Nonlinear emission spectra of quantum dots strongly coupled to a photonic mode

A. N. Poddubny, M. M. Glazov, and N. S. Averkiev

Phys. Rev. B 82, 205330 – Published 29 November 2010

Abstract

A theory of optical emission of quantum dot arrays in quantum microcavities is developed. The regime of the strong coupling between the quantum dots and photonic mode of the cavity is considered. The quantum dots are modeled as two-level systems. In the low pumping (linear) regime the emission spectra are mainly determined by the superradiant mode where the effective dipoles of the dots oscillate in phase. In the nonlinear regime the superradiant mode is destroyed and the emission spectra are sensitive to the parity of quantum dot number. Further increase in the pumping results in the emission line narrowing being an evidence of the lasing regime.

Received 18 July 2010

DOI:https://doi.org/10.1103/PhysRevB.82.205330

Authors & Affiliations

A. N. Poddubny, M. M. Glazov, and N. S. Averkiev

Ioffe Physical-Technical Institute, RAS, 26 Polytekhnicheskaya, 194021 St.-Petersburg, Russia

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 82, Iss. 20 — 15 November 2010

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(Color online) Photoluminescence spectra for $N = 1$ quantum dot in resonance with the cavity mode for different pumping rates $W$ . Panels (a)–(d) correspond to $W / Γ_{C} = 0.01$ , 1, 2, and 30, respectively, and are calculated for $ω_{X} = ω_{C}$ , $Γ_{C} / g = 0.1$ , and $Γ_{X} / g = 0.01$ . Energies of the transitions, mainly determining the spectra, are indicated in panels (a) and (b) by vertical lines. Dotted curve in panel (d) shows the Lorentzian with half width equal to $Γ_{C} / 2$ , corresponding to empty cavity spectrum in the linear regime. Photon mode energy is used as the reference point, the spectra are normalized to their maximum values.Reuse & Permissions
Figure 2
Photoluminescence spectra for $N = 1$ quantum dot detuned from the cavity resonance for different pumping rates $W$ . Panels (a)–(d) correspond to $W / Γ_{C} = 0.02$ , 2, 10, and 30, respectively, and are calculated for detuning $ω_{X} - ω_{C} = 5 g$ . Other parameters are the same as for Fig. 1. Energies of the transitions, mainly determining the spectra, are indicated in panels (a)–(c) by vertical lines. Photon mode energy is used as the reference point, the spectra are normalized to their maximum values.Reuse & Permissions
Figure 3
(Color online) Average numbers of (a) excitons and (b) photons as functions of the pumping rate, calculated for the values of detuning $(ω_{X} - ω_{C}) / g = 0, 2, 4, 5, 7$ , indicated at each curve. Other parameters are the same as for Fig. 1. The inset schematically illustrates the three lowest manifolds of Jaynes-Cummings ladder. Vertical arrows indicate radiative and nonradiative transitions between the excitonlike (X) states, governing the kinetics of the system.Reuse & Permissions
Figure 4
Photoluminescence spectra for $N = 3$ (panels a, c, e) and $N = 4$ (panels b, d, f) quantum dots for different pumping rates $W$ . Panels (a) and (b), (c) and (d), and (e) and (f) were calculated for $N W / Γ_{C} = 0.2$ , 4, and 30, respectively. Other parameters are the same as for Fig. 1. Energies of the transitions corresponding to the super-radiant mode are indicated at panels (a) and (b) by vertical lines. Photon mode energy is used as the reference point, the spectra are normalized to their maximum values.Reuse & Permissions
Figure 5
(Color online) Scheme of the radiative transitions for (a) odd and (b) even numbers of quantum dots $N$ .Reuse & Permissions
Figure 6
(Color online) Photoluminescence spectra calculated taking into account inhomogeneous broadening. Thick (solid) and thin (red) curves correspond to $N = 3$ and $N = 4$ dots, respectively. Solid and dashed curves were calculated for different particular realizations of random spread of excitonic energies. The value of pumping rate was $N W = 4 Γ_{C}$ . Arithmetic mean values of the detuning are $⟨ | ω_{X, i} - ω_{C} | ⟩ / g \approx 0.4$ , 0.5, 0.6, and 1 for thick solid, thick dashed, thin solid, and thin dotted curves, respectively. Other parameters are the same as for Fig. 1. Photon mode energy is used as the reference point, the spectra are normalized to their maximum values.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics