We study theoretically the nonlinear four-wave mixing response of an ensemble of coupled pairs of quantum dots (quantum dot molecules).We discuss the shape of the echo signal depending on the parameters of the ensemble: the statistics of transition energies and the degree of size correlations between the dots forming the molecules.
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 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.
In this study, the four-wave mixing (FWM) spectrum of a strongly pumped hybrid structure is theoretically examined. The hybrid structure consists of an asymmetric double semiconductor quantum dot (SQD) molecule and a spherical metal nanoparticle (MNP), which are coupled together via long-range Coulomb interaction. Having as a starting point the Hamiltonian of the system, in the dipole and the rotating-wave approximations, we derive a set of nonlinear density matrix equations, which are numerically solved, in the steady-state limit, and then the FWM coefficient is calculated within a range of values of the pump–probe field detuning. The spectral response of the FWM coefficient is investigated, for different values of the pump-field detuning, the electron-tunneling rate, and the energy gap between the upper states in the energy-level scheme of the double SQD molecule, while the interparticle distance between the two components of the structure is modified.
In the present work, the linear and nonlinear optical properties of quantum dot molecules composed of two quantum dots as well as three quantum dots molecules, respectively known as double quantum dot (DQD) molecule and triple quantum dot (TQD) molecules are studied using the probability amplitude method, and the obtained results are discussed and compared. By solving the state equations of these systems in the interaction picture, under the rotating wave approximation and the dipole approximation, the first and third-order susceptibilities for DQD and TQD molecules are calculated. A phenomenon called tunneling-induced transparency (TIT) which is similar to electromagnetically induced transparency (EIT) is studied in these types of quantum dot molecules. The effect of key system parameters such as tunneling couplings between quantum dots and the tunneling intensity on the linear and nonlinear optical response of multiple quantum dot molecules DQD and TQD is investigated. It was shown that the position and the width of the TIT window created in these quantum dot molecules can be tuned by changing the physical parameters.