1. Introduction

In recent years, the observation and exploitation of cavity quantum electrodynamics effects (cQED) in nano-engineered QD-microresonator systems has become a very active area of research. This is due to a large number of fundamental aspects and possible applications, such as single photon sources [1] for quantum cryptography or even the realization of all optical quantum computing [2]. In this context, the strong coupling regime, in which the spontaneous emission process becomes reversible, is of special interest for the realization of flying quantum bits. So far, this regime has been demonstrated in different optically pumped solid state micro-cavity systems, such as micropillars [3], photonic crystal (PC) cavities [4] and microdisks [5]. In most of the reported strong coupling experiments, temperature variation was used to change the QD microcavity detuning. This was done by taking advantage of the fact that the transition energy of a QD experiences a stronger temperature dependence than the cavity mode. Major drawbacks of temperature tuning are that large shifts of around 20 K are needed to tune the spectral position of a QD by approximately half a meV and that the tuning speed is limited by the thermal relaxation time of the structure. For this method, highest tuning speeds in the range of kHz to MHz are expected for PC cavities by applying local heating [6, 7]. Other methods for resonance tuning apply controlled digital etching [8] and in situ laser microprocessing [9] or exploit the refractive index change induced by thin layer or nano-dot deposition [10, 11, 12]. However, these tuning procedures are rather slow and in part also irreversible. A very attractive approach to significantly increase the tuning speed is electro-optical resonance tuning in high-Q QD-microcavity systems which has become feasible due to recent progress in the fabrication technology of microcavities [13, 14]. Electro-optical tuning enables reversible fine tuning of single QD excitons by making use of the QCSE (see e.g. [15]) in order to permit the observation of cQED effects, such as strong-coupling, on a much faster timescale. Tuning times in the GHz range could be achieved, paving the way for the development of new devices, e.g. the realization of fast electro-optical switches [16].

In this letter, we investigate the optical emission properties and the electro-optical tuning behavior of electrically contacted high-Q QD-micropillar systems. In particular, we demonstrate strong coupling of a single QD exciton which is electro-optically tuned through resonance with a photonic mode of a micropillar cavity.

2. Device fabrication and characterization

The electrically contacted high-Q micropillars were fabricated on a planar microcavity structure grown by molecular beam epitaxy (MBE) on an n-doped GaAs substrate. The undopedλ -GaAs cavity is embedded between doped highly reflective distributed Bragg reflectors (DBRs). These consist of 23 (27) pairs of alternating quarter wavelength thick layers of GaAs and AlAs in the top (bottom) DBR. A low density layer of large self assembled In _0.3Ga_0.7As QDs is embedded in the center of the cavity. Due to the low Indium content, elongated dot structures are formed leading to a high oscillator strength which facilitates the observation of the strong coupling regime [3]. The quantum nature of this type of QDs was confirmed by photon antibunching experiments yielding clear antibunching with g ⁽²⁾(0) as low as 0.11 (not shown). Figure 1(a) displays a schematic view of the whole device. The structures resemble miniaturized VCSELs with a clear top facet, free from any absorbing metal layer which facilitates efficient in- and outcoupling of light. A scanning electron microscope (SEM) image of the top ring contact whose inner diameter is matched to the micropillar’s one is shown in the inset of Fig. 1(c). Details of the actual device processing, which includes the fabrication of the micropillars by electron beam lithography, electron cyclotron etching, planarizing the sample with benzocyclobutene (BCB) and the definition of the electrical contacts are described in Ref. [13]. Figure 1(c) displays a typical I-V characteristic of the devices revealing a diode like behavior with an onset of current flow at a forward bias voltage V_bias of about 1.5V. Applying a reverse bias across the p-i-n-junction leads to an electrical field in the growth direction of the QDs. This is schematically illustrated in Fig. 1(b). The spectral emission of the QDs can thereby be electrically fine-tuned with this electrical field via the QCSE which leads to a red shift of the QD emission as the reverse bias is increased.

 

Fig. 1. (a) Sketch of the device. (b) Schematic band diagram of the structure at reverse bias. (c) Typical I-V characteristics of a 1.9 µm diameter device. Inset: SEM image of the top ring contact.

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All optical experiments are carried out in a high resolution micro photoluminescence (µPL) setup at low temperature (10 K). For electro-optical tuning experiments excitons are generated optically with a continuous wave laser operating at 890 nm, e.g. below the GaAs bandgap, in order to avoid absorption in the doped DBR. The laser beam is focused on the sample with a long working distance microscope objective with a spot size of 3µm. The same microscope objective is used to collect the µPL which is then dispersed in a 1m double monochromator and detected with a nitrogen cooled charge coupled device (CCD). In this standard operation mode, the spectral resolution of the setup is about 16µeV. To further enhance this resolution, the signal can be mapped onto a second output slit and is then magnified by a factor of approximately 4.4 and detected with a second CCD enabling a spectral resolution of 3.5µeV [18]. In Fig. 2(a) a contour plot displays µPL spectra of a micropillar (MP1) (1.9µm) for reverse bias voltages in the range from V_bias=0V to V_bias=-1.14V in steps of 30mV. The fundamental cavity mode’s twofold degeneracy is lifted such that two orthogonally polarized cavity modes are detected at 1.35330eV (C1, Q = 10,000) and 1.35317eV (C2, 11,000), respectively. The lift of the degeneracy results most probably from an asymmetry introduced by the top ring contact. This is assumed since the rather large splitting of ΔE_xy = 141µeV cannot be explained by the minutely elliptical shape typically observed for optically pumped micropillar structures without electrical contacts [18]. Besides the cavity modes, several QD emission lines are visible in the spectra. Presumably, some of those emission lines arise from charged exciton states from one dot. However, an unambiguous assignment of the charged exciton states is difficult without a detailed study, e.g. of the polarization behavior of the lines. As the reverse bias is increased, the QD emission lines shift to lower energies, as expected from the QCSE and finally the photoluminescence quenches at V_bias=-1.14V mainly due to carriers tunneling out of the QDs. Meanwhile, the energetic position of the fundamental cavity mode is not altered significantly. The energy shift of the QD exciton lines ΔE is well described by ΔE = E ₀+p_zF+β_zF ². p_z and β_z, respectively, are the permanent exciton dipole moment and the polarizabilty in the direction of the electrical field F. To obtain an estimate of the electrical field, we assume that the voltage drop occurs only over the undoped (intrinsic) cavity region and neglect a possible voltage drop along the doped DBRs. Therefore, electrical field is given by F=(V_bias-V_bi)/d where d denotes the thickness of the cavity. The build-in potential is approximated from the onset of current flow at V_bi = 1.5V. From fitting all the exciton emission lines traceable in Fig. 2(a) mean values for p_z and β_z were obtained with p_z/e=(0.7±0.2) nm and $\frac{{\beta }_z}{e}=(-53\pm 13){\frac{\mathrm{nm}}{V}}^2$. These are in agreement with values reported in Ref. [17]. Hereby, tuning ranges up to 1meV were achieved. This exemplifies that we can exploit the QCSE for resonance tuning in order to observe cQED effects which will be discussed in more detail below.

Figure 2(b) displays the µPL spectra in a narrow energy range around the fundamental cavity modes. As the reverse bias is increased, the QD emission lines X1 and X3 are tuned through resonance with the fundamental mode C1 at V_bias=-0.64V and V_bias=-0.90V, respectively, whereas the X2 line quenches at V_bias=-0.34V. When X1 is tuned through resonance of the C1 mode, the emission intensity of the QD is slightly enhanced due to the Purcell effect, whereas an entirely different resonance behavior is observed for X3: The signal broadens at resonance which indicates that the system is at the onset of strong coupling. This is further investigated by applying Lorentzian line shape fits to the cavity modes C1 and C2 as well as to the QD exciton emission lines X1, X2 and X3, respectively, in order to determine the dependence of the emission energy on the applied reverse bias (Fig. 2(c)). As the X1 line shifts to lower energies, it crosses the cavity mode C1. In contrast to this, no distinct crossing can be observed for X3. The latter case is then further investigated by taking high-resolution spectra in the mapping mode and again, the energy dispersion of C1 and X3 is analyzed by applying Lorentzian line-shape fits to the spectra which reveals a distinct anti-crossing of the energies (Fig. 2(d)), proving that the system is at the onset of strong coupling, albeit the typical dip of the vacuum Rabi-splitting in the spectrum at resonance cannot be resolved (see inset of Fig. 2(d)). The splitting of the modes at resonance obtained from Lorentzian line shape fits is ΔE_sp = 56µeV. From this value the coupling constant g=(ΔE ² _sp/4+(γC-γX)²/16)^0.5 is estimated whereby only the linewidth of the cavity γ_c needs to be taken into account since the homogeneous linewidth of the exciton γX is typically at least one magnitude smaller [3, 19]. This results in g = 43µeV and a lower estimate of the oscillator strength f = 4g2ε ₀ ε_rm ₀Ṽ/e ² = 33 is obtained [12]. ε ₀ denotes the dielectric constant, ε_r the relative dielectric constant of GaAs, m ₀ the free electron mass, Ṽ the effective mode volume and e the electron charge, respectively. The onset of strong coupling is confirmed by considering the threshold condition for strong coupling $g>\frac{{\gamma }_c}{4}=33\mu \mathrm{eV}$for the present pillar [3].

 

Fig. 2. (a) Contour plot of µPL spectra showing the fundamental mode (C1, C2) and several QD emission lines for increasing reverse bias. (b) µPL spectra in an narrow section around the fundamental cavity modes C1 and C2 showing a intensity enhancement for X1 and a broadening of the emission spectrum when resonance is is achieved for X3 and C1. (c) Energy dispersion for C1, C2 as well as for X1, X2 and X3, respectively. (d) Energy dispersion for C1 and X3 obtained from high-resolution measurements. Inset: High-resolution µPL spectra at resonance.

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We then investigated the tuning properties of a QD exciton in a different micropillar (MP2), with a diameter of 1.9µm, in which the damping due to cavity photon losses is reduced by a higher Q-factor. In Fig. 3(a) the spectra of the cavity’s fundamental modes C1 (Q=14000) and C2 (Q=10000) and a single QD exciton (X) at the high energy side are depicted for increasing reverse bias. As the reverse bias is increased, the exciton shifts towards the fundamental mode C1 and a splitting of the modes combined with a clear anti-crossing can be observed.

Figure 3(c) displays the energy dispersion of the cavity modes C1, C2 and the exciton X, which shows an avoided crossing for C1 and X. From Lorentzian fits we obtain a vacuum Rabi-splitting of about 63µeV at resonance. The resulting coupling constant g is estimated to be 40µeV which allows us to determine a lower limit of the oscillator strength of f = 29. Further indications that a system is in the strong coupling regime are manifest in an exchange of the properties of the photon and the exciton mode at resonance, i.e., linewidths and intensities which can be seen in Fig. 3(b) and (d). While tuning the photon and exciton mode into resonance, they become indistinguishable and the coupled system enters the strong coupling regime where two eigenstates of equal linewidths and intensities are formed, as experimentally most evident on resonance at V_bias=-0.52V (see Fig. 3(b) and 3(d)). The evolution of the linewidths of C1 and X for increasing reverse bias is shown in Fig. 3(d). As the exciton line X is tuned on resonance with the cavity mode C1, the linewidths become similar which is a clear indication of the normal mode mixing of the QD-micropillar system. After resonance, the linewidth of the exciton decreases, whereas the cavity’s increases to γ_c = 90µeV, slightly smaller than its initial value. The latter indicates a reduction of the detrimental absorption of the background QD as the reverse bias is increased. The reason that a pronounced dip in the resonance spectra is observed for MP2, but not for MP1, can be explained by the smaller Q-factor of MP1. Therefore the damping of the Rabi oscillations in the MP1 system is larger than for the MP2 system. This is reflected by the smaller value of $g/\frac{{\gamma }_c}{4}$of 1.3 compared to the value of 1.6 calculated for MP2.

 

Fig. 3. (a) µPL Spectra of MP2 for varying reverse bias from V_bias=-0.29V to -0.80V. A pronounced anti-crossing can be observed, owing to strong coupling. At V_bias=-0.52 V (red spectrum) the QD is tuned on resonance with the fundamental cavity mode C1. (b) Spectrum of the coupled QD-cavity-system at resonance exhibiting a vacuum Rabi-splitting of 63 µeV. The solid lines are Lorentzian fits to the coupled QD-cavity (C1)-system (green) and the second fundamental cavity mode C2 (blue). (c) Energy shift of the fundamental modes C1 and C2, as well as of X for varying reverse bias. (d) Linewidth of the fundamental mode C1 and the cavity for varying reverse bias.

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3. Conclusion

In conclusion, we have shown that precise electro-optical tuning of single QD excitons due to the QCSE is possible in electrically contacted micropillar devices and can be exploited to demonstrate strong coupling by means of electro-optical resonance tuning. These results were achieved by combining high-Q electrically contacted micropillar cavities and QDs with high oscillator strengths. In the presented case, a vacuum Rabi-splitting of 63µeV was observed in a micropillar cavity with a Q-factor of 14,000. The possibility of tuning single QD exciton lines electrically on resonance with the cavity mode has the potential of opening up a number of technical applications, such as electro-optical switches or fast electrically triggered deterministic single photon sources.