Collective Effects in Nanolasers Explained by Generalized Rate Equations

We study the stationary photon output and statistics of small lasers. Our closed-form expressions clarify the contribution of collective effects due to the interaction between quantum emitters. We generalize laser rate equations and explain photon trapping: a decrease of the photon number output below the lasing threshold, derive an expression for the stationary cavity mode autocorrelation function $g_2$, which implies that collective effects may strongly influence the photon statistics. We identify conditions for coherent, thermal and superthermal radiation, the latter being a unique fingerprint for collective emission in lasers. These generic analytical results agree with recent experiments, complement numerical results, and provide insight into and design rules for nanolasers.Comment: 5 pages, 4 figures, Supplementary materials 4 page

On collective Rabi splitting in nanolasers and nano-LEDs

We analytically calculate the optical emission spectrum of nanolasers and nano-LEDs based on a model of many incoherently pumped two-level emitters in a cavity. At low pump rates we find two peaks in the spectrum for large coupling strengths and numbers of emitters. We interpret the double-peaked spectrum as a signature of collective Rabi splitting, and discuss the difference between the splitting of the spectrum and the existence of two eigenmodes. We show that an LED will never exhibit a split spectrum, even though it can have distinct eigenmodes. For systems where the splitting is possible we show that the two peaks merge into a single one when the pump rate is increased. Finally, we compute the linewidth of the systems, and discuss the influence of inter-emitter correlations on the lineshape

Quantum Langevin approach for superradiant nanolasers

A new approach for analytically solving quantum nonlinear Langevin equations is proposed and applied to calculations of spectra of superradiant lasers where collective effects play an important role. We calculate lasing spectra for arbitrary pump rates and recover well-known results such as the pump dependence of the laser linewidth across the threshold region. We predict new sideband peaks in the spectrum of superradiant lasers with large relaxation oscillations as well as new nonlinear structures in the lasing spectra for weak pump rates. Our approach sheds new light on the importance of population fluctuations in the narrowing of the laser linewidth, in the structure of the lasing spectrum, and in the transition to coherent operation.Comment: 19 pages, 10 figure

Microscopic theory of phonon-induced effects on semiconductor quantum dot decay dynamics in cavity QED

We investigate the influence of the electron-phonon interaction on the decay dynamics of a quantum dot coupled to an optical microcavity. We show that the electron-phonon interaction has important consequences on the dynamics, especially when the quantum dot and cavity are tuned out of resonance, in which case the phonons may add or remove energy leading to an effective non-resonant coupling between quantum dot and cavity. The system is investigated using two different theoretical approaches: (i) a second-order expansion in the bare phonon coupling constant, and (ii) an expansion in a polaron-photon coupling constant, arising from the polaron transformation which allows an accurate description at high temperatures. In the low temperature regime we find excellent agreement between the two approaches. An extensive study of the quantum dot decay dynamics is performed, where important parameter dependencies are covered. We find that in general the electron-phonon interaction gives rise to a greatly increased bandwidth of the coupling between quantum dot and cavity. At low temperature an asymmetry in the quantum dot decay rate is observed, leading to a faster decay when the quantum dot has a larger energy than to the cavity. We explain this as due to the absence of phonon absorption processes. Furthermore, we derive approximate analytical expressions for the quantum dot decay rate, applicable when the cavity can be adiabatically eliminated. The expressions lead to a clear interpretation of the physics and emphasizes the important role played by the effective phonon density, describing the availability of phonons for scattering, in quantum dot decay dynamics. Based on the analytical expressions we present the parameter regimes where phonon effects are expected to be important. Also, we include all technical developments in appendices.Comment: published PRB version, comments are very welcom

Oscillatory variations in the Q factors of high quality micropillar cavities

We report on the observation of oscillatory variations in the quality (Q) factor of quantum dot-micropillar cavities based on planar Bragg reflectors. The oscillatory behavior in the Q versus diameter dependence appears in the diameter range between 1.0 and 4.0 mu m, has a characteristic period of a few hundred nanometers and increases in amplitude with increasing reflectivity of the planar microcavity structures. The experimental results are well reproduced by numerical calculations which support the interpretation that the Q oscillations are caused by coupling of propagating Bloch modes of different orders at the mirror interfaces.</p

High beta lasing in micropillar cavities with adiabatic layer design

We report on lasing in optically pumped adiabatic micropillar cavities, based on the AlAs/GaAs material system. A detailed study of the threshold pump power and the spontaneous emission beta factor in the lasing regime for different diameters d(c) is presented. We demonstrate a reduction of the threshold pump power by over 2 orders of magnitude from d(c) = 2.25 mu m down to 0.95 mu m. Lasing with beta factors exceeding 0.5 shows that adiabatic micropillars are operating deeply in the cavity quantum electrodynamics regime.Publisher PDFPeer reviewe

Age-dependent association between protein expression of the embryonic stem cell marker Cripto-1 and survival of glioblastoma patients

Exploring the re-emergence of embryonic signaling pathways may reveal important information for cancer biology. Nodal is a transforming growth factor-β (TGF-β)-related morphogen that plays a critical role during embryonic development. Nodal signaling is regulated by the Cripto-1 co-receptor and another TGF-β member, Lefty. Although these molecules are poorly detected in differentiated tissues, they have been found in different human cancers. Poor prognosis of glioblastomas justifies the search for novel signaling pathways that can be exploited as potential therapeutic targets. Because our intracranial glioblastoma rat xenograft model has revealed importance of gene ontology categories related to development and differentiation, we hypothesized that increased activity of Nodal signaling could be found in glioblastomas. We examined the gene expressions of Nodal, Cripto-1, and Lefty in microarrays of invasive and angiogenic xenograft samples developed from four patients with glioblastoma. Protein expression was evaluated by immunohistochemistry in 199 primary glioblastomas, and expression levels were analyzed for detection of correlations with available clinical information. Gene expression ofNodal, Lefty, and Cripto-1 was detected in the glioblastoma xenografts. Most patient samples showed significant levels of Cripto-1 detected by immunohistochemistry, whereas only weak to moderate levels were detected for Nodal and Lefty. Most importantly, the higher Cripto-1 scores were associated with shorter survival in a subset of younger patients. These findings suggest for the first time that Cripto-1, an important molecule in developmental biology, may represent a novel prognostic marker and therapeutic target in categories of younger patients with glioblastoma.publishedVersio