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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Cavity-QED effect on nonlinear spectra via biexciton of a quantum dot

Hiroshi Ajiki, Hajime Ishihara

Published Feb 9, 2006• 0 citations
Publisher

Abstract

We theoretically study pump and probe spectra of a quantum dot (QD) embedded in a microcavity in the cavity QED treatment. Energy levels of a QD are modeled by a four-level system consisting of the ground state, right and left-polarized excitons, and a biexciton. As a cavity-QED effect, four spectral peaks appear when the pump field frequency is tuned to the lower or upper level constituting the vacuum-field Rabi splitting. In addition, the spectral intensity dramatically enhances due to the cavity effect. The enhancement rate is independent of the coupling energy between exciton and cavity photons when the well-defined vacuum-field Rabi splitting is formed.

DOI
10.1117/12.660977

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We theoretically study pump and probe spectra of a quantum dot (QD) embedded in a microcavity in the cavity QED treatment. Energy levels of a QD are modeled by a four-level system consisting of the ground state, right and left-polarized excitons, and a biexciton. As a cavity-QED effect, four spectral peaks appear when the pump field frequency is tuned to the lower or upper level constituting the vacuum-field Rabi splitting. In addition, the spectral intensity dramatically enhances due to the cavity effect. The enhancement rate is independent of the coupling energy between exciton and cavity photons when the well-defined vacuum-field Rabi splitting is formed.
We theoretically study cross-polarized pump-probe spectra of a quantum dot (QD) embedded in a microcavity in the cavity quantum electrodynamics treatment. Recently, observations of a vacuum Rabi splitting for a QD in microcavity have been reported. The vacuum Rabi splitting is the level separation of one-excitation dressed states (1e states). However, two-excitation dressed states (2e states) have not been observed in this system. We discuss the possibility to observe pump-probe signal coming from the cross-polarized 2e states, in which the energy levels of a QD are modeled by a four-level system consisting of the ground state, right- and left-polarized excitons, and a biexciton. The signal peaks due to the cross-polarized 2e states are found when the quality factor of the cavity is extremely large. The spectral intensity is dramatically enhanced due to the cavity effect. The enhancement rate is independent of the coupling constants between the exciton (biexciton) and a cavity photon when a well-defined vacuum Rabi splitting is formed. However, a strong suppression of the signal occurs at a condition where the energy of the 1e state coincides with the energy difference between 1e and cross-polarized 2e states.
We demonstrate the simultaneous dressing of both vacuum-to-exciton and exciton-to-biexciton transitions of a single semiconductor quantum dot in a high-Q micropillar cavity, using photoluminescence spectroscopy. Resonant two-photon excitation of the biexciton is achieved by spectrally tuning the quantum dot emission with respect to the cavity mode. The cavity couples to both transitions and amplifies the Rabi frequency of the likewise resonant continuous wave laser, driving the transitions. We observe strong-field splitting of the emission lines, which depend on the driving Rabi field amplitude and the cavity-laser detuning. A dressed state theory of a driven 4-level atom correctly predicts the distinct spectral transitions observed in the emission spectrum, and a detailed description of the emission spectra is further provided through a polaron master equation approach which accounts for cavity coupling and acoustic phonon interactions of the semiconductor medium.
Theoretical study on entangled photon generation from a quantum dot (QD) embedded in microcavity is briefly reviewed within a strong coupling regime. In this system, entangled photon pairs can be generated through the cascade photon emission via dressed states in the cavity quantum electrodynamics (CQED). Excitation levels of a QD are modeled by a V-type three-level system and four-level system including a biexciton. In contrast to the entangled-photon generation until now, all four Bell states can be generated from an identical cavity system by simply selecting applied-field polarizations and frequencies as characteristic features of the CQED. The CQED effects play a crucial role in providing a high degree of entanglement: (i) spectral fi ltering can be used to extract entangled photons due to the vacuum Rabi splitting and (ii) non-entangled co-polarized photons are strongly suppressed due to the photon blockade effect.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
Abstract Inhibition and enhancement of spontaneous emission rate, first proposed by Purcell, is discussed in terms of altered density-of-modes in various types of solid-state cavities and the Purcell factor is derived for two-level atomic system. The conditions for observing Purcell factor and experimental findings in micropillars embedded with Quantum Dots (QD)s are discussed. The strong interaction between photons and matter in the form of QD excitons, dispersion relations for ground and excited states separated by Rabi splitting are discussed. Experimental photoluminescence spectra showing anticrossing of exciton lines and cavity lines by temperature and other tuning methods are used to illustrate the strong light-matter interaction. The Jayness–Cummins model based on second quantization is presented to point out Rabi oscillation, Purcell effect, and other novel features. Microcavity structures for observing cavity quantum electrodynamics effects are mentioned. Microcavity lasers predicting thresholdless operation for unity spontaneous emission coupling factors are discussed.
Summary form only given. We report studies of exciton Rabi splitting where spectrally narrow pump and probe pulses were used. In this case, coherent spectral oscillations in pump-probe spectra can be avoided by tuning the central frequency of the probe pulse. The intensity dependence of the Rabi splitting obtained from these studies reveals a distinctly nonlinear relationship between the Rabi frequency and the applied electric field, in contrast to the linear dependence expected from mean-field based theoretical models. Pump-probe experiments were performed on a 130 /spl Aring/ GaAs/AlGaAs multiple QW sample at 10 K.