High Extraction Efficiency Source of Photon Pairs Based on a Quantum Dot Embedded in a Broadband Micropillar Cavity

The generation of photon pairs in quantum dots is in its nature deterministic. However, efficient extraction of photon pairs from the high index semiconductor material requires engineering of the photonic environment. We report on a micropillar device with 69.4(10)% efficiency that features broadband operation suitable for extraction of photon pairs. Opposing the approaches that rely solely on Purcell enhancement to realize the enhancement of the extraction efficiency, our solution exploits a suppression of the emission into the modes other than the cavity mode. Furthermore, the design of the device can be further optimized to allow for an extraction efficiency of 85%.

Figure 1

(a) The $\beta$ factor (fraction of emission via the cavity mode vs total emission) shows oscillatory behavior as a function of the micropillar diameter. The presented analysis was performed for a micropillar with cavity resonance at 910 nm and a $Q$ factor of 280 (see Supplemental Material [28]). (b) Image of a micropillar device. The pillar diameter is $2.02\mu \mathrm{m}$. The bright spot in the center arises from the quantum dot (QD) photoluminescence. (c) Schematic of the device and the excitation method. The micropillars are fabricated with a deterministic placement over the site of formation of the quantum dot; hence, the quantum dot is positioned in the center of the micropillar. The top 5 and bottom 18 pairs of $\lambda /4$-thick AlAs/GaAs distributed Bragg reflector mirrors form a cavity with low $Q$ factor. The quantum dot is excited collinearly with the axis of the micropillar. The inset represents the two-photon resonant excitation scheme [13]. A laser coherently couples the ground $|g⟩$ to the biexciton state $|xx⟩$ through two-photon resonant excitation. The excitation process is carried out via a virtual state (dashed line). The quantum dot system decays to the ground state via exciton state $|x⟩$, emitting the biexciton-exciton cascade.

Figure 2

(a) Emission spectrum of a quantum dot under two-photon resonant excitation. Both the biexciton and the exciton emission lie within the linewidth of the cavity. The biexciton emission at 908.5 nm is overlapped with the cavity resonance. The micropillar device employed is shown in Fig. 1, featuring a diameter of $2.02\mu \mathrm{m}$. The inset shows a scan of the same spectrum obtained using a single-mode fiber coupled avalanche photodiode as a function of the angle of rotation of a diffraction grating. The single-mode fiber acts as spatial filter favoring the cavity mode emission. (b) Photoluminescence of the cavity with a diameter of $2.75\mu \mathrm{m}$ achieved in above-band excitation and the emission spectrum of a quantum dot far detuned from this cavity obtained in two-photon resonant excitation. The inset shows a close-up of the quantum dot emission. The laser scattering is visible between the exciton ($x$) and biexciton ($xx$) emission lines. (c) Internal efficiency as a function of wavelength for micropillar with diameter $2.02\mu \mathrm{m}$. The confidence range is derived taking into account the simulation errors and fabrication accuracy. (d) Internal efficiency as a function of wavelength for micropillar with diameter $2.75\mu \mathrm{m}$. The shorter wavelength centered at 905 nm is a higher order mode. In (b) this mode is filtered by the optics.

Figure 3

(a) Summary of values of the lifetime measurements obtained for all the investigated devices. (b) Biexciton lifetime for an on- and off-cavity emitter. (c) Rabi oscillations measured using the biexciton emission. (d) The autocorrelation measurements of the exciton and biexciton photons yielding $g_x^{(2)}(0)=0.016(3)$ and $g_{xx}^{(2)}(0)=0.009(2)$, respectively. (e) The real and the imaginary part of the measured density matrix.

Figure 4

(a) Emission enhancement on and off resonance. The blue shaded area of the strong enhancement corresponds to the micropillar diameters where we expect the reduction of the $\beta$ factor [Fig. 1]. Such a behavior roots in the presence of the side modes that, while representing an enhancement of the emission rate, actually act to deviate the emission out of the sides of the device. The detailed description on how this graph is achieved is given in the Supplemental Material [28]. The green points pertaining to the white area involve the emission via the cavity mode only and, as such, are on-resonance values of the Purcell factor. (b) Further improvement of the internal efficiency simulated for a micropillar with a diameter $1.8\mu \mathrm{m}$. The four shown results feature design improvements including increased number of bottom distributed Bragg reflectors (DBRs) from 18 to 25, a ${\mathrm{SiO}}_2$ substrate, and a minor reduction of the cavity $Q$ factor achieved by increasing the number of top DBRs from 5 to 7.