Hybrid integration of hBN quantum sources in SiN photonic circuits

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Hybrid integration of hBN quantum sources in SiN photonic circuits

Quantum Nano Photonics, School of Engineering Sciences, KTH From 10/08/2019 to 11/03/2020

Anas Skalli

Supervisors: Ali Elshaari Stephan Steinhauer Examiners: Val Zwiller Quentin Rafhay

Phelma, Ecole nationale supérieure KTH Royal Institute of Technology de physique, électronique, matériaux

Kungliga Tekniska Högskolan Bat. Grenoble INP - Minatec SE-100 44, Stockholm, Sweden 3 Parvis Louis Neel - CS 50257 Phone: +46 8 790 60 00Fax: +46 8 790 65 00 F-38016 Grenoble Cedex 01, FRANCE

Tél +33 (0)4 56 52 91 00Fax +33 (0)4 56 52 91 03

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Acknowledgments

I want to thank Dr. Ali Elshaari, who has been very supportive and kind throughout the project, and has helped me understand many aspects of photonics and experimental physics in general. The skills I leaned during this project will be extremely valuable in the future. Thank you Ali for answering my (many) questions and creating a fun working environment. Without you, this project would not have been possible.

Next I would like to thank Dr. Stephan Steinhauer, for his help throughout the project and especially in the cleanroom from sample growth to fabrication. Thank you for your invaluable guidance and contributions to this project. And of course, thank you for letting me use your oven.

I also want to thank Prof. Val Zwiller my examiner, for giving me the opportunity of doing my internship in his research group, and for always being helpful and kind.

I want to thank PhD students Samuel Gyger and Lucas Schweickert, for answering my questions and helping me with many parts of the project from CAD design to characterization and optical setup building. You were really helpful and patient with me.

Thank you to Iman Esmaeil Zadeh, who contributed to the fabrication of the samples in this project.

And Finally thank you to all the Quantum Nano Photonics group, for creating a fulfilling work environment.

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Abstract

Single photons are essential resources for quantum technologies, they can be realized through high purity, bright and stable quantum emitters. Quantum key distribution, is for instance, one of these applications which show great promise, in that it could in the future, provide us with safe encryption process guaranteed by the laws of physics. Single photon emitters when coupled to integrated photonic circuits are seen as the building blocks for future quantum technologies. Quantum dots (QDs) are currently leading the race in the field of single photon sources, their main drawback being their cryogenic operation temperatures. Thus, studying and improving the properties of single photons sources which operate at room temperature is an important goal.

Hexagonal Boron Nitride (hBN), is a material exhibiting single photon emitting centers at room temperature. It could potentially be a viable candidate for quantum applications since it hosts bright and stable emitters distributed over a wide wavelength range. In this Project, Single photon emitting defects were created in hexagonal Boron Nitride (hBN) via thermal annealing. Then the photoluminescence, polarisation and wavelength distribution of these emitters was characterized at room temperature. We then performed second order correlation measurements on the single photon sources to determine their purity both at room and cryogenic temperatures using a Hanburry-Brown-Twiss (HBT) setup. A single photon purity up to 93% was achieved and its dependence on the excitation power was studied.

Next, our goal was to couple hBN to photonic circuits. Particularly, to perform a second order correlation measurement with an on-chip HBT setup using integrated Superconducting Single Photon Detectors (SSPDs). Since most emitters we measured were located between 625 and 660 nm, the photonic circuits were designed to maximize the coupling within that range. Finite difference time domain (FDTD) methods were used to simulate the coupling of the hBN dipoles to guiding structures with varying dipole orientation and position. We realized a circuit were hBN emitters are encapsu- lated in the silicon nitride waveguides. We present all the alignment and fabrication steps that were necessary to deterministically couple the emitters to the waveguide. Lastly we show measurements on waveguide-coupled emitters, and discuss ways that could potentially improve our current results.

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1 Introduction

Ever since the discovery of graphene, the field of 2-dimensional (2D) materials has expanded rapidly, from application in optics and optoelectronics [1,2] to superconductivity [3]. Hexagonal boron-nitride (hBN) is one of these new exciting materials, it has been extensively used in optoelectronics applications combined with graphene or Transition metal dichalcogenides [4].

This project focuses on the study of single photon emitters (SPE) in hBN, which are bright, stable, and operate at room temperature [12]. This makes them a particularly interesting source to study, since other high performance emitters such as quantum dots, which are currently one of the best solid state single photon emitters, only work at cryogenic temperatures. Thus exploring quantum photonic circuits with hBN can potentially pave the way for advanced future quantum applications in communication and computing, operating at room temperature.

For SPEs in hBN to be viable candidates for quantum technologies, they need to be deterministically integrated within photonic circuits. These integrated photonic circuits, in addition to drastically reducing the footprint of optical setups (by going from the size of an optical table to an on-chip circuit), can be used to perform the first filtering steps and to couple single photons from the emitter to detectors or to fiber networks for communication applications. The goal of this thesis is to couple hBN emitters to an integrated photonic circuit with on-chip detetctors.

In section 2, we present a state of the art in the field of integrated photonic circuits,first by pre- senting different emitters while focusing on SPEs in hBN, and then on the integration of quantum sources within integrated circuits. Then, in section 3, we study the properties of SPEs induced in hexagonal Boron Nitride (hBN) via thermal annealing. The photo-luminescence, polarisation and wavelength distribution of these emitters was characterized at room temperature. We then performed second order correlation measurements on the single photon sources to determine their purity both at room and cryogenic temperatures. Next, in section 4, we present various simulations to couple the emitters to photonic circuits in order to realize on-chip second order correlation measurements with integrated superconducting single photon detectors. The steps needed to fabricate the simulated structures are presented in section 5.

Lastly, we detail in section 6 the measurements we performed on the fabricated circuit.

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2 State of the art

2.1 Single photon emission

It is important to place hBN in the broader context of single photon emitters in order to see where it stands. We will focus on solid state single photon emitters, these behave like artificial atoms, in that they resemble the optical properties of atoms when it comes to emission and have the advantage of scalability due to their solid state nature [35][36].

In solid state environments, i.e. QDs and color centers, it is advantageous to integrated large scale systems of identical emitters, unfortunately, this is a challenging goal because of variations in the surrounding environment and size of emitters. This, in turn, results in different optical emission properties. Furthermore, due to the fact that solid state systems have a high refractive index (above 2), they tend to trap the light inside the host material, making it harder to collect the emitted single photons from them. Below are general figures of merit for single photon emitters, which are essential for practical applications of the emitters [19][20]:

• Brightness, emission wavelength and band width of the emission.

• Purity: it is quantified by the second-order correlation function for zero time delays (g²(τ = 0)) ,which is a measure the single photon emission purity, a value of g²(0) = 0.01 means a single photon emission purity of 99%, it can also be viewed as the probability that a source will emit multiple photons at the same time. A g²(τ = 0) < ¹₂ signifies single photon emission.

• Coherence: is a measure of the phase relationship between the E field values at different times or locations in space. It is also a good measure of the ability of light to interfere with itself.

• Operation temperature, room temperature operation is favoured but is hard to achieve for on- demand solid state emitters. High quality on demand single photon sources either require, or, have superior performance at cryogenic temperature.

Based on the properties discussed above, we present several state of the art single photon sources[19][20]:

• Defects in 3D bulk and nanocrystals: Fluorescent point defects in solids, also called color centers, exhibit wide emission ranges and even room temperature emission. Color centers in diamond are a good example, they are caused by vacancies in the crystallographic structure of diamond, the most widely studied defect in diamond is the Nitrogen vacancy (NV), which emits at room temperature with a line-width of 1 nm between 640 and 800 nm and a single photon emission purity of 98% [18]. Other materials that exhibit colour centers include: Silicon Carbide (SiC), Yttrium Aluminium Garnet (Y AG) and Yttrium Orthosilicate Garnet (Y OS) [22], Zinc Oxide (ZnO) [21].

• 2D materials: Several 2D materials show single photon emission, these materials include transition metal dichalcogenides (TMDC), such as Tungsten Di-Selenide (W Se₂) which show single photon emission at cryogenic temperatures. Hexagonal Boron Nitride (hBN) shows single photon emission at room temperature in the 500 to 800 nm range, a linewidth of arround 10 nm at room temperature and a single photon purity that ranges from 70 to 90%.

• Quantum Dots: QDs are semiconductor nanoparticles (0-dimensional dots) that function as artificial atoms since they have discrete bound electronic states. One of the challenges when using quantum dots is to collect the emitted light. Indeed, most semiconductor QDs have high indices (around 3.6 for Gallium Arsenide), yet collection efficiencies above 75% have been demonstrated [23]. Despite this, QDs have thus far achieved the highest single photon emission purity (consistently above 99% for InAs/GaAs QDs ), they operate at cryogenic temperatures (4K) and emit narrow lines because of their atom-like nature, this also means that emitted photons have high indistinguishability up to 92% [24]. Depending on the material used the emission wavelength can vary, InAs: 923 − 950 nm, GaN : 340 − 370 nm with some reaching telecom wavelengths (1550 nm) for InAs/InP QDs.

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2.2 Hexagonal Boron Nitride

hBN is a wide bandgap semiconductor with structure similar to that of graphite, in the form of several monolayers, each layer consists of hexagonal array consisting of Boron and Nitrogen atoms, the layers are then held together by Van der Walls interactions. Further research involving hBN showed that the material exhibits fascinating optical properties, offering new ranges of applications in nonlinear and quantum optics, with integration within photonic circuits [4]. Furthermore, hBN has defects that exhibit single photon emission at room temperature [12] . Defects in hBN can be viewed as “artificial atoms", having a ground and excited state contained within the bandgap of the host material. The origin of the single photon emission is still debatable, recent literature suggests that it is due to vacancies in the crystal [39].

Figure 1: hBN molecule and its band structure [4]

A room temperature single photon source can be potentially used for quantum communication (key distribution), and sensing [5]. Typical operation at room temperature of the single photon emission, under above band excitation (532 nm pump), yields multi-photon detection probability typically around 0.1. Although, so far no measurements have been performed to characterize the coherence of the source. Other competing single photon sources that offer higher purity such as quantum dots (QDs) can reach a photon purity as low as 10⁻⁵[10] , the fact that hBN operates at room temperature, and the emitters can be easily created, as will be seen in the following chapters, makes it attractive for a variety of applications when room T operation or large scale integration are needed, especially with recent developments in CVD (chemical vapor deposition) hBN fabrication [11].

The performance of the single photon emitting defects in hBN have been studied extensively, they show high quantum efficiency (up to 40%) and brightness (saturated count rate up to 10⁶ counts per seconds ) [40], in addition to being stable [12], the defect is highly polarized both in emission and absorption.

The origin of such defects in hBN is still being investigated, but they can be created both from single crystal through exfoliation process and using commercially available solutions with suspended hBN flakes. The emission wavelengths of the quantum defects in hBN are distributed randomly over a broad spectrum, typically between 500 and 850 nm, with higher probability for specific kinds of defects to appear, as will be discussed in the thesis 41.

There are various experimentally demonstrated processes by which one can induce single photon emitters (SPEs) in hBN, such as thermal annealing, strain , or electron ion beam irradiation 25 (see section 2.3). Nevertheless, these processes are probabilistic in nature and so far there has been no definite way of deterministically (in position and wavelength) inducing defects in hBN.

2.3 Methods for creating single photon emitting defects in hBN 2.3.1 Thermal annealing

The method consists of high temperature treatment of the hBN sample (usually drop cast or exfoli- ated). The annealing temperatures reported in literature range from from 200 to 1100 degrees Celsius in a low pressure environment [12][25]. It was experimentally observed that the number of emitters

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water solution were drop cast on a Silicon sample and annealed, at different temperatures for 30 min under 1 Torr of pressure in an argon atmosphere, the results are shown in figure 2:

Figure 2: Normalized number of stable emitters found as a function of the annealing temperature [12]

2.3.2 Electron beam irradiation

Electron irradiation is another method for creating the single photon emitters, in [12], hBN flakes in a methanol and water solution were drop cast on a Silicon sample. Then, photo-lithography and metal depositions steps are performed to create a metal mask forming a grid for deterministic location of emitters. The sample is then irradiated with a electron beam (e-beam) in a scanning electron microscope under low vacuum ( H₂O 8 Pa). As seen from figure 3, the regions irradiated with electron beam show bright emission compared to the regions that were not exposed to electrons.

Figure 3: Activation of hBN defects with e-beam. a)comparison with thermal annealing, b)spectrum of the same position on the sample before (black) and after (red) e-beam treatment [12]

2.3.3 Strain

The single photon emitting defects were also shown to be created using strain. In [13], SiO₂ nano- pillars were pattern on a Si substrate, then a 20 nm hBN film grown by chemical vapor deposition (CVD) was transferred on the pillars. Through performing room temperature spectroscopy, single photon emission was observed from the pillar region. Unlike thermal annealing, were the emitter position is random, the emission from hBN originated from the locations of the pillars, implying that single photon emitting defects can be induced by strain.

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Figure 4: Strain induced activation of single photon emitters in an hBN film. a) representation of hBN film transferred on a pillar. b) 3d AFM rendering of a folded hBN flake of thickness L on a nano-pillar array. c) con-focal and optical (inset) images of the surface of the sample [13]

2.4 Tuning of emitters in hBN

Since single photon emitting defects in hBN emit in a broad spectrum and since there is no conclusive way to determiniscally select the emission range, tuning the emission wavelength is a significant aspect of integrating the emitters in photonic structures. Tuning mechanism such as strain, stark shift or thermal tuning can be used to match the resonance frequency of photonic structures [16] such as ring resonators.

2.4.1 Strain

Optical and electrical properties of materials are influenced by the molecular structure of the material.

Thus, in the case of hBN, a change in the lattice constant will result in a modification of its properties.

By applying strain to the sample supporting hBN, the lattice parameters are slightly changed which causes a shift in the emission wavelength.

Strain tuning of hBN emitters was achieved in [14], by putting hBN flakes on a flexible poly-carbonate beam fixed at one edge as can be seen in figure 5.a). Then by bending the beam in different directions a compressive or tensile strain could be applied to the emitters, which in turn shifted the emission wavelength (5.b)

Figure 5: Strain tuning of single photon emitters in hBN flakes on a bendable beam. a)The beam is fixed at one edge and the hBN sample is placed at a distance d away from that edge. Then at a distance L strain can be applied by either pushing down or pulling on the beam which respectively applies tensile or compressing strain on the sample . b) Measured emission from the sample for compressive (blue), no strain (black) and tensile (red) strains. On the left panel the values for the strain are −0.4, 0, +0.4%, on the right one −0.6, 0, +0.6% [14]

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2.4.2 Stark effect

In [15], stable hBN emitters were tuned via Stark effect. An hBN flake was placed under an atomic force microscope (AFM) tip, which was used to apply an electric field causing a shift in the emission line as can be seen in figure 6.

Figure 6: a) schematic of the experiment, the hBN is placed on an glass sample covered with indium tin oxide(ITO), an oil immersion lens objective under he sample is used to excite and collect the emission from the hBN. The AFM tip is used to apply an electric field to the sample.

b) fit of the measured spectra before (blue) and after (orange) star shift. c) spectral shift as a function of the applied voltage and electric field. [15]

2.5 Integrating quantum emitters to photonic circuits

A vital step to achieve fully integrated quantum integrated systems, is successfully integrating quantum sources to photonic passive elements (waveguides and cavities), this research area aims to deliver compact quantum circuits, to scale down the table top technologies.

2.5.1 Coupling to waveguides

Hybrid systems which combine different photonic materials to perform larger functionalities, limited by the individual constituents are becoming a hot research topic recently. A first demonstration of such integrated systems, was to combine III-V semiconductor nanowire QDs with silicon based photonic circuits. In [30]. This deterministic integration was achieved by using a nano-manipulation technique.

The nanownowires (grown vertically on a substrate) were transferred using a nano sized tungsten tip . The Van-der-Walls forces between the tip and the nanowires, allow transferring the nanowires to a target substrate, in order to design photonic structures around it.

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Figure 7: a) schematic view of the III-V QD integrated in the waveguide, b)microscope image of the device, inset (1) shows the nanowire attached to the nano-manipulator tungsten tip to allow for transfer on substrates, inset (2) shows different NW-QDs coupled to different waveguides, c) second order correlation function measured through the waveguide showing a single photon purity of g²(0) = 0.07. [30]

A similar hybrid approach was realized for hBN, since it is not trivial to form a monolithic quantum circuit in hBN. In [31] hBN emitters were coupled to waveguides. The waveguides were prefabricated on an aluminium nitride (AlN ). Then, hBN flakes were drop-cast on the waveguides. AlN was chosen since it is transparent from ultraviolet to infrared, it also has a low fluorescence and its index of refraction (2.08) is close to that of hBN (n=2.1) [32, 33], this is desirable since it reduces reflections at the interface between the two materials. A grating coupler was placed at the end of the waveguide to scatter the propagating light and collect the hBN emission in the waveguide from the top. Then the collected light can be directed to a second order correlation measurement setup to characterize the single photon emission. The main challenge in the work, is the non deterministic nature of integration, which we will try to solve in the current thesis, thus integrating the hBN emitters in a controlled fashion within a photonic device.

Figure 8: a) schematic view of the fabricated AlN waveguide with the hBN flake on top, b)AFM image of the fabricated structure, c) AFM height measurement across the red line shown in (b) [31]

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Figure 9: a) confocal map of the device under continuous 532 nm excitation , b)spectrum and second order correlation measurement collected via reflection c) schematic and confocal map of the excitation on the hBN flake (point A) and collection through the waveguide (point B), d)spectrum and second order correlation measurement through the waveguide collected via the grating coupler [31]

2.5.2 On chip filtering

On chip filtering of integrated quantum light sources is an important step towards light manipulation on chip. Photonic structures such as cavities, Bragg mirrors, or ring resonators can be used in order to select or filter specific lines from quantum emitters.

Ring resonators are optical cavities coupled to waveguides. The rings have a set of resonance frequencies, at resonance light will couple, via evanescent coupling, to these resonant modes:

Figure 10: Simplified drawing showing how a ring resonator works Several resonators can be cascaded to create high order optical filters [37] .

In [38], two quantum sources were deterministically coupled to a waveguide, terminated by an electri- cally controlled ring resonator. Then, by applying a given voltage on the gold contacts one can filter a specific transition of the QD for multiplexing applications.

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Figure 11: Illustration of 2 QDs emitting at different wavelengths (depicted with blue and red) coupled to a photonic structure consisting of a ring resonator coupled to waveguides. a) Measured emission spectra (from the through port) of both QDs b) . By applying a voltage between the 2 gold contacts at the top the ring is heated and therefore changes its resonances frequencies. Selected and filtered emission lines are shown as a function of the applied voltage. c) Integrated emission intensity of the emission from both QDs as a function of the applied voltage.

On chip filtering is beyond the scope of this thesis but it has been realized for other types of emitters, particularly QDs [38]. Generally, for circuit reconfiguration (tuning of the properties of photonic devices), several methods can be used such as strain, temperature, or carrier injection [45], but since since our circuit will be realized using SiN, which is an isolating material, strain [43] or thermal tuning [44] can be used.

2.5.3 Summary

hBN is a wide band-gap semiconductor which hosts centers capable of single photon emission. These centers can be engineered in the material via various methods, the most common of which are: Ther- mal annealing, electron beam irradiation or strain. Thermal annealing, is the simplest way of inducing single photon emitters in the material. It is a random probabilistic process in which neither the position nor the emission wavelength of the emitters is determined. Strain and e-beam irradiation are on the other hand, more position-controlled.

The goal of this project will be to create single photon emitters in hBN via thermal annealing, study their properties, and integrate them within photonic circuits to perform on-chip second order correlation measurements.

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3 Study of single photon emitters in hBN

3.1 Activation of defects via thermal annealing

Following the experimental study performed previously in the group[25], we can directly employ the activation parameters that yield the best results for the emitter density after thermal annealing. The reported results suggest that the annealing pressure or time (above 30 min) have no significant effect on the brightness and the density of emitters created, within the statistical errors. The highest, experimentally measured, density of emitters was found for samples annealed at 1100^◦C. It is important to note here that hBN was typically activated on silicon dioxide substrates, when the emitter brightness and density was compared with other substrates such as silicon or silicon nitride, less emitters were observed 25, the exact reason is still under investigation. In order to produce single photon emitting defects in hBN, we followed the following steps:

-The hBN flakes are purchased in a solution of methanol from “GRAPHENE SUPERMARKET c ”, the details of the flake sizes and the concentration are shown in Figure 12:

Figure 12: hBN Solution and its properties

- Substrates (SiO₂ or SiN ) are prepared through cleaning in ultra-sonic bath consisting of iso- propanol to remove surface impurities.

- The hBN is then drop-cast on prepared substrates with a 10 µL pipette.

Figure 13: a) substrate ultrasonic cleaning, b) hBN drop-casting

-The drop is then left to dry for around 1h, then drop casting and drying process is repeated for 5 times to increase the density of hBN flakes on the sample.

-After the sample is dry, we anneal it in a tube furnace. The tube is first flushed with argon two times to eject any impurities that got in while sample was being loaded. During this process, the tube is filled with argon until it reaches atmospheric pressure then Argon is evacuated with a pump until the pressure drops to around 3 mBar (the lowest pressure we could reach). Finally the sampled is annealed for 30 min with a starting pressure of 3 mBar. It is during this annealing step that the defects in hBN are activated. Figure 14 shows the annealing cycle of the hBN flakes, it starts with a ramp up phase with a rate of 20^◦/min, then an annealing phase, and finally a cool-down phase. The figure also shows the sample placed on a sapphire holder within the tube furnace.

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Figure 14: (a) annealing process, (b) tube furnace, (c) sample inside the tube furnace

-Figure 15 shows a microscope image of a typical hBN chip prepared using our process. We see several regions with different colors, the surface was characterised with profilometer, the darkest regions correspond to the heights of around 400nm. Based on optical characterizations, as will be discussed below, the majority of emitters were located at the drop edges not at the center, which might be caused to the movement of the flakes to the drop edges when the drying process takes place.

Figure 15: microscope image of the sample surface after annealing (x20)

After this process the hBN sample are ready to be characterised in a room temperature photoluminescence spectroscopy setup.

3.2 Characterisation: Photoluminescence spectroscopy

In order to characterise the emitters, we first locate them on the processed sample. Since drop casting and activation of single photon emitters are random processes, the location of the emitters on the sample is also random. But as a rule of thumb, most of the emitters were located at the edges of the drop. To characterize the emitters, we used a room temperature confocal microscopy (described in figure 16) setup to perform photoluminescence (PL) spectroscopy.

A 532 nm laser pump laser is directed towards two input irises (I1 and I2), to ensure that the beam is perpendicular to the sample surface. This step ensures that the beam is centred when hitting the objective (ThorLabs RMS40X, NA=0.65). This gives a circular laser spot when the laser beam is focused on the sample. Part of the reflected light from the sample is then directed towards a camera (with the use of a thin pellicle beam splitter with splitting ration 45/55) allowing for simultaneous excitation and white-light imaging of the mounted chip. The reflected beam from the pellicle is directed towards another pair of irises (I3 and I4), with the use of 2 mirrors (M3 and M4), these two irises align the beam to the spectrometer. Two rotating attenuators at the input help set the power of the laser through a combined attenuation of 30 ND. Before going to the spectrometer, the pump laser is filtered out through a long pass 550 nm filter (LP 550 nm). The signal from the sample is finally focused on the spectrometer’s input slit using a lens mounted on a movable stage with focal length of 7cm. The last alignment step is to make sure the signal is centered and in focus with the slit, the input slit progressively closed, and the reduction of the signal is compensated through movement of the lens. The slit is kept at width of approximately 50 micrometer, which can be opened further for higher counts at the expense of the resolution. The spectrometer used is Acton SP2750, Princeton instruments, equipped with two gratings that offer different resolution (1200 lines/mm and 150 lines/mm). At room temperature the FWHM of the emission lines given by hBN is around 5 nm.

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measurments at room temperature.

To characterize an emitter, we start by first locating the drop of the hBN solution. Then, move around inside the drop with a differential micrometer stage while performing live acquisition of integration time (0.1s). Most of the time, we are able to excite a single defect at a time, but occasionally, several emitters with different emission wavelength are located at the same position. We use a set of band-pass filters to study the single photon statistics of individual emitters. The filters are positioned just before mirror M4 (figure 16). Since the emission wavelength of the emitters is random, we used several 10nm bandpass filters each separated by approximately 50nm, with center wavelength starting from 600 nm to 800 nm. The center wavelength of the bandpass filter can be tuned to lower wavelength by tilting the filter as shown in figure 17.

Figure 16: Room temperature photoluminescence spectroscopy setup

Figure 17: Impact of tilting the filter on the center bandpass wavelength

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3.3 Photoluminescence measurements 3.3.1 Substrate fluorescence

We conducted two hBN activation experiments, the quality of the emitters will determine how the silicon nitride photonic circuit in the later chapters will be fabricated. The two substrates used for annealing hBN consist of silicon wafers with a top layer being either Low Pressure chemical Vapor Deposition (LPVCVD) SiN or thermal SiO₂. Under 532nm illumination, and no hBN fabrication, defects in annealed SiN have higher fluorescence compared to SiO2, additionally the different thermal expansions of the layers cause the silicon nitride to form cracks, thus limiting the sizes of the fabricated photonic devices on it. Based on these two problems, especially the fluorescence of the annealed silicon nitride which can overlap with the single photon emitters in hBN, we will focus our attention on activation of emitters on silicon dioxide substrate.

The figure bellow shows two representative emitters with matching emission wavelength found on SiN and SiO₂ substrates. Both spectra were taken after optimization of the emission lines both in terms of position and Signal to background ratio, the excitation power used was 70 µW for SiO₂ and 20 µW for SiN .

Figure 18: Emitters found on SiN (red) and SiO₂ (blue) substrates 3.3.2 Photoluminescence of emitters

In this section several properties of hBN emitters are characterised. Using the setup thoroughly described in the previous section we show several representative emitters on SiO2 samples, their emission spectra and location on the sample are shown in figure 19. Ideally the emission should consist of single bright emission line, possibly with phonon assisted transition side bands [12] , with low background emission. The background emission depends on the substrate used for the thermal annealing, but also on the local environment of the emitters which is determined by how the hBN flakes dry after the drop casting, this part of the background radiation is random and cannot be controlled.

Some representative emitters before and after filtering as well as the sample surface imaged with the camera are shown in figure 19:

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Figure 19: Emitters and their location on an SiO₂ substrate, peak brightness is given at saturation power

To further characterise the emission lines from hBN, we need to focus on a single emission line (a single emitter), and study its behavior, particularly the evolution of the emission intensity with the excitation power and how it compares with the background fluorescence of the substrate. Many quantum emitters which exhibit single photon emission (including hBN), can be approximated by a three level system [42] as shown in figure 20:

Figure 20: A quantum emitter approximated by a three energy level system. The third level is here to take into account the transitions to phosphorescent, triplet or dark states [42].

hBN defects will create new energy levels that will most likely be within the band gap because hBN is a wide bandgap semiconductor. Level 1 and 2 can be viewed respectively as the ground and excited singlet states of the hBN defect, while level 3 represents the triplet state ( with lower energy) and is responsible for the phosphorescence of the material, this phosphorescence is different from the fluorescence of the emitter (which corresponds to the decay from level 2 to level 1) by occurring on a much longer time scale. This approximated representation neglects any vibrational states or broadening of the energy levels. Furthermore, the coefficient k₃₁ can be neglected when compared with the other transition rates. By using these excitation and de-excitation rates, we can formulate a system of differential equations describing the evolution of the populations of each energy levels [42]:

˙

p₁ = −k₁₂p₁+ (k_r+ k_nr) p₂+ k₃₁p₃

˙

p₂ = k₁₂p₁− (k_r+ k_nr+ k₂₃) p₂

˙

p₃ = k₂₃p₂− k₃₁p₃ 1 = p1+ p2+ p3

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The fluorescence decay coefficient k₂₁ can be split into two parts, consisting of a radiative and non- radiative decay corresponding to the electron decaying to a lower energy level and losing its energy in the from of heat or phonons. Note than when measuring photoluminescence, we detect photons

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decaying radiatively from level 2 to 1. We can write this as R = p₂k_r.

We consider the system in the steady state condition meaning that the population of each level does not vary over time. Then, solving for p₂ yields:

R(P ) = R∞ P/Ps

1 + P/Ps

(2) Where, P = k₁₂hν is the excitation power, P_s is the saturation power and R_∞is the emission rate at saturation. These constants are given bellow:

R∞= k₃₁k_r k₂₃+ k₃₁

P_s= (k_r+ k_nr + k₂₃) k₃₁ k₂₃+ k₃₁ hν

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Next, we focus on a single defect, we start by characterising the dependence of the emission line on the excitation power, the results are shown in figure 21, the results measured for the defects created in the project match the reported results in [12]. In the figure, we compare the hBN emission intensity for two emitters the first at 583 nm and the second at 630 nm with the background emission. The hBN emission shows saturation behavior that can be explained and fitted using a three level system model, as explained previously. The emission intensity as a function of the excitation power is given by the following equation (equation 2) [12][25]:

I(P ) = I∞P P + P_sat

Where, I is the intensity or counts, I_∞is the asymptotic limit of the intensity and P_satis the saturation power. On the other hand, the background radiation grows linearly with the excitation power:

Figure 21: Emission saturation curve (red) and background radiation (blue) and their respective fits for two hBN emitters. The fit on the emission gave for a) P_sat = 290 µW and I∞ = 8.3 ∗ 10³cts/s, and for b) P_sat = 544 µW and I∞= 3.2 ∗ 10³cts/s

A crucial parameter that can be extracted from the previous measurement, shown in 21, is the signal to noise ratio. It provide us with the optimal power at which to conduct all subsequent measurements, such as second order correlation measurement for a given emitter. Through wide characterization of several emitters we find that the optimum excitation power is usually between 50 and 100µW

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Figure 22: Signal (hBN emission) to noise (background fluorescence) ratio of the hBN emitter presented in figure 21.a). The optimal power to measure, for this emitter, is around 50µW .

The emission lines from hBN presented in this section are zero phonon lines (ZPL), they show typical emission at room temperature with a Lorentzian line shape [42]. They can be fitted to the following generic Lorentzian function to extract the FWHM and the center wavelength.

L(λ, λ₀, γ) = γ²

γ²+ 4(λ − λ0)² (4)

Where, λ₀ is the peak wavelength and γ is the full width at half maximum (FWHM).

Figure 23: Emission line from an hBN sample and its lorentian fit

Figure 24 shows the spectrum of the same hBN emitter at room and cryogenic temperatures (200mK). At cryogenic temperatures, the 150 mm/line grating shows splitting in the spectrum which was initially unresolved at room temperature due to phonon broadening, with clear decrease in the FWHM [34]. Further investigation of the emission using higher resolution grating in figure 24.b re- vealed a more complex spectrum. At 200 mK, it appears that the original emission line is made of several narrower lines. At room temperature, these emission lines are broadened due to lattice vibrations, appearing as one broad peak on the spectrometer. The FWHM goes from 3.8 nm at room temperature to 0.3 nm at 200 mK. We ruled out the possibility that these could be several emitters close to each other by filtering the broad emission line and performing a second order correlation measurement demonstrating single photon emission, the results of the correlation measurement is presented the following sections.

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Figure 24: Spectrum of an emitter at 300 and 200 mK with a low (150 lines/mm), a) and high (1200 lines/mm), b) resolution gratins

3.3.3 Polarisation

The single photon emitters in hBN are modeled as dipoles, in this section we measure their emission and absorption dipole orientation as a function of the wavelength difference between the excitation (532 nm laser) and emission (hBN emitter). In order to do the absorption and emission polarization measurement, some adjustments were made to the setup presented in figure 16.

The laser first passes through a horizontal polariser, then through a half-wave-plate (HWP) which rotates the polarisation in the horizontal / vertical polarisation plane. We can then record the intensity of the emission as a function of the angle of the HWP.

Figure 25: Drawing showing how a half wave plate rotates polarisation by twice the angle the input polarisation makes with its optical axis

The polariser and HWP were place between the laser and attenuators in figure 16.

Figure 26: Position of the polariser and HWP with respect to the setup shown in figure 16 To measure the polarisation of the emission from hBN, we send polarized light at the maximum absorption angle to excite the emitters, then placed a HWP and a second horizontal polariser in front of the spectrometer in the collection path. By rotating the HWP and measuring the counts we can deduce the polarisation state of the emitter. This setup, allows us to study the absolute rotation between the excitation and emission polarization, which takes into account any indirect transitions in the hBN which might cause such rotation [30].

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Figure 27: Position of the polariser and HWP with respect to the setup shown in figure 16 For an ideal dipole the emission as a function of the polarisation angle is given by a sin θ² law. In our case, the angular dependence of the emission intensity will be fitted with the following equation [34], which takes into account the the non ideal nature of the dipole assumption, resulting in partially polarized emission.

a ∗ sin(θ − θ²₀) + c (5)

Figure 28: Polarisation spectroscopy measurements of the excitation / absorption (red) and collection / emission (blue) with data fit (solid lines) for several emitters at different wavelengths.

The relative rotation between the two profiles is: around 10^◦ for the emitters at λ = 578 and λ = 594 nm, 60^◦ for λ = 635 and λ = 594 nm and 70^◦ for λ = 740 nm

The polarisation profiles are consistent with an emission from a linearly polarized single dipole [39]. From figure 28, we notice that emitters of longer wavelength experience a higher relative rotation between the excitation and collection polarisation profiles. This is due to the use of a 532 nm excitation wavelength, indeed for emitters of longer wavelength, the energy of the laser much larger than the transition between the ground and excited states of the emitter. Thus, the emission mechanism can go through indirect transition as shown in figure 29. In this indirect regime, the fact that the electron is de-excited two times creates a greater polarization shift [34][47]. In contrast, the shorter wavelength emitters are closer to the laser excitation wavelength which suggests higher probability for direct transition:

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Figure 29: Two different excitation regimes, the indirect regime induces a greater polarization shit.

3.3.4 Statistics on emitters

In order to couple the hBN emitters to photonic circuits, their emission wavelength should lie within the allowed bandwidth of the photonic devices. Thus a thorough characterization of the distribution of the emitters is needed to guide the design of the photonic waveguides. The following graph shows the distribution of emitters grown on silicon dioxide substrates. The emitters are randomly distributed over more than 100 nm bandwidth, thus the photonic waveguide should support the majority of these emitters under single and multimode operation. Moreover, we see that there are several emission lines that stand out and have a higher occurrence than the others, the most frequent emission lines are highlighted by the red columns in the figure. After thermal annealing, the most common emission that we measured were around 630 and 660 nm, this is in-line with previous experiments reported in [25]. The photonic circuit design will take into account the most common emission lines.

Figure 30: Wavelength distribution of hBN emitters (1100^◦C annealing)

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3.4 Quantum description of light

After optimizing the intensity of the emission with the triple axis differential micrometer with resolution of 0.5µm. We need to further characterize the emission to prove the sub-poissonian statistics indicating non classical emission.

We start by discussing the theory, (adapted from [7],[8],[28],[29]), we will explain the different statistical distributions given by light in photon counting experiments (there-of photon statistics). In such experiments light incident on a photodetector produces electrical pulses corresponding to detection events. Electronic counters register these electrical pulses which over times generate a statistical distribution of the arrival time of photons. We will see how light can be categorized in three categories, each one obeying a different statistical distribution which implies different light sources properties. In order to achieve that goal, a quantum description of light is required .

In the quantum description of light, each mode of the light field can be seen as an independent harmonic oscillator. The quantum harmonic oscillator is expressed as follows [6]:

H =b pˆ² 2m+1

2k ˆx² = pˆ² 2m+1

2mω²xˆ² (6)

Where ˆx and ˆp are the position and momentum operators and ω = qk

m.

Its eigenfunctions (expressed with the help of Hermit polynomials H_n) and eigenvalues (Energy levels) are well known [6]:

Ψn(x) = AnHn

x b exp

−x² 2b²

, b =p

~/mω; En= ~ω

n + 1

2

(7) To find the eigen values of this Hamiltonian Dirac used the so called “ladder operators” which allows us to express the energy eigenvalues without solving a differential equation. These operators are defined as:

ˆ

a⁺=r mω 2~

ˆ x + i

mωpˆ

; ˆa =r mω 2~

ˆ x − i

mωpˆ

(8) It is also useful to express the position and momentum operators as function of these new ladder operators:

ˆ x =

r

~

2mω aˆ⁺+ ˆa

; ˆp = r

~

2mω ˆa⁺− ˆa

(9) Thus, we can express the Hamiltonian as follows:

H = ~ωb

ˆ a⁺a +ˆ 1

2

(10) The operator bN = ˆa⁺ˆa (also written ˆn ) has all positive integers as eigenvalues [6]:

N |ni = ˆb a⁺a|ni = n|ni,ˆ n = 0, 1, 2, 3, 4 . . . (11) Which gives:

E_n= ~ω

n + 1

2

(12) Which is consistent with [7]. ˆa⁺ and ˆa act on the energy eigenstates as follows:

ˆ

a⁺|ni =√

n + 1|n + 1i; ˆa|ni =√

n|n − 1i (13)

Thus ˆa⁺ and ˆa add or subtract a quantum of energy ~ω, they thus called the creation and annihilation operators, ¯N is called the number operator. In the quantum description of light, classical field amplitudes are replaced by the creation and annihilation operators. These two operators obey the bosonic commutation relation:

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ˆa⁺, ˆa = 1

Let us consider the fundamental mode, we can write its Hamiltonian as follows:

H = ~ωb

N +b 1

2

(14) The number operator thus gives the number of photons of energy ~ω that are in the fundamental mode. The different statistical distributions of light are given by the relationship between the average photon number hni and the variance of the photon number (∆n)².

3.5 Spacing of photons in a beam:

Let’s consider a monochromatic beam of light of angular frequency ω and constant intensity I. Suppose this beam is incident on an ideal photon counter / detector [7]:

Figure 31: Light beam incident on an ideal single photon detector

The photon flux Φ can be expressed as a function of the mean photon number hn(τ )i passing through a cross section S in a time window τ :

Φ = hn(τ )i/τ = ISτ

~ωτ = P

~ω

(15) With P being the average power of the light beam. If we have P = 10nW and ~ω = 3eV, the flux is Φ = 2.10¹² photons. s⁻¹. This mean that in a tube of length 3.10⁸m contains 2.10¹⁰ photons.

Similarly, a segment of the beam of length 7.5cm contains 5 photons, let’s divide that segment in 5 and look at the distribution of photons traveling in the beam:

Figure 32: Spatial distribution of 5 photons in a beam divided into 5 equals segments

In the table above, for all three cases the average photon number per cell is 1, yet the distribution is different. Such states of light are also sometimes referred to as:

-bunched or super-Poissonian light (e.g thermal light) -coherent ,random or Poissonian light (e.g laser sources) -anti-bunched light (e.g single photon sources)

3.6 Photon statistics 3.6.1 Super-Poissonian Light

Super-Poissonian light such as thermal light is a mixed state in quantum mechanics it can be expressed as the sum of all possible number states (|ni) in a given mode weighed with their probability. To express this, we can use the density matrix[28][7]:

∞

X

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Where P_thermal(n) is the probability of finding n photons in the given mode of the thermal light.

P_thermal(n) is given by Bose-Einstein statistics:

P_thermal(n, hni) = hniⁿ

(1 + hni)ⁿ⁺¹ (16)

The variance of a thermal state is:

(∆n)² = hni²+ hni (17)

Thus, Thermal states obey super-Poissonian statistics, (∆n)² > hni. The number state with highest probability is always the state corresponding to n = 0, also called the vacuum state:

Figure 33: Probability distribution of a thermal state of light for different hni 3.6.2 Poissonian Light: The coherent state

Poissonian light describes an ideal spatially and temporally coherent light source. In a real-life situ- ation, this can be used to describe a laser light source. In quantum mechanics such light sources are described by coherent states. The coherent state (also called Glauber state) is an eigenstate of the annihilation operator ˆa and it can be expressed in the basis of the photon number operator[28][7]:

ˆ

a|αi = α|αi ; |αi =

∞

X

n=0

αⁿ

√

n!exp −|α|² 2

|ni

Computing the probability distribution as a function of n gives:

P_coherent(n) = |hn|αi|²

Pcoherent=

exp −|α|² 2

^∞ X

m=0

α^m

√

m!hn|mi

2

Pcoherent= |α|²ⁿ

n! exp −|α|² , since hn|mi = δ_nm (18) This gives us a Poissonian distribution, which describes the probability distribution of events occurring with a constant mean rate and independently from the last event. We can calculate the mean photon number hni and the variance (∆n)² :

hni = hα|ˆn|αi = |α|²; (∆n)² =n² − hni² = |α|²= hni (19) In this case the maximum probability is at the mean value hni :

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Figure 34: Probability distribution of a Poissonian state of light for different hni 3.6.3 Sub-Poissonian Light: The Fock state

This kind of light cannot be described by classical electromagnetism. It is a result of the quantization of the electromagnetic field. The Fock state is a number state and thus, it is defined as the eigenstate of the number operator[28][7]:

bn|ni = n|ni

In this case the eigen value n of the operator is the number of photons in the given mode. The probability distribution of this state is:

P_Fock(n) = hn|mi = δ_km (20)

The photon number is always determined. The variance and mean are:

hni = hn|ˆn|ni = n; (∆n)² =n² − hni² = 0 (21) Thus, Thermal states obey sub-Poissonian statistics, (∆n)² < hni. When n = 1, the emitter emits a single photon.

Figure 35: Probability distribution of a Sub-Poissonian state of light for different hni Since we have now categorized light into 3 different categories:

• Super-Poissonian: (∆n)² > hni (black body radiation)

• Poissonian: (∆n)² = hni (coherent light, lasers)

• Sub-Poissonian : (∆n)² < hni (single photons sources)

Before discussing the experimental setup, which will let us characterize any light source and determine

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3.6.4 Second order intensity correlation function

In classical electromagnetism the second order intensity correlation function is written as follows:

g²_classical(τ ) = hI(t)I(t + τ )i

hI(t)i² = hE^∗(t)E^∗(t + τ )E(t)E(t + τ )i

hE^∗(t)E(t)i² (22)

It is a function of the field intensities at a given time with I(t) ∝ |E(t)|². This function gives the correlation between fields from a light source separated by an interval of time τ. Now let’s replace classical fields of a given mode by their quantum mechanical counterpart. This approach comes from second quantization. Using the creation and annihilation operator introduced previously [8]:

E(t) = bb E⁺(t) + bE⁻(t) (23)

Where:

Eˆ⁺(t) ∝ exp(−i(ωt − ~k · ~r)) · ˆa Eˆ⁻(t) ∝ exp(+i(ωt − ~k · ~r)) · ˆa⁺

(24) Taking into account the negative and positive angular frequencies ω parts of the mode. For this mode we can express the new correlation function as follows:

g²_quantum(τ ) = hI(t)I(t + τ )i hI(t)i² =

D

E⁻(t) Ê⁻(t + τ ) Ê⁺(t) Ê⁺(t + τ )E

D ˆE⁻(t) ˆE⁺(t)E2 (25)

τ →0limg²_quantum(τ ) = hâ⁺aˆ⁺ââi

hˆa⁺ˆai² = hn(n − 1)i

hni² (26)

In the quantum description of light photons are the smallest quanta of the light field. Thus, they can not be further divided. This means that upon a detection at time t a photon is destroyed leading the number of photons at time t + τ to be smaller. In our case one of the most important figure of merit when it comes to light source characterization is g²(0). Indeed, g²(0) represents the conditional probability of detecting two photons simultaneously. It tells us how the photons coincide in time which is required to differentiate light states. We can express g_quantum² (τ = 0) as follows:

g_quantum² (0) = n² − hni

hni² = (∆n)²+ hni²− hni

hni² = 1 + (∆n)²− hni

hni² (27)

Now we can take the values of (∆n)², calculated in the previous section for each of the three states of light giving us the following results:

Light state Variance g²_quantum(0) Thermal state (∆n)²= hni²+ hni 2

Coherent state (∆n)² = hni 1

Fock state (∆n)²= 0 1 −_n¹(n ≥ 1); 0(n = 0)

Figure 36: Second order correlation function for different types of light

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Looking at the previous table, for the Fock state, we notice that for n = 2, g_quantum² (0) = ¹₂, this is an important figure of merit since it means that 0 ≤ g_quantum² (0) < ¹₂ corresponds to single photon emission.

In the case of single photon emitters the expression for g²_quantum(τ ) is:

g²_quantum(τ ) = A − (1 − (1 − B)exp(−|τ |

C )) (28)

Where, A (it can be shown that A=1 [7]) is the value of the correlation for τ → ∞, B is the multi- photon detection probability which determines how "pure" a single photon source is, and C is the lifetime of the emission mechanism in the material.

3.7 Experimental setup: Hanburry-Brown-Twiss

Having established that there are different states of light that differ via their photon statistics, and that we can distinguish between them by looking at the second order correlation function. We need a way to measure g_quantum² (τ = 0) experimentally, in order to characterize our emitters and determine if they are exhibit single photon statistics. The Hanbury-Brown-Twiss (HBT) setup shown in figure [37] achieves that purpose:

Figure 37: Hanburry-Brown-Twiss setup

The incident light from the emitter is split by a 50:50 beam splitter (BS). In front of each output of the BS lies a single photon detector (in room temperature measurements avalanche photodiodes or APDs were used). These detectors produce electrical pulses (corresponding to photon counts) when detecting incident photons. In turn these counts are time correlated by the correlator: the time difference () between two consecutive detection events is measured with high time resolution (ranging from 10-50 ps for SSPDs to around 300 ps for APDs SOURCE). Now, let’s suppose that emission from the hBN is incident on the beam splitter, in the case that it consists of single photons, they can only be detected by one of the two detectors at a time (never on both detectors at the same time), this means that for a time difference of 0 between two detection events the correlation function should be 0, g²(τ = 0) = 0.

In practice g²(0) is never 0 due to several factors:

-The so-called single photon emitter might be on a substrate that also exhibits emission under laser excitation, this background signal reduces the purity of the emitted single photons as a source of noise in the experiment. This can be mitigated by reducing the excitation power, thus making the overall emission from the sample lower, note that is also reduces the single photon emission counts. The optimum excitation power, which we previously measured is characterised by the highest signal to noise ratio at around 50µW .

-Stray light coming from the environment, this can be mitigated by making sure the environment protecting the detectors from stray light (covering the detectors with dark cloth, using pinholes to couple to the detectors, and working in darkness).

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-Dark counts which correspond to detection events in the detectors with no input signal applied, these can be considered as an intrinsic noise level in the detector which can be reduced by cooling the detectors down or using low noise detectors.

The room temperature second order correlation setup used in the experiment is shown below:

Figure 38: Complete room temperature g²(τ ) measurement setup the HBT apparatus can be seen in the top right corner

The setup was modified from the PL setup, with additional alignment steps to ensure that the signal beam is focused properly, perpendicular to the detector, in order to hit the detectors in the centre of their active area, this was done with the help of several irises. A magnetic mirror is used to switch between viewing the signal on the spectrometer and coupling to the APD pair as shown in the figure.

Two Lenses are used in front of each APDs,with focal length of 30mm, to focus light on the active region of the device. In addition, two long-pass 550 nm filters (LP 550) were used in order to block the incident light from the laser, the first one blocks the reflected laser light from the sample.

The second one blocks the reflected and scattered laser light from the mounted optics in the experiment from passing to the APDs. A pinhole was also placed in front after the second filter to further block stray light (wavelengths above 550nm ). Finally, the whole HBT setup was carefully wrapped in opaque thick cloth to block stray light as can be seen in [39]. The dark counts were thus reduced to 100 -200 cts/s. For comparison, the signal count coming from the hBN emission is in the order of few thousand counts per second at the highest signal to substrate background noise ratio, thus achieving an order of magnitude signal to dark counts ratio.

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Figure 39: Covered HBT setup

A problem that rose when performing correlation measurement with the APDs was cross-talk between the detectors. We determined that the cross-talk was optical and was due to the APDs’s breakdown flash. The breakdown flash is a photon emission from the APD after a detection event (real or dark count), this photon then travels back to the other APD through the optical setup and causes a detection event (as shown in figure [40]). The breakdown flash spectrum of Si APDs was measured in [9].

Figure 40: Break down flash of Si APDs and how it causes optical cross-talk between the detectors, the breakdown flash of silicon APDs was characterized in [9]

We measured dark counts correlation, i.e. no signal incident on the detectors. The breakdown flash of the APDs caused two sharp peaks in the second order correlation function. The peaks do not have the same height because the two APDs have different detection efficiencies and signal amplification factors. In order to eliminate this cross talk, we tilted the beam splitter connecting the two APDs through an angle of less than 5 degrees. Figure 41 shows the second order correlation function of the dark counts before and after tilting the beam splitter, we clearly minimized the cross talk between the APDs, thus enabling the characterization of hBN emitters [41]:

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Figure 41: Two second order correlation measurements taken before (blue) and after (red) tilting the beamspliter

3.8 Photon statistics measurements

We measured the second order correlation function for several hBN emitters to verify the single photon nature of emission. Furthermore as explained previously, this measurement establishes the purity of the single photon source, and we can infer the time scale of the photon emission through fitting the second order correlation function. In particular we studied the influence of the excitation power on the single photon purity g²(0). Figure 42 bellow shows measurements performed on a single hBN defect grown on SiO₂ at annealing temperature of 1100^◦C. The figure presents the emission spectrum and the measured second order correlation as a function of the excitation power. From the data, we fitted a single decay function and extracted the multi-photon emission probability at each laser power.

Figure 42: Second order correlation function and spectra taken for different excitation powers We can see the the photon purity g²(0), is reduced with higher excitation power. This is due to the increased background radiation from the substrate which as we have shown previously, increases with excitation power, effectively giving lower signal (hBN emission) to noise (background fluorescence) ratio. We can plot the variation of g²(0) with the excitation power.

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Figure 43: Variation of g²(0) with the excitation power plotted on a log x-axis of base 2 We can see that g²(0) grows linearly with the log of the excitation power. Thus we can expect to measure lower values of the second order correlation function at lower powers due to low noise.

Nevertheless, at low powers, the Signal counts start approaching the dark counts of the APDs giving us in the end a more noisy measurement and thus a higher error on the value of g²(0) as can be seen in figure 42.

This behavior of the photon purity is not unique to this emitter and was measured on others as can be seen below, we also checked that the same behavior is still observed at higher powers as shown in the following figure. Note than, in all the previous measurements a band-pass filter of 10nm was used to filter a single emission peak of the observed spectrum

Figure 44: Variation of g²(0) with the excitation power for a different emitter

Interestingly, some of the located pure emitters deliver non classical emission characteristics , even without using a bandpass filter. We measured second correlation function of the emitter shown in figure 45, under two conditions, the first is unfiltered emission and the second was using 10nm band-pass filter, the coupled spectra to the APD in both cases are shown in the figure.

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Figure 45: Filtered and unfiltered g²(τ ) for an emitter at 630 nm at 250 µW

For the unfiltered measurement we can see that the value g²(0) is about 0.86 meaning that we observe anti-bunching, but not single photon emission. After filtering, most of the background noise is removed and g²(0) dips bellow 0.5 confirming the single photon nature of the source. This result remarkably shows the potential of hBN as single photon emitters on chip, the fact that non classical behaviour was observed with mainly laser filtering is very promising. Indeed, hBN could be used on-chip as a single photon source without setting challenging requirements for the filtering to retain the quantum nature of the emission [38].

At low temperature, the same linear behavior of the second order correlation function was observed. In addition, due to lower background fluorescence, we managed to take several unfiltered (meaning that only the exciting laser was filtered using a 550 nm long pass filter as shown in figure 16) correlation measurements which all yielded g²(0) values under 0.5. Proving the quantum nature of the emitter presented in figure 24.

Figure 46: Variation of g²(0) (unfiltered) with the excitation power for the emitter presented in figure 24 at 200 mK

This is an additional argument for the potential use of hBN as a viable single photon source, since it provides singles photon statistics without need of any filtering. This in turns simplifies greatly the design of photonic circuits by removing filtering elements such as Bragg gratings and ring resonators.

By using superconducting single photon detectors (SSPDs) the measured photon purity could be higher still, given the potentially noiseless operation of these detectors.

Hybrid integration of hBN quantum sources in SiN photonic circuits