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arXiv:0906.4532 · Physical Review B

Photon antibunching in strongly coupled exciton–semiconductor cavity systems: Role of off-resonant coupling to multiple excitons

E. Illes, Stephen Hughes

Published Mar 29, 2010• 10 citations

Abstract

We present a master equation approach to study the second-order quantum autocorrelation functions for up to two quantum-dot excitons, coupled to an off-resonant cavity in a semiconductor-single quantum-dot cavity system. For a single coupled off-resonant exciton, we observe unusual oscillatory behavior in the early time dynamics of the cavity autocorrelation function, which leads to decreased antibunching relative to the exciton mode. With a second coupled exciton in the system, we find that the magnitude and the lifetime of these oscillations greatly increases, since the cavity is then able to exchange photons with multiple excitonic resonances. These results demonstrate that for incoherent pumping, the ubiquitous two-level atom model completely breaks down and that multiple excitonic resonances act in concert to spoil the antibunching characteristics of the cavity quasimode. We connect these findings to a series of recent surprising experimental results for single quantum dot-semiconductor cavity systems, including photonic crystal systems and micropillar cavities.

DOI: 10.1103/physrevb.81.121310

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We present a master equation approach to study the second-order quantum autocorrelation functions for up to two quantum-dot excitons, coupled to an off-resonant cavity in a semiconductor-single quantum-dot cavity system. For a single coupled off-resonant exciton, we observe unusual oscillatory behavior in the early time dynamics of the cavity autocorrelation function, which leads to decreased antibunching relative to the exciton mode. With a second coupled exciton in the system, we find that the magnitude and the lifetime of these oscillations greatly increases, since the cavity is then able to exchange photons with multiple excitonic resonances. These results demonstrate that for incoherent pumping, the ubiquitous two-level atom model completely breaks down and that multiple excitonic resonances act in concert to spoil the antibunching characteristics of the cavity quasimode. We connect these findings to a series of recent surprising experimental results for single quantum dot-semiconductor cavity systems, including photonic crystal systems and micropillar cavities.

We investigate the influence of multiple excitons on the photon emission properties of a quantum dot (QD)-cavity system via the master equation for the density matrix. We show that in the intermediate to strong coupling regimes, the multiple excitons lead to the suppressed QD emissions as well as the absence of anti-crossing near zero detuning, arising from the interaction between the multiple excitons and cavity. Furthermore, we analyze the role of the cavity-biexciton detuning in the photon emission properties of cavity and exciton through the second-order correlation function. The small cavity-biexciton detuning yields the significant Purcell effect and the high probability of single photon emissions. The proposed model offers the fundamental approach in developing efficient single-photon emitting devices.

The models presented simulate pumping techniques that can be used on modern semiconductor devices which are capable of coupling a quantum dot and cavity mode in order to determine a more efficient method of producing a single-photon emitter while taking into consideration typical parameters which are achievable given today's standards of coupling strength. Cavity quantum electrodynamics are incorporated in the calculations as we compare various pumping schemes for the system that either use on-resonant laser excitation or nonresonant excitation due to a wetting layer. In particular, we look to study how antibunching effects change for each method as the cavity finesse is increased toward the strong coupling regime. Experimentally these studies are equivalent to nonlinear pump-probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam.

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.

We theoretically investigate the photon statistics in a cavity quantum electrodynamics system of a single quantum dot coupled to a bimodal nanocavity. It is shown in a recent work [A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vu\ifmmode \check{c}\else \v{c}\fi{}kovi\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. Lett. 108, 183601 (2012)] that the system can generate strongly sub-Poissonian light when one of the cavity modes is driven coherently and resonantly. We study the two-mode coherent driving regime of the coupled system. The effect of additional cavity mode driving on statistical characteristics of photon emission is presented by evaluating the zero-delay second-order correlation function

{g}^{2}

(0). The antibunching character can be optimized by regulating the ratio between driving strengths of two cavity modes to achieve optimal combination of superbunched and coherent light. As a result

{g}^{2}

(0) can be reduced up to several orders of magnitude [

{g}^{2}

(0)$\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}

10

{}^{\ensuremath{-}7}

] with proper system parameters, compared with the one-mode driving system [

{g}^{2}

(0)

\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}$0.1].

Single quantum dots (QDs) are frequently used as single-photon sources, taking advantage of the final exciton decay in a cascade that produces energetically detuned photons. We propose and analyze a new concept of single-photon source, namely, a few-QD microcavity system driven close to, but below the lasing threshold under strong excitation. Surprisingly, even for two or three QDs inside a cavity, antibunching is observed. To quantify the results, we find that a classification of single-photon emission in terms of antibunching in the autocorrelation function

{g}^{(2)}(0)

is insufficient and more details of the photon statistics are required. Our investigations are based on a quantum-optical theory that we solve to obtain the density operator for the quantum-mechanical active medium and radiation field.