and two photon states are directly observed and the validity of the Janes-Cummings model is tested.
Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes–Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model the coherent anharmonic response of this strongly coupled exciton–cavity system at resonance. Injecting two photons into the cavity, we demonstrate a larger polariton splitting with respect to the vacuum Rabi splitting. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.
We review our recent advances in four-wave mixing spectroscopy of single semiconductor quantum dots using heterodyne spectral interferometry, a novel implementation of transient nonlinear spectroscopy allowing the study of the transient nonlinear polarization emitted from individual electronic transitions in both amplitude and phase. We present experiments on individual excitonic transitions localized in monolayer islands of GaAs/AlAs quantum wells and in self-assembled CdTe/ZnTe quantum dots. We investigate the formation of the photon echo from individual transitions, both with increasing number of transitions in the ensemble, and in the presence of temporal jitter of the energy of a single transition. The detection of amplitude and phase of the signal allows the implementation of a two-dimensional femtosecond spectroscopy, in which mutual coherent coupling of single quantum dot states can observed and quantified.
The Jaynes-Cummings (JC) model is at the heart of cavity QED and suitable to describe many different systems. Here, the authors use it to investigate a quantum dot strongly coupled to a micropillar cavity. Supported by experiments, they apply four-wave mixing spectroscopy to study the system's dynamics. They push the limits of JC physics by injecting up to $\ensuremath{\sim}20$ photons using ultrashort laser pulses. Starting with complicated dynamics, the signal evolves into a single-frequency oscillation monitoring the relaxation down the JC ladder.
Light and matter can be unified under the strong coupling regime, creating superpositions of both, called dressed states or polaritons. After initially being demonstrated in bulk semiconductors and atomic systems ,strong coupling phenomena have been realized in solid state optical microcavities. They form an essential ingredient in the exciting physics spanning from many-body quantum coherence phenomena, like Bose-Einstein condensation and superfluidity, to cavity quantum electrodynamics (cQED). A widely used approach within cQED is the Jaynes-Cummings (JC) model that describes the interaction of a single fermionic two-level system with a single bosonic photon mode. For a photon number larger than one, known as quantum strong coupling (QSC), a significant anharmonicity is predicted for the ladder-like spectrum of dressed states. For optical transitions in semiconductor nanostructures, first signatures of the quantum strong coupling were recently published. In our latest report we applied advanced coherent nonlinear spectroscopy to explore a strongly coupled exciton-cavity system. Specifically, we measured and simulated its four-wave mixing (FWM) response, granting direct access to the first two rungs of the JC ladder. This paper summarizes the main results of Ref. 15 and adds FWM experiments obtained on a micropillar cavity in which a doublet of quantum dot (QD) excitons interacts with the cavity mode in the limit of weak to strong coupling.
We develop an exact analytical approach to four-wave mixing and higher-order optical nonlinearities of a quantum dot-microcavity system. This approach allows us \nto analyse the non-linear response in terms of coherent transitions between rungs \nof the Jaynes-Cummings ladder, finding their complex amplitudes and frequencies. \nIncreasing the pulse area of the excitation field, a transition from quantum strong \ncoupling to coherent classical regime is observed, which manifests itself in a formation of the famous Mollow triplet, with the observation in the three-level model \nof a quantum dot, including a biexciton, to predict two new effects: One is the \nexistence of a Mollow-like quintuplet, the other is a complete elimination of the \nfour-wave-mixing optical non-linearity under certain parameter constraints. We further develop a simple and accurate approximation in the low-damping limit of the \nJaynes-Cummings model of the quantum dot-microcavity system, for nonlinear response of any order in a closed analytic form, predicting the positions and widths \nof the spectral lines. For higher damping, we demonstrate a strong relaxation down \nthe ladder, shown by both numerical and analytic calculation.
While the advanced coherent control of qubits is now routinely carried out in low frequency (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven dynamics of a single exciton quantum state confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi oscillation dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the frequency domain this oscillation generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states.