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arXiv:cond-mat/0310570 · Physical Review B

Dynamics of the excitations of a quantum dot in a microcavity

J. I. Perea, Diego Porras, C. Tejedor

Published Sep 9, 2004• 60 citations
arXivHTMLPDF

Abstract

We study the dynamics of a quantum dot embedded in a three-dimensional microcavity in the strong coupling regime in which the quantum dot exciton has an energy close to the frequency of a confined cavity mode. Under the continuous pumping of the system, the confined electron and hole can recombine either by spontaneous emission through a leaky mode or by stimulated emission of a cavity mode that can escape from the cavity. The numerical integration of a master equation including all these effects gives the dynamics of the density matrix. By using the quantum regression theorem, we compute the first- and second-order coherence functions required to calculate the photon statistics and the spectrum of the emitted light. Our main result is the determination of a range of parameters in which a state of cavity modes with Poissonian or sub-Poissonian (nonclassical) statistics can be built up within the microcavity. Depending on the relative values of pumping and rate of stimulated emission, either one or two peaks close to the excitation energy of the dot and/or to the natural frequency of the cavity are observed in the emission spectrum. The physics behind these results is discussed.

DOI
10.1103/physrevb.70.115304

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We study the dynamics of a quantum dot embedded in a three-dimensional microcavity in the strong coupling regime in which the quantum dot exciton has an energy close to the frequency of a confined cavity mode. Under the continuous pumping of the system, the confined electron and hole can recombine either by spontaneous emission through a leaky mode or by stimulated emission of a cavity mode that can escape from the cavity. The numerical integration of a master equation including all these effects gives the dynamics of the density matrix. By using the quantum regression theorem, we compute the first- and second-order coherence functions required to calculate the photon statistics and the spectrum of the emitted light. Our main result is the determination of a range of parameters in which a state of cavity modes with Poissonian or sub-Poissonian (nonclassical) statistics can be built up within the microcavity. Depending on the relative values of pumping and rate of stimulated emission, either one or two peaks close to the excitation energy of the dot and/or to the natural frequency of the cavity are observed in the emission spectrum. The physics behind these results is discussed.
The master equation for the microcavity-quantum dot coupled system is established based on the quantum regression theorem,and the time-dependent evolution of the density matrix of the two-level system for a quantum dot in a microcavity is studied under pumping by laser pulses.The characteristics such as the number of emitted photons and the second-order corelation function are derived from the density matrixes.Parameters of the microcavity and the pumping conditions are optimized for single-photon sources.The relativity between the microcavity decay rate and coupling coefficient is critical for single photon emission.
We present a study of the strong coupling between radiation and matter, considering a system of two quantum dots, which are in mutual interaction and interact with a single mode of light confined in a semiconductor nanocavity. We take into account dissipative mechanisms such as the escape of the cavity photons, decay of the quantum dot excitons by spontaneous emission, and independent exciton pumping. It is shown that the mutual interaction between the dots can be measured off-resonance only if the strong coupling condition is reached. Using the quantum regression theorem, a reasonable definition of the dynamical coupling regimes is introduced in terms of the complex Rabi frequency. Finally, the emission spectrum for relevant conditions is presented and compared with the above definition, demonstrating that the interaction between the excitons does not affect the strong coupling.
A system consisted of a three-level quantum dot coupled to a single mode of an optical microcavity is investigated.Using the numerical calculation method,the net stimulated emission dynamical evolution with the variation of the coupling strength between the quantum dot and the single mode of the optical microcavity is studied,which is based on quantum-optical master equations. The effect of the decay rate between the laser levels on the net stimulated emission is also studied. When the coupling strength between the quantum dot and the single mode of the optical cavity is larger, the net stimulated emission is prone to a saturation curve sooner. These saturation curves get to a limit value with the increasing value of the coupling strength sooner. The net stimulated emission curves show the opposite law with the increasing value of the decay rate between the laser levels.
The behaviour of the photoluminescence spectra of a single quantum dot in a semiconductor microcavity is modeled numerically in the presence of an external and constant magnetic field. The dynamics of the density operator is calculated using the master equation in the Lindblad form for decoherence processes: spontaneous emission, losses through cavity mirrors, and dephasing. An incoherent pumping of excitons is used to feed the system. It is found in the photoluminescence spectra that for magnetic fields lower than 2 T the system is in the strong coupling regime and for magnetic fields greater than 2 T the system emits light like three independent systems. The line that uncouples faster is the σ line.
We study the photon emission from a quantum dot embedded in a microcavity. Incoherent pumping of its excitons and biexciton provokes the emission of leaky and cavity modes. By solving a master equation we obtain the correlation functions required to compute the spectrum and the relative efficiency among the emission of pairs and single photons. A quantum regime appears for low pumping and large rate of emission. By means of a post-selection process, a two beams experiment with different linear polarizations could be performed producing a large polarization entanglement visibility precisely in the quantum regime.
The optical emission spectrum of a quantum dot in strong coupling with the single mode of a microcavity is obtained in the nonlinear regime. We study how exciton-exciton interactions alter the emission spectrum of the system, bringing the linear Rabi doublet into a multiplet structure that is strongly dependent on the cavity-exciton energy detuning. We emphasize how nonlinearity can be used to evidence the genuine quantum nature of the coupling by producing satellites peaks of the Rabi doublet that originate from the quantized energy levels of the interactions.