1. Introduction

Single photons are important resources for distributed quantum computing, quantum communication, and quantum sensing [1–3]. The advances of photonic quantum information processing have raised stringent requirements for single photon sources. Conventional sources based on nonlinear processes of optical crystals are inherently probabilistic and difficult to scale up [4]. In the past decades, single photon sources of semiconductor quantum dots have been developed as a comparable or even superior candidate, showing enormous application prospects.

However, as a solid-state system, quantum dots (QDs) are not isolated from their environment and thus suffer from various dephasing processes, resulting in degradation of photon indistinguishability [5]. Moreover, the relatively high refractive index of the semiconductor significantly limits the photon flux that can be collected by an optical lens in free space [6–9].

One way to circumvent these problems is to embed single QDs in photonic microcavities. Such a microcavity can redirect the photon flux, thereby improving the photon extraction efficiency. In addition, a well-designed microcavity enhances the strength of light-QDs interaction via the Purcell effect. This shortens the radiative lifetime of QD and thereby reduces the dephasing during the radiative decay. Narrowband cavities are mostly exploited for the application of single photon sources. The micro-pillar system and the open cavity system have both shown near transform-limited emission [10–15]. However, in such systems, the QD-cavity coupling is crucial and often external tuning techniques are indispensable, which makes the fabrication process more complicated [16–20].

In recent years, embedding single QDs into broadband photonic microcavities has shown a lot of progress in pursuing ideal single-photon sources featuring simultaneous high-degree of the source brightness, single-photon purity and photon indistinguishability [21–24]. In particular, the bullseye cavities, or hybrid circular Bragg grating (CBG) structures led to the realization of a highly-entangled photon source with high-brightness and photon indistinguishability. Thanks to the broadband, the chance to find coupled dots dramatically increases. It is also worth noting that the dot emission could shift a bit after cycles of cooling and warm up. The broadband cavities alleviate small spectra mismatch and facilitate the plug and play single photon sources.

Here we exploit QDs embedded in bullseye cavities as single photon emitters. The bullseye cavities are made by CBGs which are shallowed etched and subsequently transferred to a dielectric mirror with the assistance of a polymer spacer. The mirror acts as a back reflector. At an optimal spacer thickness, the theoretical collection efficiency of single photons is boosted up to 90%. Experimentally, a collection efficiency of 30% is measured with a multi-photon probability as low as 0.05 ${\pm} $ 0.005 and a moderate Purcell factor of 3.1 is observed. Taking advance of the dielectric mirror, we also propose a feasible way to integrate the semiconductor pumping laser as well as its fiber coupling. This would open doors for the true plug and play single photon sources.

2. Design and experiment

2.1 CBGs structure and simulation

Coupling QDs with microcavity redirects the photon flux and therefore enhances the light extraction efficiency [25]. CBGs emerged recently as an attractive concept for embedding QDs and showed a unique combination of high collection efficiency, radiative time shortening and enhanced photon indistinguishability. These were demonstrated using a new fabrication process for the integration of a backside gold mirror [15,22,23,26] and high collection efficiencies are achieved. However, a gold mirror, opaque for a large band of light, excludes the possibility of laser pumping from the back. Compared with metal mirrors, dielectric mirrors have less optical absorption and their reflection/transmission spectra can be engineered. We here instead use a dielectric mirror which permits the transmission of laser photons while reflects QD photons. The device is sketched in Fig. 1(a). The CBGs consist of a gallium arsenide (GaAs) micro-disk surrounded by a serial of shallowly etched trenches and form a second-order Bragg gratings. Photons emitted from the QDs are mostly confined in micro-disk. Due to anisotropic etching, parts of the emitted photons from the QDs are scattered upwards for collection. Still, there is substantial number of photons emitting downwards. This part of photons are effectively guided upwards with a backside dielectric mirror. The spacer between the mirror and the CBGs is carefully chosen to make the reflected downward and forward emitted photons interference constructively.

 

Fig. 1. The design concept of the bullseye cavities with backside dielectric mirrors. (a) The sketch of the device. The bullseye cavities sit on top of a DBR reflector consisting of alternative SiO2/TiO2 layers. (b) The DBR reflectance spectra where reflection band edge lies between the laser line and QDs emission peak. (c) The calculated Purcell factor and collection efficiency with a 200 nm spacer. Inset is the far-field pattern of QD emission. (d) The collection efficiency as a function of spacer thickness.

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To find out the optimal spacer thickness, we carry out a finite-difference time-domain simulation. The membrane thickness is 140 nm, with an etching depth of 100 nm. The radius of the center disk ${R_c}$ is 520 nm, and the period the of CBGs is 360 nm with a trench width of 110 nm. The structure is sketched in Fig. 1(a). The desired reflection spectra of the bottom distributed Bragg reflector (DBR) is plotted in Fig. 1(b). The band edge resides between the QDs emission peak and the laser emission line. The dielectric mirror reflects QDs photons while permitting the transmission of lasers. In such a configuration, a semiconductor laser could excite the QDs from the bottom. More detailed discussions can be found at the last part of the paper. We define the collection efficiency as the ratio of photons that can be collected by a NA = 0.7 objective.

The efficiency exhibits a varying dependence on spacer thickness at a fixed wavelength. In order to maximize efficiency, the downwardly emitted photon and the forwardly reflected photon should interfere destructively, producing a negligibly low field intensity below GaAs membranes. And the majority of the photons inside CBGs efficiently radiate upward. At an optimal spacer thickness of 200 nm, the Purcell factor and collection efficiency reach up to 5 and 90%, as is shown in Fig. 1(c) (with a DBR made up of 8 pairs of 160 nm SiO2/110 nm TiO2 in the simulation in order to maintain consistency with the experiment). The highly-directional single-photon emissions can be clearly identified from far-field profile (Inset), exhibiting a divergent angle within 10 degrees. The Gaussian intensity distribution is also beneficial for fiber coupling. The collection efficiency at various spacer thickness is calculated in Fig. 1(d). The structure with a 200 nm spacer remains a high collection efficiency above 70% over a large band above 50 nm.

Here, the Purcell factor is a compromise made to achieve great collection efficiency. We may readily change the structure to achieve this in situations where a high Purcell factor is preferred. We could modify the spacer thickness, for instance. With a 400 nm spacer, a Purcell factor of 35 can be achieved, although the efficiency falls to about 20%.

2.2 Device fabrication

The quantum dots are fabricated by molecular beam epitaxy. A buffer layer of 200 nm thickness is firstly grown on the GaAs substrate, followed by a 100 nm Al0.7Ga0.3As as the sacrificial layer. The optical active layer is low-density indium arsenide (InAs) QDs sandwiched between a thin (150 nm) GaAs. The density (∼10⁸cm⁻²) of self-assembled InAs quantum dots varies continuously along the wafer by stopping the rotation of the substrate during InAs deposition. The QDs are buried in the GaAs matrix, and their positions are randomly distributed. Deterministic fabrication i.e. making photonic structures around pre-selected QDs, is highly favored. In order to obtain the position of quantum dots, there are several common schemes, such as using scanning microscope localization method [27,28], and in-situ processing method [20,29]. Although the above schemes can realize the positioning of quantum dots, their efficiency is limited. Therefore, we adopt a wide-field photoluminescence imaging method to locate single quantum dots and realize deterministic coupling between the quantum emitters and the photonic nanostructures [30]. By illuminating the wafer with a halogen lamp over the whole microscope field of view, a single optical image is obtained. The image contains both bright PL spots from the QDs and reflected light from the alignment marks. The image is then used for extracting the QDs’ relative positions. The central positions of the bright spots (i.e., the QDs) were then determined by image analysis with sub-pixel size resolution [31]. The CBGs are fabricated with an E-beam lithography process, followed by inductively coupled plasma etching. After that, the sample is undercut with hydrogen fluoride solvent and transferred on a dielectric mirror by transfer print method. The fabrication flow is illustrated in Fig. 2(a). The microscope pictures of the CBGs prior to, during and after the transfer are shown in Fig. 2(b). The undercut is clearly visible. The yield or success rate of the transfer print method is very high. An array of CBGs ($4 \times 6$) are picked up by a micro-sized Polydimethylsiloxane (PDMS) stamp and placed on the target dielectric mirror.

 

Fig. 2. The fabrication-flow of the CBGs on DBRs device. (a) Quantum dots containing CBGs are transfer-print on the DBR reflector. (b) The microscope images of CBGs prior to (up panel), during (middle panel) and after (lower panel) the transfer process.

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2.3 Optical characterization

The sample is loaded in a closed circle cryostat with a base temperature of 5 Kevin for optical measurement. The QDs photon-luminescence features a narrow bright line, as is shown in Fig. 3(a). By shining a broadband white laser on the CBGs and recording the reflection spectra, a mode with a bandwidth (full-width half maximum) of 12 nm, corresponding to a quality factor of 75, is clearly observed (shaded area in Inset). To verify Purcell enhancement, we performed time-resolved fluorescence measurements. The lifetime of exciton in cavity-coupled QDs and plain QDs is measured. The decay curves are plotted in Fig. 3(b). For plain QDs, a time constant of 1.18 ns has been recorded, while for a cavity-coupled QD, the lifetime is substantially shortened. In such a case, we use phonon-assist excitation to exclude the relaxation processes. The decay curve is marked in red. As comparison lifetime is shortened to 0.38 ns, which suggests a Purcell factor of 3.1 is obtained for cavity-coupled QDs.

 

Fig. 3. The optical characterization of quantum dots embedded in CBGs. (a) Micro-PL of a quantum dot. Inset is the reflection spectra of a white light laser shining on a CBG. Shaded area is the cavity mode. (b) Lifetime of the QDs embedded in Bulk and in CBGs. (c) The autocorrelation measurement of a coupled quantum dot. Vanishing peak in the zero-time delay indicates a ${g^2}(0 )$ around 0.05. (d) Power mapping of a quantum dot.

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To characterize the single photon nature of the emission. We then perform the auto-correlation of the photons by sending them to a beam splitter. Both outputs of the beam splitter are tailed with a single photon detector, respectively. The time correlation of both detectors is plotted in Fig. 3(c). The strong antibunching at zero delay indicates the almost vanishing multiphoton probability. By fitting these data, a ${g^2}(0 )$ of 0.05 ${\pm} $ 0.005 is obtained. The non-zero value of ${g^2}(0 )$ originates from non-perfect rejection of laser during phonon-assisted excitation. The cavity-coupling is also beneficial to the collection efficiency. A femtosecond (fs) pulsed laser with a repetition rate of 79.6 MHz is used to characterize the extraction efficiency of the sample. The power-dependent photoluminescence intensity is plotted in Fig. 3(d). By measuring the count rate in the single-photon detector and carefully calibrating the system detection efficiency, an extraction efficiency of 30% was obtained for the hybrid integrated SPSs. The detailed method is discussed in Ref. [32]. The discrepancy between the simulation value and experimental data possibly originates the positioning error for this batch of samples. The fiber coupling efficiency is another element that influences the collection efficiency. The far-field is not Gaussian when the QDs are out of the center. This would have a negative impact on overall efficiency.

2.4 Discussion

So far, QDs are among the best single photon sources. In this part, we discuss their application in the plug-and-play sources [33,34]. Based on the device developed in the paper, we propose a ‘zero-change’ method for fiber coupling as well as semiconductor laser integration. The sketch of the proposed device is illustrated in Fig. 4(a). Compared with previous works [15,22,23], a dielectric mirror instead of a metal mirror is used in the device design. The dielectric mirror composed by alternative layers of SiO2/TiO2 is deposited on a glass substrate. A single mode fiber hanging above the CBG is flexibly tethered with a copper house. We use a backside illumination for the alignment of the CBG center and fiber core since both of them can be viewed through the dielectric mirror [35,36]. An accuracy better than 1 micro-meter should be achieved, which is sufficient considering the 5 micro-meter sized fiber core.

 

Fig. 4. The plug-and-play single photon sources based on quantum dots embedded in CBGs and the far-field profile. The CBGs reside on a DBR reflector and the VCSEL are integrated at the bottom for excitation. A fiber placed at the top collects most of the single photons (a). The proposed device features a convergent emission which resembles a Gaussian profile. The full width at half maximum is 6.3 degrees, suggesting a high fiber coupling efficiency (b).

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The emission from a QD must have a Gaussian and convergent far field in order to have a high fiber coupling efficiency. We plot the exhibited device's far-field pattern and perform the 3D Gaussian curve fitting in Fig. 4(b). A Gaussian curve closely mimics the far-field. The data is then projected on a second screen using a slice taken at the y = 0 plane. The full width at half maximum is only 6.3 degrees. The acceptance angle is roughly 13 degrees when a commercial fiber with NA = 0.12 is used. This indicates that the fiber can capture all of the light emitted by the demonstration device (10-degree beam divergence).

Pumping lasers, e.g. vertical-cavity surface-emitting laser (VCSEL), are placed at the bottom of the glass. VCSEL are mature compact lasers. For the specific case here, an 850 nm VCSEL is used to excite the QDs with an emission peak at 920 nm. The reflection band of the mirror can be easily adjusted by the layer thickness. By setting the reflection band edge between 850 nm and 920 nm, the QD photons are reflected, with the laser photon being transmitted. The other end of the fiber is coated with DBRs to filter out the laser and thus opens doors to the on-demand generation of single photons.

The goal of the current study is to present a turnkey high-flux single photon source that is simple to link to fiber and has potential applications in quantum communications, which do not require indistinguishable photons. Despite this, single photon sources that can produce indistinguishable photons are essential in two-photon interference studies, even if doing so would make the entire system more vulnerable and complicated. It is necessary to create new designs to implement the polarization-extinction resonant excitation. Making an ellipse-shaped VCSEL to produce polarized laser and tethered CBGs that allow for the electric contact is one potential solution.

3. Conclusion

To conclude, we have demonstrated bright SPSs based on QDs embedded in CBGs. The CBGs are shallowly etched and subsequently transferred to a dielectric mirror by transfer-printing method with a near unity success rate. This greatly simplifies the fabrication process for the mirror integration compared with previous works. Mediated by deterministic fabrication, a Purcell factor of 3.1 and an extraction efficiency of 30% are achieved due to the cavity coupling. A low ${g^2}$(0) of 0.05 ${\pm} $ 0.005 is demonstrated. We also discuss the ‘zero-change’ integration pumping laser as well as the fiber coupling. Note that there are commercially available [37], the device can be packed into such small cryostats to act as a true plug-and-play single photon source.