The dynamics of semiconductor quantum wires and wells that are coupled to a single-mode quantum field are analyzed. Within a two-band tight-binding model the Coulomb interaction between electrons and holes is included on a microscopic basis and the light-matter interaction is quantized. The dynamics of the system is described by equations of motion for the relevant set of expectation values of the coupled electronic-photonic system. Starting from the initial condition of a single photon occupying the field mode, we study the dynamics of the mean photon number. To analyze effects arising from the many-body Coulomb interaction, we use an exact truncation of the electronic hierarchy problem by employing the fact that N photons cannot excite more than N electron-hole pairs. We compare Rabi oscillations with and without Coulomb interaction for different excitation conditions. When the quantum field mode is initially occupied by two photons, two interacting electron-hole pairs, i.e., biexcitons, can be generated which characteristically modify the dynamics. Within a consistent and fully-quantized approach we show consequences of biexcitonic many-body correlations that are coupled to a quantum field and discuss the obtained dynamics.
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.
We consider an electronic three-level system with two dipole-allowed transitions that are resonantly excited with two single-mode quantum fields, respectively. The interaction is described with a Jaynes-Cummings type model. In such a fully-quantized system, quantum correlations between initially independent quantum fields are found to arise. Their theoretical analysis is an important but challenging task since each field appears in a mixed state and the known criteria of entanglement are not suitable for such a multi-partite case. Here, we present a detailed insight into the formation of such correlations by using the cluster-expansion approach. With this approach, the hierarchy problem that arises due to the light-matter interaction can be truncated and analyzed by classifying many-body quantities systematically into clusters and omitting clusters above a predefined size. This leads to explicit expressions for the correlated part of high-order N-particle operators, which do not allow for further factorization. In our case, we consider N-particle operators that are composed of at least one bosonic operator of the respective fields, where the number of bosonic operators is limited by the chosen maximum cluster size. The obtained correlated parts are processed into a single measure for the correlation between the fields. We perform simulations based on the obtained equations for the expectation value of the correlated parts, which allow a deeper insight into the formation of quantum correlations and to study the contribution and behavior of different cluster sizes. Numerical results for the correlation between the two quantum fields are presented and discussed.
We analyze four-wave-mixing experiments with three incident laser pulses performed on a semiconductor quantum well embedded in a microcavity. The coupling of the intracavity field and the exciton transition leads to exciton polaritons. The many-body hierarchy problem that arises due to the Coulomb interaction is treated by the dynamics-controlled truncation scheme, which leads to a set of Bloch equations that contain optical nonlinearities including biexcitonic many-body correlations and contributions beyond the coherent limit, which have not been thoroughly explored for a microcavity yet. A numerical solution of these Bloch equations is performed by projecting onto the 1s-exciton and biexciton states. We present the two-dimensional Fourier transform of the four-wave-mixing signal for different polarization directions of the incident pulses, which allows us to investigate the absorption and emission of the system and the couplings among the different resonances from the lower polariton, the upper polariton, and the biexciton. The numerical results are compared with measurements, in which a GaAs quantum well sample enclosed in distributed Bragg reflectors is investigated for four different polarization configurations, and we find a good agreement.
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.
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