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arXiv:0808.3280 · Physical Review B

Photon antibunching and nonlinear effects for a quantum dot coupled to a semiconductor cavity

Frank Bello, David M. Whittaker

Published Sep 28, 2010• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.82.115328

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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 observe antibunching in the photons emitted from a strongly coupled single quantum dot and pillar microcavity in resonance. When the quantum dot was spectrally detuned from the cavity mode, the cavity emission remained antibunched, and also anticorrelated from the quantum dot emission. Resonant pumping of the selected quantum dot via an excited state enabled these observations by eliminating the background emitters that are usually coupled to the cavity. This device demonstrates an on-demand single-photon source operating in the strong coupling regime, with a Purcell factor of 61+/-7 and quantum efficiency of 97%.
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.
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.
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 g2{g}^{2}g2(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 g2{g}^{2}g2(0) can be reduced up to several orders of magnitude [g2{g}^{2}g2(0)$\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}101010{}^{\ensuremath{-}7}]withpropersystemparameters,comparedwiththeone−modedrivingsystem[] with proper system parameters, compared with the one-mode driving system []withpropersystemparameters,comparedwiththeone−modedrivingsystem[{g}^{2}(0)(0)(0)\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}$0.1].
Chip-based cavity quantum electrodynamics (QED) devices consisting of a self-assembled InAs quantum dot (QD) coupled to a high quality factor GaAs microdisk cavity are coherently probed through their optical channel using a fiber taper waveguide. We highlight one particularly important aspect of this all-fiber measurement setup, which is the accuracy to which the optical coupling level and optical losses are known relative to typical free-space excitation techniques. This allows for precise knowledge of the intracavity photon number and measurement of absolute transmitted and reflected signals. Resonant optical spectroscopy of the system under both weak and strong driving conditions are presented, which when compared with a quantum master equation model of the system allows for determination of the coherent coupling rate between QD exciton and optical cavity mode, the different levels of elastic and inelastic dephasing of the exciton state, and the position and orientation of the QD within the cavity. Pump-probe measurements are also performed in which a far off-resonant red-detuned control laser beam is introduced into the cavity. Rather than producing a measurable ac Stark shift in the exciton line of the QD, we find that this control beam induces a saturation of the resonant system response. The broad photoluminescence spectrum resulting from the presence of the control beam in the cavity points to sub-band-gap absorption in the semiconductor, and the resulting free-carrier generation, as the likely source of system saturation.
A theoretical description for a single quantum-dot emitter in a microcavity is developed.We analyze for increasing steady-state pump rate the transition from the strong-coupling regime with photon antibunching to the weak-coupling regime with coherent emission. It is demonstrated how Coulomb interaction of excited carriers and excitation-induced dephasing can strongly modify the emission properties. Our theoretical investigations are based on a direct solution of the Liouville-von Neumann equation for the coupled carrier-photon system. We include multiple carrier excitations in the quantum dot, their Coulomb interaction, as well as excitation-induced dephasing and screening. Similarities and differences to atomic systems are discussed and results in the regime of recent experiments are interpreted.