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Cavity-QED assisted attraction between a cavity mode and an exciton mode in a planar photonic-crystal cavity T. Tawara, H. Kamada, T. Tanabe, and T. Sogawa NTT Basic Research Labs, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan H. Okamoto Graduate School of Science and Technology, Hirosaki University, 3 Bunkyou-cho, Hirosaki, Aomori, 036-8561, Japan P. Yao, P. K. Pathak, and S. Hughes Department of Physics, Queen’s University, Kingston, ON K7L 3N6, Canada tawara@nttbrl.jp Abstract: The photoluminescence spectra from a quantum-dot exciton weakly-coupled to a planar photonic-crystal cavity is experimentally investigated by temperature tuning. Significant resonance shifts of the cavity mode are observed as the cavity mode spectrally approaches that of the exciton mode, showing the appearance of cavity-to-exciton attraction or mode pulling. Cavity-mode spectral shifts are also found theoretically using a master equation model that includes incoherent pump processes for the coupled exciton and cavity, pure dephasing, and allows for photon emission via radiation modes and the leaky cavity mode. Both experiments and theory show clear cavity mode spectral shifts in the photoluminescence spectra, when certain coupling parameters are met. However, discrepancies between the experimental data and theory, including more pronounced spectral shifts in the measurements, indicate that other unknown mode-pulling effects may also be occurring. © 2010 Optical Society of America OCIS codes: (270.5580) Quantum electrodynamics; (350.4238) Nanophotonics and photonic crystals. References and links 1. J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of single photons from one atom trapped in a cavity,” Science 303, 1992 (2004), 2. A. Boca, A. D. Boozer, J. R. Buck, and H. J. 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Introduction The study of light-matter interactions between an electronic two-level system and a quantized optical field gives rise to interesting regimes of light-matter interaction and has applications in quantum information science. The regime of cavity-quantum electrodynamics (cQED) has been intensively studied in atomic physics for several decades, and has found use for the creation of single photon sources [1], one atom lasers [2], and for demonstrating the violation of Bell’s inequalities [3]. Motivated in part by the prospect of developing compact sources for quan- tum cryptography, the regime of solid-state cQED has also recently been carried out in various semiconductor systems, whereby a quantum-dot (QD) exciton serves as a single photon emit- ter within a suitably designed cavity, e.g. a micropillar [4–6], a microdisk [7, 8], or a planar photonic crystal cavity [9, 10]. The prominent feature of most of these cQED systems is the coupling of a single photon emitter (atom or QD) to a suitably large Q/Vm-ratio cavity, where Q is the cavity quality factor and Vm is the effective mode volume. In the weak-to-intermediate coupling regime, the photon emission rate is enhanced through the Purcell effect [11], and the strong coupling regime [12], vacuum Rabi splitting can be observed in the photoluminescence (PL) spectrum. In the past few years, there have been several experimental reports on the off-resonant cou- pling between a single exciton and a cavity mode in semiconductor cavities. Hennessy et al. [10] reported on the off-resonant excitation of the cavity mode from an excited exciton using a pho- tonic crystal - single QD system, and Kaniber et al. [13] also observe similar cavity coupling mechanisms, as do Press et al. [14] for micropost cavities. These works have posed the ques- tion of whether the usual simple atomlike models of the QD fail. However, modified theoretical models that account for the leaky nature of the cavity show that such couplings are expected for a planar PC cavity medium. Hughes and Yao [15] introduced a quantization procedure for any arbitrary inhomogeneous dielectric that was utilized to derive simple analytical spectral formu- las in terms of the cavity mode emission and the radiation (exciton) mode emission; when used to calculate the QD emission from a typical PC cavity, the leaky cavity quasi-mode emission was found to completely dominate the detected spectra, whereby it contains both the dressed exciton resonance and the dressed cavity resonance. Leaky cavity mode spectra have also been reported by Cui and Raymer [16], Auffeves et. al. [17], Yamaguchi et. al. [18], and Naesby et. al. [19], for simple cavities, where the cavity emission can be geometrically separated from the radiation emission. In the case of a planar PC medium, no geometrical separation of radia- tive decay and cavity decay is possible, and, in general, both exciton (via radiation modes) and cavity mode decay processes contribute to out-of-plane photon detection. Further experimental reports by Suffczynski et al. [20] support the model that fast exciton dephasing is responsi- ble for the cavity mode feeding. Tawara et al. [21] also suggest that the bright cavity mode emissions with nonzero detuning may be influenced by radiative recombinations of deep-level defects in the barrier layers. Very recently, Winger et al. [22] propose that the QD confinement ensures the presence of a quasicontinuum of excitonic transitions, part of which overlaps with the cavity resonance; however, for our samples and excitation powers below, we see absolutely no evidence of a quasicontinuum and we still obtain a very clear cavity mode resonance over a wide range of spectral detunings. Thus, this subject matter is still under debate, and we have found that from a modeling perspective, a simple intuitive master equation approach is conve- nient to obtain significant off-resonant coupling over a wide spectral range for various QD - cavity systems. In this work, we experimentally study the detuning dependence between a weakly-coupled exciton and a leaky cavity mode, and observe an unusual cQED spectral signature in the PL spectra: cQED-assisted attraction between a cavity mode and an exciton mode. This observa- tion is persistent, and is observed in several different samples, and for several different exciton- #117676 - $15.00 USD Received 25 Sep 2009; revised 3 Dec 2009; accepted 22 Jan 2010; published 26 Jan 2010 (C) 2010 OSA 1 February 2010 / Vol. 18, No. 3 / OPTICS EXPRESS 2721 cavity couplings. To help explain this novel observation, we adopt a recent master equation model that includes fermion statistics and pure dephasing processes for the target exciton, as well as an incoherent pump terms for the target exciton and cavity mode [23]. This model is similar to previous master equation works applied to semiconductor cavities [24, 25], but also accounts for stimulated emission processes of the incoherent cavity pump [23, 26] and emis- sion via radiation modes as well as the leaky cavity mode. Reasonable qualitative agreement between the experimental data and the theory is obtained, though further discrepancies suggest that other unknown effects may be occurring which lead to more pronounced mode pulling. Our results should help stimulate further theoretical developments, and systematic experimen- tal measurements, in this rapidly growing field. 2. Experiment A line-defect cavity with a local width modulation in a 2D planar photonic crystal [27] con- sists of a triangular lattice of air holes in a 200 nm-thick GaAs membrane containing a single InAs/InGaAs dot-in-well layer. The structural parameters of the photonic crystal include a lat- tice constant (a) of 315 nm and an air hole radius (r) of 81 nm. The air holes of the width modulation area in the line defect, which act as a cavity, were shifted by 6, 4 and 2 nm, respec- tively, outwards from their original positions. The cavity mode energy is around 1050 meV, and the mode volume of this cavity is about 2.0(λ/n)3 = 0.09 µm3. The samples were mounted in T e m p e ra tu re ( K ) Energy (meV) T e m p e ra tu re ( K ) Energy (meV) (b) (c) C C X X InGaAs linear array Laser Sample in cryostat 0.5 m spectrometer Objective NA: 0.42 (a) ������� Fig. 1. (a) Schematic of the PL measurement setup and image of the fabricated cavity by scanning electron microscope (SEM). The area enclosed by the dotted line indicates the cavity region with width modulation. (b) PL spectra with temperature scanning and (c) peak plot for exciton ‘X’ and cavity ‘C’. The dotted lines in (c) are guides to the eye. #117676 - $15.00 USD Received 25 Sep 2009; revised 3 Dec 2009; accepted 22 Jan 2010; published 26 Jan 2010 (C) 2010 OSA 1 February 2010 / Vol. 18, No. 3 / OPTICS EXPRESS 2722 T e m p e ra tu re ( K ) (meV) T e m p e ra tu re ( K ) Energy (meV) T e m p e ra tu re ( K ) (meV) T e m p e ra tu re ( K ) Energy (meV) ��� ��� � � � � � � � � � �� �� � �� �� Fig. 2. Temperature dependent PL spectra and spectral peak plot of X and C for two different cavities with ωx > ωc at 4 K. (a) Spectrum evolution, and (b) peak energies of sample one, and (c) and (d) show another set for a different sample. The crossover energy of the exciton and cavity, ω0, is 1043 meV for (a) and (b), and is 1053 meV for (c) and (d). a continuous flow liquid-helium cryostat. Photoluminescence spectra were obtained by using an excitation source that consist of a YAG (1064 nm = 1.17 eV) continuous-wave laser. The excitation laser was focused to a spot with a ∼ 1 µm diameter through an objective lens with a numerical aperture of 0.42. We use the excitation power of 30 µW, which is weak enough to excite no charging states of an exciton. We note that the contribution of the deep level emission from GaAs Barrier and InGaAs QW can likely be neglected under this excitation condition [21]. Figures 1(b) and (c) show the PL emission from the QD exciton and cavity mode detuned by temperature scanning (4-50 K) with no energy crossing (ωx < ωc). While the cavity-mode con- tinuously redshifts at a rate of about 9µeV/K according to temperature dependence of refractive index of GaAs slab, the exciton energy changes much faster because of the bandgap shift. In Fig. 2, we display two examples of a temperature-scanning PL, showing temperature- evolutions of the cavity-exciton spectra and peak energies for two different samples, as panels (a) and (b), and (c) and (d). The photon energies are represented as detuning relative to the cavity-exciton crossover ω0. In these cavities a relation of ωx > ωc applies at 4 K. As the tem- perature raises, these two peaks continuously redshift thereby the relative energy separations decrease. These cavities show no anti-crossing behavior of the vacuum field Rabi splitting near ωx = ωc, inferring that they are only weakly coupled, primarily because the QDs are not po- sitioned at the anti-node positions of cavity fields. However, surprisingly, as the two peaks approach one another near the crossover, the cavity modes clearly blueshift toward the exci- ton resonances, which is opposite to the trend expected from Fig. 1(c), becoming attracted by the exciton resonances for small cavity-exciton detunings. This attraction can be easily distin- guished from the normal energy shift by a sudden blueshift and overall temperature scanning #117676 - $15.00 USD Received 25 Sep 2009; revised 3 Dec 2009; accepted 22 Jan 2010; published 26 Jan 2010 (C) 2010 OSA 1 February 2010 / Vol. 18, No. 3 / OPTICS EXPRESS 2723 trends as shown in Figs. 1(b-c). We have observed similar attraction features in several other samples. A check was undertook to exclude a probable unwanted gas deposition to the cav- ity, that may substantially shift the cavity resonance [28]. We raised the temperature up to room temperature once to evaporate the adsorbed gas species, recooled the sample to 4 K, and performed a similar experiment. It was found that every time we carried out a similar measure- ment, exactly the same results were obtained. Thus, the apparent attraction of the cavity-mode energy is not an experimental artifact, but is a universally observed phenomenon when specific exciton-cavity coupling and pump conditions meet. Below we will introduce a master equation theory that uses the exciton and cavity decay rates, so here we briefly summarize the experimentally determined spectral widths: cavity linewidth Γc = 0.10 meV (Q = 10 000), total exciton linewidth (including radiative and non-radiative contributions), Γ totx = 0.07 meV (0.14 meV) at 4 K (35 K) [ω0 = 1043 meV] as obtained from Fig. 2(a) and (b), and Γc=0.18 meV (Q = 5800), Γ totx1 = 0.14 meV (0.16 meV) at 4 K (23 K), and Γ totx2 = 0.13 meV (0.17 meV) at 4 K (43 K) (ω0 = 1053 meV) as from Figs. 2(c) and (d), all of which are represented as the full width at half maximum (FWHM). The total radiation lifetime of single QD excitons was determined in the sample (with a substrate and before cavity fabrication) by time-domain measurements to be 1.3 ns, which corresponds to a width of 3 µeV in FWHM. The exciton-cavity coupling constant g is smaller than that expected to satisfy the strong-coupling condition, approximately when g2 > (Γc−Γx)2/4; however, as mentioned earlier, because the both QDs are not placed at anti-node positions of cavity fields, they are only in t