Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system

S. Hughes, P. Yao, F. Milde, A. Knorr, D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams

Phys. Rev. B 83, 165313 – Published 21 April 2011

Abstract

We present a quantum optics approach to describe the influence of electron-acoustic phonon coupling on the emission spectra of a strongly coupled quantum-dot cavity system. Using a canonical Hamiltonian for light quantization and a photon Green function formalism, phonons are included to all orders through the quantum-dot polarizability function obtained within the independent boson model. We derive simple user-friendly analytical expressions for the linear quantum light spectrum, including the influence from both exciton- and cavity-emission decay channels. In the regime of semiconductor cavity QED, we study cavity emission for various exciton-cavity detunings and demonstrate rich spectral asymmetries as well as cavity-mode suppression and enhancement effects. Our technique is nonperturbative and non-Markovian, and can be applied to study photon emission from a wide range of semiconductor quantum-dot structures, including waveguides and coupled cavity arrays. We compare our theory directly to recent and apparently puzzling experimental data for a single site-controlled quantum dot in a photonic crystal cavity and show good agreement as a function of cavity-dot detuning and as a function of temperature.

Received 6 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.165313

Authors & Affiliations

S. Hughes^* and P. Yao

Department of Physics, Queen’s University, Kingston, Ontario, Canada K7L 3N6

F. Milde and A. Knorr

Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Technische Universität Berlin, Hardenbergstraße 36, PN 7-1, DE-10623 Berlin, Germany

D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, R. Cheriton, and R. L. Williams

Institute for Microstructural Sciences, National Research Council, Ottawa, Canada K1A 0R6

^*shughes@physics.queensu.ca

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Vol. 83, Iss. 16 — 15 April 2011

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Images

Figure 1
Phonon self-energies for InAs QDs for two different temperatures ( $T = 4$ and 40 K), where the red (solid) curves represent the imaginary contribution and the blue (dashed) curves represent the real contribution. The broadening parameters are $Γ_{rad} = 2 μ$ eV and $Γ_{x}^{'} = 75 μ$ eV. As discussed in the text, $ω_{x}$ is considered to already include a polaron shift.Reuse & Permissions
Figure 2
(a) Cavity-emitted spectra for various QD cavity detunings, obtained for a temperature of $T = 4$ K. The red (dark) and grey (light) curves display the Green function solution with and without LA phonon interactions. The corresponding imaginary part of the polarizability with [red (dark) curve] and without [grey (light) curve] phonon coupling is shown in (b). The lower-frequency phonon bath is suppressed in part due to the low temperatures and in part due to the relatively large ZPL. The polaron shift $Δ ~ 30 μ$ eV is not included as this just adds in a fixed resonance shift for all detunings and temperatures. The parameters are $Γ_{rad} = 2 μ$ eV, $ω_{x} = 830$ meV, $Γ_{x}^{'} = 75 μ$ eV, $Γ_{c} = 100 μ$ eV, and $g = 0.13$ meV (see Ref. 55).Reuse & Permissions
Figure 3
As in Fig. 2, but with $T = 40$ K and $Γ^{'} = 150 μ$ eV.Reuse & Permissions
Figure 4
A single InAs quantum dot nucleated at the apex of a InP pyramid. The pyramid is grown using selective-area epitaxy on a electron-beam patterned SiO $_{2}$ -coated InP substrate. The scale bar is 210 nm.Reuse & Permissions
Figure 5
(a) Recently published experimental data [Dalacu et al. (Ref. 34)], taken at $T = 4$ K, normalized to show the effect of detuning on the exciton and cavity mode. (b) Theoretical simulations with [red (dark)] and without [grey (light)] phonon interactions. The parameters are similar to those used in Fig. 1, except that $Γ^{'} = 150 μ$ eV and we have convolved with a Lorentzian function with FWHM $Γ_{spec} = 250 μ$ eV to account for the spectral resolution in the experiment (Ref. 34). The detunings are not exactly fit to experiment, but rather are chosen to cover a similar range to the experiments with equal frequency spacing. Both sets of calculations are normalized to their peak value for clarity. We also include the radiation-mode emission, with $F_{c} = 2 F_{r}$ .Reuse & Permissions
Figure 6
(a) Measured spectra at various temperatures, taken at $T = 10$ , 20, and 40 K. (b) Theoretical simulations with [red (solid) curve] and without [grey (light) curve] phonon interactions. The parameters are similar to those used in Fig. 5, except that $Γ^{'} = 225$ –300 $μ$ eV (increasing linearly with temperature) and we have convolved with a Lorentzian function with FWHM $Γ_{spec} = 400 μ$ eV (Ref. 62).Reuse & Permissions

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