Coherent single photon source

Abstract

The invention relates to a coherent single photon source (100) comprising: a nanodiamond (120) having a quantum emitter (140), wherein the nanodiamond (120) and the quantum emitter (140) are designed and configured such that the quantum emitter (140) emits coherent, indistinguishable photons (160). The invention further relates to a system (300) comprising: a first coherent single photon source (101); and a second coherent single photon source (102); wherein the first coherent single photon source (101) and the second coherent single photon source (102) are designed and configured such that photons (160) emitted from a first quantum emitter (151) of a first nanodiamond (121) of the first coherent single photon source (101) are indistinguishable from photons (160) emitted from a second quantum emitter (152) of a second nanodiamond (122) of the second coherent single photon source (102).

Description

[0001] Description

[0002] COHERENT SINGLE PHOTON SOURCE

[0003] The invention relates to a coherent single photon source, a system comprising two such single photon sources, and a use of such a coherent single photon source or such a system to generate entanglement.

[0004] In the emerging field of quantum technologies, the distribution of entanglement is a key ingredient, for example to establish long-distance quantum state transfer and quantum networks. One possible source of distributed entanglement generation is two-photon interference, commonly known as Hong-Ou-Mandel (HOM) interference. A prerequisite are single photon sources that produce indistinguishable photons. Two-photon interference has been demonstrated with different sources of single photons, for example atomic vapors, quantum dots, molecules, coupled atom-cavity systems and negatively-charged Nitrogen-Vacancy (NV-) centers in bulk-diamond.

[0005] In the prior art coherent single photon sources are known. It is known in the prior art how to produce nanodiamonds. It is known that nanodiamonds with SiV" centers can alternatively be produced by chemical vapor deposition (CVD).

[0006] An object of the invention is to improve the prior art. In particular, it is an object of the invention to supply an alternative coherent single photon source that produces indistinguishable photons. It is another object of the invention to supply such a single photon source which is miniaturized. It is yet another object of the invention to supply such a single photon source wherein the coupling strength of the emitted photons to a cavity can be controlled to a high degree. Another object of the invention is to supply at least a building block of a quantum network. It is yet another object of the invention to increase an operational bandwidth of a quantum node which may be realized using an above mentioned coherent single photon source. It is yet another object of the invention to supply a miniaturized coherent single photon source which can be nano manipulated. It is yet another object of the invention to supply a tool which can realize quantum key distribution, entanglement swapping between remote nanodiamonds and to realize a quantum repeater. It is yet another object of the invention to supply a means by which it is possible to create remote entanglement between remote quantum emitters in remote nanodiamonds. It is yet another object of the invention to supply a building block comprising a quantum emitter which can be scaled up to a large-scale system comprising a large number of entangled quantum emitters or a large quantum network. It is yet another object of the invention to supply a quantum emitter system which can be coupled with existing photonics materials to build a hybrid quantum photonics device, i.e. a device that combines a quantum emitter system with a well- studied photonic material. It is yet another object of the invention to supply a basic building block with which novel cooperative quantum materials can be build.

[0007] The object of the invention is solved by a coherent photon source having the features of independent claim 1. Preferred embodiments of the invention are disclosed in the dependent claims.

[0008] A nanodiamond is understood to be a diamond particle which is so small that it is measured in nanometers, i.e. a size of this particle is smaller than 1000 nm. The size of a particle is understood to be the largest extent of the particle along a given axis when measured in different coordinate systems.

[0009] A quantum emitter may be understood to be a quantum system that is capable of radiative optical transitions. When observing the spontaneous decay of a single excited quantum emitter, the emission of a single photon is expected. When suppressing non- radiative decay mechanisms, a quantum emitter can principally act as 100% efficient single-photon sources. The variety of systems offered by nature allows a multitude of possible experiments and implementations of photonic applications. A quantum emitter may e.g. be a single atom in a high-finesse cavity, a colloidal nanocrystal of different size, a color center in a solid, a quantum dot, or a nanowire quantum dot structure.

[0010] In the past decades, single quantum emitters have become a manifold tool for the development of new light sources, such as lasers, LEDs, and single-photon sources, for nano-electronic devices, but also in chemistry and life sciences where they act as nanoscopic probes and labels. Especially in the emerging field of quantum information processing, quantum emitters are utilized as sources for single photons or as stationary quantum bits.

[0011] The present claim deals with a single photon source comprising a single nanodiamond having at least one quantum emitter, wherein the nanodiamond and the quantum emitter are designed and configured such that the quantum emitter emits coherent, indistinguishable photons.

[0012] For this case that a single particle or a single source emits coherent, indistinguishable photons it is necessary that emitted photons of this single source are temporally indistinguishable with themselves. An advantage of the coherent single photon source according to the present invention is that a miniaturized coherent single photon source of indistinguishable photons is supplied.

[0013] Another advantage of the present invention is that this coherent single photon source of indistinguishable photons constitutes an alternative solution to the coherent single photon sources of indistinguishable photons known in the prior art.

[0014] A cooperative quantum material may be defined by indistinguishable quantum emitters, e.g. individual SiV- centers in a nanodiamond or nanodiamonds, which can be positioned within a spatial distance on the order of or below the optical transition wavelength such that the quantum emitters can behave collectively with increased dipole strength, in particular, in form of superabsorption or superradiance.

[0015] As the coherent single photon source of indistinguishable photons according to the present invention is miniaturized in the nanometer scale it can be nano manipulated and be placed inside a resonator, e.g. in the mode of a resonator, with almost arbitrary precision, i.e. on the nanometer scale, using atomic force microscopy(AFM)-based nanomanipulation. Thus, a coherent single photon source of indistinguishable photons is supplied wherein the coupling strength of the emitted photons to the cavity mode can be controlled to a very high degree.

[0016] Yet another advantage of the present invention is that the coherent single photon source may be used as a quantum node in a larger quantum network.

[0017] Yet another advantage of the coherent single photon source is the possibility of engineering of quantum light fields, in particular path-entangled light fields such as NOON states, based on a deterministic scheme resting on the principle of Hong-Ou- Mandel Interference. A NOON state or NOON state is a quantum-mechanical manybody entangled state, which represents a superposition of N particles in mode a with zero particles in mode b, and vice versa. Current schemes of the prior art are based on probabilistic schemes utilizing typically parametric down-conversion sources (PDCS) with limitations in scaling to large photon number states, e.g. N > 20. Such entangled, quantum light fields can advantageously be utilized for quantum sensing of, e.g. phase estimation, offering sensitivity beyond the classical limits given by the standard quantum limit. The integrateability of the nanodiamonds enables on-chip operation of such sensing device in the future.

[0018] Yet another advantage of the coherent single photon source is that it can be used as a quantum repeater. A quantum repeater is an important component for quantum communication over long distances which overcomes the drawbacks in quantum communication of decoherence and photon loss in long distance fiber communication. As with the classical repeater in digital communication technology, repeaters are used to renew the signal between transmitter and receiver. However, since due to the nocloning principle amplification or copying of a signal is not possible in a quantum mechanical state, the quantum repeater is based on the principle of entanglement swapping and / or entanglement distillation or purification. Between the stations of sender Alice and receiver Bob there are a number of repeater stations, which can receive, store, and transmit classical and quantum mechanical signals, respectively. The storage of quantum mechanical states is done in a quantum memory. For the quantum repeater protocol, states are first entangled in quantum memories of neighboring repeater stations. Now, each of the inner repeater stations shares at least two entangled states, one with each neighbor. Such a pair of entangled states enables entanglement swapping to create entanglement between states of neighboring stations. Entanglement swapping at each station generates entanglement between the first and last repeater stations, which then enables transmission of quantum states via quantum teleportation from Alice to Bob.

[0019] A single nanodiamond may comprise multiple quantum emitters, preferably between 1 and 100. A single substrate may comprise multiple single nanodiamonds, e.g. more than 1000. The quality of the produced single nanodiamonds depends on their production method.

[0020] Each nanodiamond may be addressed individually. It is possible to measure a photoluminescence spectrum of various atomic transitions of each quantum emitter. An individual atomic transition of an individual quantum emitter is addressable by resonant photoluminescence excitation (PLE).

[0021] Preferably only a single quantum emitter is used in a nanodiamond. Preferably the single quantum emitter is located inside the nanodiamond.

[0022] Preferably the single quantum emitter is located in the center of a nanodiamond, where it is well-protected from any influence of the surface. At the same time it is preferred that it is located close enough to the surface, i.e. well below the wavelength of light, to enable efficient optical coupling to the outside.

[0023] Preferably, a quantum emitter which should not be used inside a nanodiamond can be modified to become dark. This can be done using a plasma treatment or in particular a hydrogen or oxygen termination of the surface of the nanodiamond. According to another embodiment, a specific quantum emitter of the nanodiamond can be spectrally selected, which means that only the atomic transition of this specific quantum emitter is used while the atomic transitions of other quantum emitters are spectrally blocked or not used.

[0024] It is preferred that a nanodiamond comprises a single quantum emitter which is used to generate coherent, indistinguishable photons.

[0025] According to a preferred embodiment the nanodiamond is selected from a sample of produced nanodiamonds. According to another preferred embodiment a method to produce the sample of nanodiamonds is a high pressure-high temperature (HPHT) fabrication method or chemical vapor deposition (CVD).

[0026] An advantage of the high pressure-high temperature (HPHT) fabrication method is that the produced nanodiamonds usually have low strain, which implies that the inhomogeneous linewidth is narrower. An advantage of the chemical vapor deposition (CVD) fabrication method is that the produced nanodiamonds comprise a higher isotopic purity.

[0027] The nanodiamond is preferably selected from the sample of produced nanodiamonds according to at least one of the following criteria: homogeneous linewidth, inhomogeneous linewidth, optical properties, addressability of the nanodiamond on a substrate, frequency stability of a relevant atomic transition, in particular the atomic transition which is used to generate indistinguishable photons, yielding frequency stability to enable the emission of temporal coherent single photons and a high likelihood of finding multiple indistinguishable SiV- centers in multiple nanodiamonds, brightness, single photon purity.

[0028] The nanodiamonds may be produced in samples. The number of produced nanodiamonds in a produced sample may be larger than 100, preferably larger than 1000.

[0029] A method of selecting a nanodiamond from a sample of produced nanodiamonds, wherein each of the produced nanodiamonds comprises a quantum emitter, may comprise the following steps. The nanodiamond is selected from the sample of produced nanodiamonds such that a homogeneous linewidth of an atomic transition of the quantum emitter of the nanodiamond is smaller than two times a Fourier-Transform limit of this atomic transition, and that for a time scale larger than 1 minute a difference between a maximum of a frequency of the atomic transition and a minimum of the frequency of the atomic transition is smaller than two times the Fourier-T ransform limit of this atomic transition. This selection surprisingly enables the coherent single photon source to emit coherent, indistinguishable photons.

[0030] If two nanodiamonds are selected, these two nanodiamonds may be used to generate indistinguishable photons that may generate two-photon interference.

[0031] According to another method a single nanodiamond may be selected such that a homogeneous linewidth of the atomic transition of the quantum emitter of the nanodiamond is smaller than two times a Fourier-Transform limit of this atomic transition, wherein the atomic transition is used to emit indistinguishable photons. This selected nanodiamond may be used to generate indistinguishable photons.

[0032] Preferably the method to select one or more diamonds may include a spectrum of the used atomic transitions, a strength and / or distribution of a strain inside the nanodiamond and other quality features of a quantum emitter inside a nanodiamond.

[0033] According to a preferred embodiment the second order correlation function at zero-time delay of the emitted light or the emitted photons is smaller than 0.5, preferably smaller than 0.35. The second order correlation function g^(r) is well known in the art. It is a standard measurement known in the art to determine whether the nature of the measured light is quantum or classical. Here the second order correlation function refers to an intensity correlation between two output ports of a beam splitter with just one input signal from one quantum emitter. A correlation measurement between the intensity of the two output ports of a beam splitter with two input components is performed to determine the indistinguishability of the photons of the two input ports. A correlation measurement with two input components is performed to determine the second order correlation function. A first input component of the correlation measurement comprises light emitted from the quantum emitter and a second input component of the correlation measurement comprises light from the quantum emitter which may be time delayed relative to the first component by an amount At. T from the second order correlation function g^(r) is a time delay between the first output signal and the second output signal of the beam splitter. The second-order correlation function g^(r) at point T equals zero is zero for identical, i.e. indistinguishable photons and 0.5 for distinguishable photons. The formula g^(r = 0) < 0.5 means that the photons of the first input component and the second input component are indistinguishable.

[0034] The time delay At may e.g. 0 seconds. According to another preferred embodiment the time delay At is larger than a time difference which is larger than 1 second. This means that the coherence time is larger than above-mentioned time difference. This advantageously achieves an extremely large coherence time which is way longer than for comparable systems realized in solid states.

[0035] According to another embodiment in which there is noise present during the measurement of the second order correlation function (r) it is preferred to use an efficiency factor g as an alternative measure to decide when the quantum emitter emits indistinguishable photons. The efficiency factor g is part of equation 1 which is at the end of the description and can be determined by a fit which is explained with respect to equation 1 . For the emission of indistinguishable photons, the efficiency coefficient g is larger 0. It is preferred that the efficiency coefficient g is larger than 0.3, and it is even more preferred that it is larger than 0.9.

[0036] These indistinguishable photons can advantageously be used for entanglement distribution, which is a key ingredient, for example to establish long-distance quantum state transfer and quantum networks.

[0037] According to a preferred embodiment of the invention the size of the nanodiamond is smaller than a wavelength of the emitted photons. Here, the relevant wavelength of the emitted photon preferably is a used atomic transition as described below. It is further preferred that the size of the nanodiamond is smaller than 100 nm. It is yet further preferred that the size of the nanodiamond is smaller than 30 nm.

[0038] According to a preferred embodiment the quantum emitter is a color center. According to another preferred embodiment the quantum emitter is a group IV defect center, in particular a group IV color center. A group IV color center may e.g. be a neutral- charged silicon vacancy (SiVO) center, a negatively-charged germanium vacancy (GeV- ) center, a negatively-charged tin vacancy (SnV') center or a negatively-charged lead vacancy (PbV') center. According to yet another especially preferred embodiment the quantum emitter is a single negatively charged silicon vacancy (SiV") center. Group IV color centers in diamond and, in particular, the negatively-charged Silicon Vacancy (SiV-) center have intrinsic spectral stability and narrow homogeneous and inhomogeneous line distribution.

[0039] A homogeneous linewidth of an atomic transition of the quantum emitter is the individual linewidth of one specific quantum emitter in a specific nanodiamond. The homogeneous linewidth depends on the temperature of the color center and the crystal environment, a charge environment and an interaction of the environment with the color center. An inhomogeneous linewidth of an atomic transition of the quantum emitter refers to a width of a distribution of the linewidths of a multitude of quantum emitters which are in e.g. a whole sample of nanodiamonds which are e.g. on a common substrate. This inhomogeneous linewidth of an atomic transition of the quantum emitter depends on the quality or homogeneity of the sample of nanodiamonds, in particular the present strain in the nanodiamonds. Further, a local environment around the nanocrystal or nanodiamond has an influence on e.g. spectral diffusion, etc.

[0040] The homogeneous linewidth of an atomic transition used to generate indistinguishable photons is preferably smaller than two times the Fourier-Transform limit of this atomic transition.

[0041] The Fourier-Transform limit of an atomic transition is given by the Fourier transformation of the radiative lifetime of the optical transition given by the spontaneous emission rate in a free-space environment. The Fourier-Transform limit can be calculated by the formula Ato = 1 / T. The Fourier-Transform limit does not have any temperature dependence, if only the radiative relaxation channel is considered.

[0042] The SiV' center 150, which is a known quantum emitter 140 in the art, is a point defect in the lattice of a diamond crystal where one silicon atom Si is replacing two carbon atoms C and where the silicon atom Si is located between two adjacent vacant lattice sites V as depicted in Figure 1.

[0043] The SiV' center 150 can be thought of an artificial atom. The electronic level structure of the SiV' center 150 is illustrated in Fig. 2. Both the ground state 200 and the excited state 210 show a level splitting due to spin orbit coupling. Therefore, both the ground state 200 and the excited state 210 have doublets which are separated by AGS and AES respectively. The ground state 200 has a lower ground state 202 and an upper ground state 204. The excited state 210 has a lower excited state 212 and an upper excited state 214. This level splitting results in four optically active transitions, which can be observed at cryogenic temperatures. We refer to them as transitions A, B, C, D, as depicted in Fig. 2. Transition D is between the lower excited state 212 and the upper ground state 204, transition C is between the lower excited state 212 and the lower ground state 202, transition B is between the upper excited state 214 and the upper ground state 204, transition A is between the upper excited state 214 and the lower ground state 202. The wavelengths of the transitions A, B, C, D are known in the art.

[0044] The negatively-charged silicon-vacancy (SiV") center has robust intrinsic properties. In bulk diamond SiV" centers show good optical properties, with a high Debye-Waller factor of about 0.7, a narrow inhomogeneous linewidth in the range of few GHz and Fourier-Transform limited homogeneous linewidth at cryogenic temperatures. The spectral stability arises from the D3dsymmetry of the SiV" center and enables to achieve excellent optical properties even in close proximity to the diamond surface. Protecting the high-degree of symmetry demands high quality of the diamond host, in particular, a low strain environment. In chemical vapor deposition (CVD) nanodiamonds single photon emission from SiV" centers and photostable quantum emitters with subgigahertz linewidth were experimentally demonstrated. The production of low-strain nanodiamonds via high pressure-high temperature (HPHT) fabrication method enables to preserve the excellent optical properties of SiV" centers also in nanodiamonds.

[0045] In the case of the negatively-charged silicon-vacancy (SiV") center, the transition C is preferably used to generate indistinguishable photons or indistinguishable light. This is advantageous because the intensity of transition C is larger than the intensity of the other transition A, B or D. The natural linewidth of transition C is about 94 MHz at low temperatures of about 4 K, corresponding to the aforementioned Fourier-Transform limit. With increasing temperature the lifetime can be modified yielding an increase in natural linewidth by less than one order of magnitude at room temperature.

[0046] The linewidth of a quantum emitter inside a solid state depends inter alia from the environment and the environmental temperature. The linewidth of transition C of the negatively-charged silicon-vacancy (SiV") center is preferably smaller than 300 MHz, more preferably smaller than 200 MHz. According to even more preferred embodiments the transition C is smaller than 180 MHz and 100 MHz, respectively.

[0047] According to one embodiment, the inhomogeneous linewidth of the atomic transition C is smaller than 50 GHz, preferably smaller than 2 GHz. According to even more preferred embodiments the inhomogeneous linewidth of the atomic transition C is smaller than 500 MHz and 200 MHz, respectively. Preferably, the negatively-charged Silicon Vacancy (SiV-) center has a low strain environment, such that the above mentioned inhomogeneous linewidth can be achieved. The advantage of this feature is that the inhomogeneous linewidth of the atomic transitions of an ensemble of quantum emitters gets smaller leading to a higher yield of finding indistinguishable quantum emitters.

[0048] According to another preferred embodiment a surface of the nanodiamond is plasma treated, in particular hydrogen-terminated. This feature advantageously causes a negatively-charged Silicon Vacancy (SiV-) center which is close to the surface of the nanodiamond to become dark, i.e. it is not resonant any more. This can reduce the number of optically-active SiV- centers in the relevant wavelength range, where the spectrally more stable quantum emitters remain with an overall narrower inhomogeneous linewidth. This can achieve that an inhomogeneous ensemble linewidth is below the excited state splitting. In an experiment excellent spectral stability under resonant excitation was achieved with a surface of the nanodiamond being hydrogen-terminated.

[0049] According to another preferred embodiment the coherent single photon source further comprises a substrate on which the nanodiamond is located. The substrate may comprise a photonic device, an open resonator, a plasmonic device, a plasmon mode channel, and / or a metasurface. A device which is a photonic device and a phononic device at the same time is called a phonophotonic device.

[0050] A material for a photonic or phonophotonic device may e.g. be Si3N4. This material advantageously is a preferred material for industry-relevant chip technology enabling future integration into scalable photonic chip technology. Alternatively, the substrate could comprise a low fluorescence material with good thermal conductivity such as diamond, e.g. an electronic grade diamond plate, a quartz plate, a sapphire plate or a quartz coverslip. An optical resonator, in particular an open Fabry-Perot resonator or a fiber-based resonator, and on chip photonics, in particular a photonic crystal cavity or a bullseye antenna may comprise a such a material.

[0051] A coherent single photon source with an above-mentioned quantum emitter which comprises a photonic material as a substrate may alternatively be called a hybrid quantum photonics device.

[0052] According to another preferred embodiment a temperature of the photon source including the nanodiamond is below 20 K. This has the advantage that there are less phonons than at higher temperatures which means that e.g. the optical transitions of the used quantum emitter can be resolved much better. Both, the homogeneous and inhomogeneous linewidths are less broadened by electron-phonon interaction, and are therefore much narrower. Further, a coherence time of the quantum emitter is increased which is advantageous for quantum applications. With an increased coherence time, fewer quantum repeaters are required and quantum computer calculations are less prone to errors.

[0053] The coherence time of the quantum emitter determines the possible distance over which the quantum communication can be achieved. For the SiV- center the coherence time at 4 K is limited due to orbital relaxation in the two ground state levels introduced by phonons from a surrounding thermal bath with a frequency of about 46 GHz. The lifetime between these levels is called T1. There are three different methods to eliminate the mixing of ground states by phonons. First, cooling to milli- Kelvin temperatures achieves suppressing these phonons. Second, introducing strain thus increasing a splitting of the ground state. Third, by changing the size and / or geometry of the SiV- center surrounding material, it is also possible to eliminate mixing of ground states by phonons. As a result, phononic decoupling and prolonged orbital relaxation times can be achieved. It is further preferred that the temperature of the photon source is below 10 K. It is yet further preferred that the temperature of the photon source is below 5 K. The above-mentioned advantages increase with lower temperatures.

[0054] According to another embodiment the nanodiamond may be positioned and / or oriented using an atomic force microscope (AFM). This method is widely used and therefore standardized. It allows to pick and place nanodiamonds in an easy and reliable way.

[0055] According to a further preferred embodiment, the coherent single photon source further comprises a filter which is designed and configured to filter the photons which are emitted from the quantum emitter of the coherent single photon source. This advantageously achieves that distinguishable photons are filtered out such that the remaining photons have a higher degree of indistinguishability which is an object of the present invention. To filter the photons, a filter may be used. The filter may e.g. be a spectral filter, an etalon, a dichroic mirror, a prism, a grating or another wavelengthsensitive element. Preferably the filter has a center wavelength which corresponds to transition C of the SiV- center.

[0056] According to a different embodiment the coherent photon source further comprises a cavity which is designed and configured such that an atomic transition of the quantum emitter is coupled to a mode of the cavity.

[0057] This coupling advantageously achieves that the quantum state of the quantum emitter can be transferred to an electric field or photon inside the cavity. The photon inside the cavity may be coupled to a fiber which may be connected to a remote location which might be hundreds of kilometers away or to a waveguide on a photonic chip to distribute entanglement between different nodes on a chip or to a waveguide of on-chip quantum light field engineering. As mentioned above a quantum emitter which is part of the coherent single photon source may realize a quantum node. With the above-mentioned coupling different quantum nodes may be connected to form a quantum network.

[0058] Preferably the cavity is a photonic crystal cavity (PCC), an open Fabry-Perot cavity, a ring resonator, a plasmonic ring cavity, a bullseye antenna or a fiber-based cavity.

[0059] The photonic crystal cavity may e.g. be a one-dimensional photonic crystal cavity.

[0060] The cavity may be realized as a on chip resonator. Alternatively, the cavity may be an open resonator, e.g. a Fabry-Perot or fiber resonator.

[0061] In the case of a photonic crystal cavity, the cavity may be realized as a waveguide, in particular a waveguide including two 1D photonic crystal cavity mirrors.

[0062] According to a preferred embodiment the quantum emitter is located at a maximum of the field. This maximum may be a global or local maximum. Preferably the quantum emitter is located in an antinode of the cavity field.

[0063] According to a preferred embodiment a Purcell factor for the cavity, and the atomic transition of the quantum emitter is larger than 1. The Purcell effect is the shortening of a quantum system's excited state lifetime by its environment, e.g. an atom inside a resonant cavity. The magnitude of the enhancement is given by the Purcell factor which is well known in the art. The Purcell factor depends on a vacuum wavelength of the used atomic transition of the quantum emitter, a refractive index of the cavity material, a quality factor Q and a mode volume V of the used mode in the cavity. If the Purcell factor is greater than 1, the majority of photons are emitted into the single mode of the cavity. Preferably the used atomic transition is the transition C of the SiV- center. A high Purcell factor implies a strong coupling of the cavity field to the quantum emitter. Preferably the Purcell factor is larger than 4. More preferably the Purcell factor is larger than 14. A high coupling implies a high operational bandwidth of the quantum node which may be realized by the coherent photon source. A high Purcell factor increases the operation bandwidth due to a shorter lifetime and a high directionality of photon emission into the cavity mode. Furthermore, at highest Purcell factors a further boost can be realized due to improved quantum yield, meaning a suppression of non- radiative channels. Furthermore, a lifetime shortening due to the Purcell effect yields a correspondingly broadened Fourier-Transform limit of that transition, which in turn yields a relaxed condition to obtain indistinguishable photons. In the case of a quantum node, where atomic transitions are coupled to a PCC, the number of emitted photons into the cavity mode is one limiting factor for the operation bandwidth. The rate of the quantum node, which characterizes the bandwidth of an input-output channel, is a critical limiting factor for its operating speed. An enhancement of coupled emission using the Purcell effect increases the performance of a potential quantum network. Furthermore, improving the quantum yield leads to efficient connection of distant quantum nodes, high operation bandwidth and gives access to a larger variety of applicable protocols with, for example, improved security, better fault tolerance or higher fidelity.

[0064] According to an embodiment two or more quantum emitters can be located in a single nanodiamond. In that case the two or more quantum emitters are preferably located such that the maximum distance between each two quantum emitters is smaller than a wavelength of an emitted photon. This advantageously achieves that collective effects arise because at least two indistinguishable quantum emitters are positioned in a small volume, whose diameter is smaller than the wavelength of the optical transition. The increased dipole strength of the collective system leads to superradiance and / or superabsorption.

[0065] According to another aspect of the invention, the object of the invention is solved by a system which comprises a first coherent single photon source and a second coherent single photon source. Both the first coherent single photon source and the second coherent single photon source may be a coherent single photon source as described above. The first coherent single photon source and the second coherent single photon source are designed and configured such that photons emitted from a first quantum emitter of a first nanodiamond of the first coherent single photon source are indistinguishable from photons emitted from a second quantum emitter of a second nanodiamond of the second coherent single photon source. This system can alternatively be called an entity.

[0066] For the first quantum emitter or the second quantum emitter a wavelength of an emitted photon may correspond to an atomic transition of the respective quantum emitter.

[0067] This system advantageously realizes a source which can emit mutually indistinguishable photons. With such a source of indistinguishable photons one can perform two-photon interference, commonly known as Hong-Ou-Mandel (HOM) interference, in particular between remote locations. Here, a first input port of a beam splitter is impinged by photons from the first quantum emitter and a second input port of the beam splitter is impinged by photons from the second quantum emitter. The second-order correlation function may be measured between the two output ports to prove photon indistinguishability.

[0068] This system advantageously supplies a tool which can realize quantum key distribution, entanglement swapping between remote nanodiamonds and a quantum repeater.

[0069] Two-photon interference can be used for distributed entanglement generation which in turn is a key ingredient to establish long-distance quantum state transfer and quantum networks. Two-photon interference can also be used for multipartite entanglement distribution which is a basic building block for quantum computing, quantum networks and many other applications.

[0070] Two-photon interference was experimentally demonstrated for this system which will be explained with respect to the Figures.

[0071] Preferably a transition frequency of the first quantum emitter and the second quantum emitter is both spectrally stable, preferably on a time scale longer than one minute, and Fourier Transform limited.

[0072] According to another preferred embodiment the system comprises two or more coherent single photon sources. Each of the two or more coherent single photon sources may be a coherent single photon source as described above. For each pair of two coherent single photon sources of these two or more coherent single photon sources the photons emitted from a first quantum emitter of a first nanodiamond of this pair of two coherent single photon sources are indistinguishable from photons emitted from a second quantum emitter of a second nanodiamond of the second coherent single photon source of this pair of two coherent single photon sources. Preferably the system comprises more than two coherent single photon sources.

[0073] According to the embodiment according to which the system comprises two or more coherent single photon sources, it is further preferred that the atomic transition of each quantum emitter of each of the two or more coherent single photon sources is coupled to a single cavity mode of a common cavity. This advantageously achieves that collective effects arise because at least two indistinguishable quantum emitters are coupled to the same single mode of a cavity or optical resonator. The increased dipole strength of the collective system leads to superradiance and / or superabsorption.

[0074] According to a further preferred embodiment, both photons emitted from a first quantum emitter of the first coherent single photon source and photons emitted from a second quantum emitter of the second coherent single photon source are filtered. Photons emitted from the first quantum emitter of the first coherent single photon source and / or photons emitted from the second quantum emitter of the second coherent single photon source may be subject to different optical elements, like e.g. half-wave plates, polarizers or quarter-wave plates, spectral filter or the like.

[0075] This advantageously achieves that distinguishable photons are filtered out such that the remaining photons have a higher degree of indistinguishability which is the goal of the present invention. To filter the photons, the above-mentioned filters may be used.

[0076] According to another preferred embodiment the first coherent single photon source may comprise a first substrate and the second coherent single photon source may comprise a second substrate. This may be the case when the first coherent single photon source and the second coherent single photon source are separated from each other. However, according to a different embodiment the first coherent single photon source and the second coherent single photon source may comprise a common substrate on which both the first coherent single photon source and the second coherent single photon source are arranged.

[0077] This advantage of a first nanodiamond of the first coherent single photon source and a second nanodiamond of the second coherent single photon source being are arranged on the same substrate is that the nanodiamonds are subject to the same or very similar physical environment, e.g. temperature, vibrations, etc. According to yet another embodiment, more than two coherent single photon sources are arranged on the same substrate. Preferably the number of coherent single photon sources is larger than 1000. In this embodiment it is preferred that nanodiamonds with similar atomic transitions are spectrally selected such that an inhomogeneous linewidth is smaller than in a selection where the nanodiamonds are not spectrally selected.

[0078] The methods to produce the sample of nanodiamonds for the system are the same as for the coherent single photon source.

[0079] A method of selecting two nanodiamonds from a sample of produced nanodiamonds, wherein each of the produced nanodiamonds comprises a quantum emitter, may comprise the following steps. The first nanodiamond of the first coherent single photon source and the second nanodiamond of the second coherent single photon source are selected from a common sample of produced nanodiamonds such that a difference between a first frequency of an atomic transition of the first quantum emitter of the first nanodiamond and a second frequency of the atomic transition of the second quantum emitter of the second nanodiamond is smaller than two times a Fourier-T ransform limit of this atomic transition, and that both the first homogeneous linewidth of the atomic transition of the first quantum emitter of the first nanodiamond and the second homogeneous linewidth of the atomic transition of the second quantum emitter of the second nanodiamond are smaller than two times the Fourier-T ransform limit of this atomic transition, and that for a time scale larger than minute both a first difference between a maximum of the first frequency and a minimum of the first frequency and a second difference between a maximum of the second frequency and a minimum of the second frequency is smaller than two times the Fourier-T ransform limit of this atomic transition. This selection surprisingly enables the system to emit coherent, photons which are indistinguishable with respect to each other.

[0080] Preferably the atomic transition is used to emit indistinguishable photons.

[0081] According to a preferred embodiment of the system a second order correlation function at zero-time delay of the emitted light or the emitted photons is smaller than 0.5, preferably smaller than 0.35. Here, the second order correlation function refers to the two-photon wave function. Similar as in the case of the coherent single photon source a correlation measurement with two input components is performed to determine the second order correlation function. A first input component of the correlation measurement comprises light or photons emitted from the first quantum emitter and a second input component of the correlation measurement comprises light or photons emitted from the second quantum emitter. The second input component may also be time delayed relative to the first component by an amount At, however preferably there is no time delay. The statement about the second-order correlation function for the coherent single photon source which has only one quantum emitter which was given above also applies to the second-order correlation function for the system which uses two quantum emitters on two input ports. The second-order correlation function g2(r) at point T equals zero is zero for identical, i.e. indistinguishable photons and 0.5 for distinguishable photons. This means that the photons emitted from the first quantum emitter and the second quantum emitter are indistinguishable because the second- order correlation function g2(0) at zero time delay is below 0.5. This will be shown in detail with reference to the description of the Figures.

[0082] According to another embodiment in which noise is present during the measurement of the second order correlation function g^(r) it is preferred to use an efficiency factor g as an alternative measure to decide when the emitted photons from the first quantum emitter and the second quantum emitter are indistinguishable with respect to each other. The efficiency factor is explained in equation 1 at the end of the description and can be determined by a fit which is explained with respect to equation 1. For the emission of indistinguishable photons, the efficiency coefficient is larger 0. It is preferred that efficiency coefficient is larger than 0.3, and it is even more preferred that it is larger than 0.9.

[0083] These photons can advantageously be used for entanglement distribution which is a key ingredient, for example to establish long-distance quantum state transfer and quantum networks. It is preferred that the second order correlation function at zero-time delay of the emitted light or the emitted photons is below 0.1.

[0084] According to a preferred embodiment of the system a distance between the first nanodiamond of the first coherent single photon source and the second nanodiamond of the second coherent single photon source is larger than 1 meter. Preferably the distance between the first nanodiamond and the second nanodiamond is larger than 100 meters. It is further preferred that this distance is larger than 1 km and it is yet further preferred that the distance is larger than 100 km.

[0085] Preferably, the system comprises a first cavity and a second cavity, wherein the first cavity is designed and configured such that an atomic transition of the first quantum emitter is coupled to a mode of the first cavity, the second cavity is designed and configured such that an atomic transition of the second quantum emitter is coupled to a mode of the second cavity, and the first cavity and the second cavity are coupled. Preferably the first cavity and the second cavity are coupled with a fiber or free space. Alternatively, the outputs of the first cavity and the second cavity are sent on the two input ports of a beam splitter to perform the HOM interference measurement.

[0086] The advantage of this feature is that for the first quantum emitter and the second quantum emitter an entangled quantum state can be generated using two-photon interference. The emitted, indistinguishable photons from both the first quantum emitter and the second quantum emitter mediate an information exchange, e.g. via optical fiber or free-space transmission, finally impinging on the two input ports of a beam splitter to perform the Hong-Ou Mandel interference measurement. The system according to this embodiment can be used to generate a quantum network. This system has two indistinguishable quantum emitters. However, this system can be expanded such that it has a given number N of indistinguishable quantum emitters, wherein N is an integer number larger than two. According to another preferred embodiment of the system a distance between the first nanodiamond of the first coherent single photon source and the second nanodiamond of the second coherent single photon source is smaller than a wavelength of the emitted photon.

[0087] For the embodiment that the system comprises two or more coherent single photon sources, this means necessarily that the two or more coherent single photon sources have a maximum distance of the wavelength of the emitted photon. This advantageously achieves that collective effects arise because at least two indistinguishable quantum emitters are positioned in a small volume, whose diameter is smaller than the wavelength of the optical transition. The increased dipole strength of the collective system leads to superradiance and / or superabsorption.

[0088] An alternative formulation is that the first nanodiamond of the first coherent single photon source and the second nanodiamond of the second coherent single photon source are arranged in a volume that is smaller than the third power of the wavelength of the emitted photon.

[0089] For the first quantum emitter or the second quantum emitter a wavelength of an emitted photon may correspond to an atomic transition of the respective quantum emitter. The photons from the first quantum emitter and the second quantum emitter are indistinguishable.

[0090] That feature advantageously achieves superradiance effects of the coherent single photon sources. It is possible to use such a system to build or construct cooperative quantum materials. It is possible to prepare collective states in the Dicke regime.

[0091] According to another preferred embodiment the system further comprises a common cavity wherein an atomic transition of the first quantum emitter and an atomic transition of the second quantum emitter are coupled to a mode of the common cavity. This advantageously achieves that collective effects arise because at least two indistinguishable quantum emitters are coupled to the same single mode of a cavity or optical resonator. The increased dipole strength of the collective system leads to superradiance and / or superabsorption.

[0092] According to another preferred embodiment the system comprises a cavity, in particular a common cavity, wherein the first nanodiamond of the first coherent single photon source and the second nanodiamond of the second coherent single photon source are arranged within a volume of a single mode of the cavity. The mode is preferably a collective mode. Preferably the mode volume is smaller than 100 times, preferably 10 times, the third power of a wavelength of the emitted photon.

[0093] According to another aspect of the invention, the object of the invention is solved by a use of a nanodiamond having a quantum emitter as a coherent single photon source. As was shown above the coherent single photon source comprises a nanodiamond having a quantum emitter. It was shown above that such a nanodiamond can be used as a coherent single photon source.

[0094] According to another aspect of the invention, the object of the invention is solved by a use of two nanodiamonds each having a quantum emitter as a system having a first coherent single photon source and a second coherent single photon source.

[0095] According to another preferred embodiment, the above described system which comprises a first coherent single photon source and a second coherent single photon source may alternatively be realized with a single nanodiamond.

[0096] This alternative system comprises a nanodiamond having a first and a second quantum emitter, wherein a distance between the first quantum emitter and the second quantum emitter is smaller than a wavelength of an emitted photon. This advantageously achieves that collective effects arise because at least two indistinguishable quantum emitters are positioned in a small volume, whose diameter is smaller than the wavelength of the optical transition. The increased dipole strength of the collective system leads to superradiance and / or superabsorption.

[0097] Embodiments of the invention are shown in the drawings and will be explained in more detail in the following description.

[0098] Figure 3 shows a schematic illustration of a coherent single photon source according to an embodiment of the invention;

[0099] Figure 4 shows a photoluminescence spectrum of a SiV" center of a nanodiamond of a coherent single photon source according to an embodiment of the invention;

[0100] Figure 5 shows a sample of produced nanodiamonds on a substrate;

[0101] Figure 6 shows a basic experimental setup to realize a coherent single photon source according to an embodiment of the invention;

[0102] Figure 7 to 9 show a pick a place procedure to realize a coherent single photon source which is coupled to a photonic crystal cavity; Figure 10 shows an experimental setup to realize Hong-Ou-Mandel two-photon interference using a system having two coherent single photon sources according to an embodiment of the invention;

[0103] Figure 11 illustrates the basic principle of the Hong-Ou-Mandel interference;

[0104] Figure 12 shows an overview of a distribution of transition C in a sample of produced nanodiamonds;

[0105] Figure 13 shows a zoomed view into the distribution of Figure 12 showing multiple possible transitions suitable for measuring two-photon interference;

[0106] Figures 14 and 15 show photoluminescence spectra of two SiV" centers of a system according to an embodiment of the invention;

[0107] Figure 16 shows a filtered photoluminescence spectrum of one of the two SiV" centers of the system according to an embodiment of the invention;

[0108] Figure 17 shows a photo-luminescence-excitation (PLE) spectrum of the two SiV" centers of the system according to an embodiment of the invention;

[0109] Figure 18 and 19 show normalized correlation functions of the two SiV" centers of the system according to an embodiment of the invention;

[0110] Figure 20 shows a measurement result for a second order correlation function for a two-photon interference measurement;

[0111] Figures 21 and 22 show normalized correlation functions for the two SiV" centers of the system according to an embodiment of the invention in a zoomed-out version of Figure 18 and 19;

[0112] Figure 23 shows a measurement result for the second-order correlation function for a two-photon interference measurement in a zoomed-out version of Figure 20.

[0113] Figure 3 shows a coherent single photon source 100 comprising a nanodiamond 120 having a quantum emitter 140 which is a single negatively charged silicon vacancy (SiV") center 150. The nanodiamond 120 is depicted in a stylized manner. Fig. 3 should merely illustrate that the silicon vacancy (SiV") center 150 is located inside the nanodiamond 120. The nanodiamond 120 and the silicon vacancy (SiV") center 150 are designed and configured such that the silicon vacancy (SiV") center 150 emits coherent, indistinguishable photons 160.

[0114] A method to produce the sample of nanodiamond (120) is a high pressure-high temperature (HPHT) fabrication method or chemical vapor deposition (CVD). The SiV" centers 150 used in a series of embodiments are located inside nanodiamonds 120 with an average size of around 30 nm. The photoluminescence spectrum of the SiV" center 150 of Figure 3 for the atomic level structure the SiV" center 150 of Figure 2 is shown in Figure 4. A continuous-wave 532 nm laser may be used to excite the individual color centers off-resonantly. Figure 4 shows the intensity I in relative units as a function of the emitted wavelength A. The four peaks correspond to the 4 transitions A, B, C, and D. The wavelength difference between transitions B and A and transitions D and C corresponds to AGS of Figure 2 and the wavelength difference between transitions C and A and transitions D and B corresponds to AES of Figure 2.

[0115] According to this embodiment, the atomic transition used to generate coherent, indistinguishable photons 160 is the transition C of the SiV' center 150. The wavelength of transition C is about 737 nm. Therefore, the size of the nanodiamond 120 is much smaller than the wavelength of the emitted indistinguishable photons 160.

[0116] The nanodiamonds 120 are coated onto a diamond substrate 220 to ensure good thermal conductivity, see Figure 5.

[0117] For the coherent single photon source 100 there are several methods how to select the nanodiamond 120 from a sample of produced nanodiamonds 120. According to one embodiment the nanodiamond 120 is selected from a sample of produced nanodiamonds 120 such that a homogeneous linewidth of the atomic transition C of the silicon vacancy (SiV") center 150 of the nanodiamond 120 is smaller than two times a Fourier-T ransform limit of this atomic transition C and that for a time scale larger than 1 minute a difference between a maximum of a frequency of the atomic transition C and a minimum of the frequency of the atomic transition C is smaller than two times the Fourier-T ransform limit of this atomic transition C.

[0118] Nanodiamonds 120 which have SiV" centers 150 which blink or are located at an unwanted position inside the SiV" centers 150 can be plasma treated, in particular the surface of the relevant nanodiamond 120 may be hydrogen-terminated. This will make the relevant SiV" center 150 off resonant with the preferably used transition C.

[0119] The sample may be investigated by off-resonant photo-luminescence (PL) and resonant photo-luminescence-excitation (PLE) measurements showing predominantly single SiV" centers 150 and a spectral distribution of about 50 GHz for transition C. This means that the inhomogeneous linewidth of transition C is about 50 GHz. Figure 6 shows a schematic drawing illustrating an experimental setup to realize a quantum node. Figure 6 shows merely the basic elements to illustrate the working principle of such a quantum node, however a person skilled in the art understands that for clarity reasons not all elements are shown in detail in this Figure.

[0120] Figure 6 shows a coherent single photon source 100 with a cavity 280 which is designed and configured such that the atomic transition C of the SiV" center 150 is coupled to a mode of the cavity 280. The cavity 280 is realized as a photonic crystal cavity 282. The coherent single photon source 100 comprises a nanodiamond 120 having a SiV" center 150, wherein transition C of the SiV" center 150 is coupled to a mode of the photonic crystal cavity 282.

[0121] Efficient coupling is achieved by spatial overlapping the dipole of the SiV" center 150 with the cavity field maximum by means of AFM-based nanomanipulation and by frequency overlapping the resonance condition of the mode of the cavity 282 with the transition frequency of the SiV" center 150 by means of, e.g. resonance gas tuning.

[0122] A Purcell factor of the coupling of the photonic crystal cavity 282 with the atomic transition C of the single SiV" center 150 is larger than 10, in particular 14. The lifetime of the atomic transition C is shortened by the Purcell factor from which follows that the operational bandwidth of the quantum node is increased by the Purcell factor resulting in a significant efficiency boost of the quantum node. The lifetime shortening corresponds to an increased Fourier-Transform limited linewidth which relaxes the condition of finding indistinguishable optical transitions.

[0123] Figure 6 depicts the quantum node including its optical infrastructure up to the interface where the photons are coupled into an optical fiber 354 or collimated free-space optics for long range photon exchange.

[0124] The nanodiamond 120 and the photonic crystal cavity 282 are placed inside a cryostat 320. An objective 332 of a home-built confocal microscope is placed inside of the cryostat 320 while all other components of the confocal microscope are placed outside of the cryostat 320. The cryostat 320 may e.g. be a continuous flow-cryostat which can be operated at temperatures as low as 2.5 K. Here the temperature of the coherent single photon source 100 and the nanodiamond 120 is at local temperatures close to the temperature of the cryostat cold finger, at approximately 3 to 5 K. The cryostat 320 could also be a closed-cycle cryostat if no liquid Helium supply is present at the location of the quantum node. A laser 340 is used to excite the nanodiamond 120 inside the cryostat 320. The laser may e.g. be a continuous-wave 532 nm laser which could off-resonantly excite the SiV" center 150.

[0125] The laser beam 342 emerging from the laser 340 is deflected by a pellicle beam splitter 344 and focused into the objective 332 of the confocal microscope using two lenses 346. The optical path can be adjusted such that the laser beam 342 hits the nanodiamond 120.

[0126] The part inside the cryostat 320 which is located inside the square having a dashed line is shown enlarged on the right-hand side of Figure 6.

[0127] The photonic crystal cavity 282 comprises a first part which in the view of Figure 6 is depicted on the right-hand side and which is rod- or bar-shaped wherein the bar has a rectangular cross-section and comprises multiple holes 284 which are arranged along a longitudinal axis of the bar of the photonic crystal cavity 282. The axes of the holes 284 each run perpendicular to the axis of the bar of the photonic crystal cavity (PCC) 282. The nanodiamond 120 of the single photon source 100 is placed inside one of the holes 284. The nanodiamond 120 is located in an upper portion of this hole 284. The nanodiamond 120 can be placed inside one of the holes 284 by the so-called pick and place method which will be explained with reference to Figures 7 to 9.

[0128] The nanodiamonds 120 which are coated onto a diamond substrate 220, see Figure 5, can be picked up by a cantilever 230 of an atomic force microscopy (AFM), see Figure 7. The picked up nanodiamond 120 sticks to the cantilever 230 of the atomic force microscope and can be moved onto the photonic crystal cavity 282, see Figure 8, and be placed inside a specific hole 284 inside the photonic crystal cavity 282, see Figure 9.

[0129] A second part of the photonic crystal cavity 282 which in the view of Figure 6 is depicted on the left-hand side comprises a waveguide portion 286 which guides the photons 160 emitted from the SiV" center 150 into the mode of the photonic crystal cavity 282 towards a mirror portion 288 which reflects the photons 160 towards a lens portion 290 from which the photons 160 are focused into the objective 332 of the home-built confocal microscope.

[0130] After the laser beam 342 has excited the SiV" center 150 inside the nanodiamond 120, the SiV" center 150 will be in the excited state. A photon 160 emitted from the SiV" center 150 towards the mirror portion 288 will be reflected by the lens portion 290 into the objective 332 of confocal microscope. An optical path 348 of the emitted photons 160 emerges from the objective 332, goes through the two lenses 346, through the beam splitter 344 and is deflected by a galvo-scanner 350 from which the optical path 348 goes further through a long pass filter 352. Finally, the emitted photons 160 are coupled into a fiber 354. The emitted photons 160 may be sent through the fiber 354 to a remote location which can be more than 100 km away from the experimental setup of Figure 6. A quantum node may then be developed based on different protocols. For example, a projective measurement, done by the Hong-Ou-Mandel interferometer, could project two setups in a remotely entangled state, which could be the starting point to implement a quantum network technology. For the application of non-classical light field engineering a quantum sensor would be mostly implemented on chip while the optical setup delivers the optical addressing of the indistinguishable single photon sources on chip.

[0131] Figure 10 shows an experimental setup of a system 300 comprising a first coherent single photon source 101 and a second coherent single photon source 102, wherein the first coherent single photon source 101 and the second coherent single photon source 102 are designed and configured such that photons 160 emitted from a first SiV" center 151 of a first nanodiamond 121 of the first coherent single photon source 101 are indistinguishable from photons 160 emitted from a second SiV" center 152 of a second nanodiamond 122 of the second coherent single photon source 102. This indistinguishability can be proven by the Hong-Ou-Mandel effect and / or performing a two-photon interference, commonly known as Hong-Ou-Mandel interference, and measuring that the second order correlation function at zero-time delay of the emitted photons or the emitted light is smaller than 0.5 which will be shown in the following. As the setup of Figure 10 is complicated, the basic principle of the Hong-Ou-Mandel interference will be explained with reference to Figure 11.

[0132] Figure 11 shows a schematic illustration of a Hong-Ou-Mandel interference experiment.

[0133] The first coherent single photon source 101 comprises the first nanodiamond 121 and the first SiV" center 151. The second coherent single photon source 102 comprises the second nanodiamond 122 and the second SiV" center 152.

[0134] Both the first SiV" center 151 and the second SiV" center 152 can be prepared in the excited state using a laser which is not shown in Figure 11. In that state both the first SiV" center 151 and the second SiV" center 152 will emit a photon 160 at a random point of time. For the case that the photon 160 emitted from the first SiV" center 151 and the photon 160 emitted from the second SiV" center 152 are two identical photons 160 and enter a 50:50 non-polarizing beam splitter 367 within a so-called coalescence time window from two different input ports, the probability amplitudes for leaving at the same port will interfere constructively while the ones for leaving at different output ports interfere destructively. This means, that the two photons 160 entering the nonpolarizing beam splitter 367 will leave the non-polarizing beam splitter 367 together as a photon pair, either through the first exit port or the second exit port. For this case it is excluded, that the photons 160 exit through different exit ports. A measurement of the second-order correlation function g2(r) with identical photons 160 will therefore result in antibunching with a dip g2(0) = 0 in contrast to a dip g2(0) = 0.5, which is expected for two single but distinguishable photons 160.

[0135] In the following, the experimental setup of Figure 10 will be explained in detail.

[0136] The two nanodiamonds 121 , 122 of the system 300 are selected from a sample of produced nanodiamonds 120 in a similar way as a single nanodiamonds 120 is selected for the coherent single photon source 100. According to one embodiment the first nanodiamond 121 of the first coherent single photon source 101 and a second nanodiamond 122 of the second coherent single photon source 102 are selected from a common sample of produced nanodiamonds 120 such that a difference between a first frequency of the atomic transition C of the first SiV" center 151 of the first nanodiamond 121 and a second frequency of the atomic transition C of the second SiV" center 152 of the second nanodiamond 122 is smaller than two times a Fourier- Transform limit of this atomic transition C and that both the first homogeneous linewidth of the atomic transition C of the first SiV" center 151 of the first nanodiamond 121 and the second homogeneous linewidth of the atomic transition C of the second SiV" center 152 of the second nanodiamond 122 are smaller than two times the Fourier-Transform limit of this atomic transition C and that for a time scale larger than 1 minute both a first difference between a maximum of the first frequency and a minimum of the first frequency and a second difference between a maximum of the second frequency and a minimum of the second frequency is smaller than two times the Fourier-Transform limit of this atomic transition C.

[0137] The sample of produced nanodiamonds 120 was placed inside a continuous-flow cryostat 320 and cooled with liquid helium to around 4 K. The nanodiamonds 120 are coated onto a diamond substrate 220 for good thermal conductivity and reach local temperatures between 5 K and 10 K. To select or find a matching SiV" pair, i.e. a first SiV" center 151 and a second SiV" center 152 which fulfil the above-mentioned requirement, one may first fix a frequency of a scanning laser to the resonance of transition C of either the first SiV" center 151 or the second SiV" center 152 and then scan the sample laterally. By doing that only SiV" centers which are resonant with the fixed laser frequency will be found.

[0138] Figure 12 shows a bar chart distribution 390 for a number or occurrences N of how many SiV" centers 150 of the nanodiamonds 120 have a specified position P for the transition C in a sample of produced nanodiamonds 120. The specified position P for the transition C is given in THz. E.g. in the sample of produced nanodiamonds 120 there are 14 SiV" centers 150 with a frequency for the transition C of about 406.82 THz. A fit function 392 was fitted to the bar chart distribution 390. The fit function 392 is a Gaussian distribution with a standard deviation of around 50 GHz. That means that the fit function 392 shows an inhomogeneous distribution for the position P of the transition C of around 50 GHz. Stated differently, the inhomogeneous linewidth for transition C is around 50 GHz in the sample of produced nanodiamonds 120.

[0139] The two nanodiamonds 121 , 122 may be selected from the sample of produced nanodiamonds 120 such that the two SiV" centers 151, 152 fulfil the above-mentioned condition.

[0140] Figure 13 shows for a part of the sample of produced nanodiamonds 120 for each plotted SiV" center 150 of a nanodiamond 120 the measured homogenous linewidth LW in MHz for the position P for the transition C. The size of each dot is the same, however, two or more dots whose corresponding SiV" centers 150 have an overlap of their corresponding frequency distribution are easy to find. This frequency distribution can also be called distribution of transition C. For each measured dot the frequency distribution is centered at position P and has a linewidth LW. Vertical dotted lines indicate different SiV" centers 150 with significant overlapping frequency distribution. Two SiV" centers 150 which are used as the first SiV" center 151 of the first nanodiamond 121 and the second SiV" center 152 of the second nanodiamond 122 are marked with a circle. These two SiV" centers 151, 152 are used for the two-photon interference. The two SiV" centers 151, 152 are in two remote nanodiamonds 121, 122, which are separated by approximately 100 pm.

[0141] A spectrum 400 of the first SiV" center 151 of the first nanodiamond 121 is shown in Figure 14. The first nanodiamond 121 is the same nanodiamond as in Figures 3 and 4 of the embodiment of the coherent single photon source 100. A spectrum 410 of the second SiV" center 152 of the second nanodiamond 121 is shown in Figure 15. In both Figure 14 and Figure 15 the atomic transitions A, B, C and D are indicated. Further, in both Figure 14 and Figure 15 the ground state spitting AGS and the excited state splitting AES are indicated. The ground state spitting AGS of first SiV" center 151 and the ground state spitting AGS of the second SiV" center 152 differs by 12 GHz. However, transition C shows a good overlap for the first SiV" center 151 and the second SiV" center 152. The fact that transition C overlaps although the ground state spitting of both the first SiV" center 151 and the second SiV" center 152 differs can be explained by different combinations of axial and transverse strain of the host crystal.

[0142] Coming back to Figure 10 which shows the experimental setup of system 300 which is used to show two-photon interference.

[0143] Both the first coherent single photon source 101 and the second coherent single photon source 102 are placed inside the cryostat 320 on the substrate 220. The part inside the cryostat 320 which is inside a circle with a dashed line is shown enlarged next to it. The first nanodiamond 121 and the second nanodiamond 122 are placed on the substrate 220.

[0144] The first nanodiamond 121 comprises the first SiV" center 151, and the second nanodiamond 122 comprises the second SiV" center 152. A laser 340 is used to off- resonantly excite the first SiV" center 151 and the second SiV" center 152. The beam of the laser 340 is first deflected by a mirror 356 and then after a half wave plate 362 and a 50:50 polarizing beam splitter 358 split into two optical paths, i.e. a first optical path 359 and a second optical path 360 which both end inside the cryostat 320. The half wave plate 362 and the 50:50 polarizing beam splitter 358 allow to adjust the excitation power for the first optical path 359 and a second optical path 360 and thus balance the emission from the first SiV" center 151 and the second SiV" center 152.

[0145] In the first optical path 359, there is a mirror 356, a dichroic mirror 364, a galvo 350, a lens 346, another mirror 356, a knife edge prism 365 and another lens 346 before the cryostat 320. In the second optical path 360 there is a dichroic mirror 364, a galvo 350, and a lens 346. The knife edge prism 365 is used to divide the field of view of the confocal setup into two independent channels. The beam of the laser 340 is focused on the first SiV" center 151 using the first optical path 359, and on the second SiV" center 152 using the second optical path 360.

[0146] Photons 160 emitted from the first SiV" center 151 can travel back via the first optical path 359 through the dichroic mirror 364. After the dichroic mirror 364 the optical path is drawn by a dashed line. After the dichroic mirror 364 the emitted photons 160 hit two mirrors 356, and go through a long pass filter 352, an etalon 361 and a half wave plate 362 before entering a first port of a 50:50 non-polarizing beam splitter 367.

[0147] Photons 160 emitted from the second SiV" center 152 can travel back via the second optical path 360 through the dichroic mirror 364 in the second optical path 360. The optical path after the dichroic mirror 364 is drawn by a dashed line. After the dichroic mirror 364 the emitted photons 160 hit a mirror 356, and go through a long pass filter 352, an etalon 361 and a half wave plate 362 before entering a second port of the 50:50 non-polarizing beam splitter 367. This non-polarizing beam splitter 367 is the place, where the two-photon interference or Hong-Ou-Mandel interference takes place.

[0148] The dichroic mirror 364, the long pass filter 352, and the etalon 361 are used both in the first optical path 359 and second optical path 360 to filter the photons 160 emitted from the first SiV" center 151 and the second SiV" center 152. If further suppression of unwanted signal is required, a second etalon per path can be used with slightly varied thickness to enable suppression over a broad wavelength range.

[0149] The long pass filter 352 is a 740 / 13 band-pass filter. The etalon in the first optical path 359 has a free spectral range (FSR) of 850 GHz and a linewidth of 90 GHz, the etalon 361 in the second optical path 360 has a FSR of 10 GHz and a linewidth of 1 GHz.

[0150] The two half wave plates 362 before the 50:50 non-polarizing beam splitter 367 are used to adjust the polarization in the respective optical paths 359, 360.

[0151] If a photon 160 from the first optical path 359 enters the non-polarizing beam splitter 367 simultaneously with an indistinguishable photon 160 from the second optical path 360, i.e. within a coalescence time window, the two-photon interference will take place. This means, that the two indistinguishable photons 160 entering the beam splitter 367 will leave the non-polarizing beam splitter 367 together as a photon pair, either through the first exit port or the second exit port.

[0152] The photons 160 exiting the non-polarizing beam splitter 367 at the first exit port or the second exit port are collected with two single mode fibers 369 which each are coupled to fiber couplers 366, detected by single photon counting modules (SPCM) 368 and correlated with a time tagger device 370.

[0153] To increase the probability that two indistinguishable photons 160 arrive at the nonpolarizing beam splitter 367 it is preferred that the photons 160 emitted from the SiV" centers 151, 152 are filtered. Figure 16 shows the filtered emission 420 from the first SiV" center 151.

[0154] A photo-luminescence-excitation (PLE) measurement 430 of the transition C for the first SiV" center 151 and a corresponding measurement 432 for the second SiV" center 152 show linewidths of 158 MHz and 177 MHz with a detuning A of ^=83 MHz to each other, as shown in Figure 17. Both the measurements 430 and 432 are measured as a function of the relative frequency v which is the frequency of the exciting laser minus a mean frequency of the peak values of the measurements 430 and 432. Both for the first SiV" center 151 and the second SiV" center 152 off-resonant, second-order correlation measurements were performed which were normalized.

[0155] The measured second-order correlation functions g^(r) for the first SiV" center 151 is shown in Figure 18, and the measured second-order correlation functions for second SiV" center 152 is shown in Figure 19. For the first SiV" center 151 ^2)(T = 0) equals 0.33 and for the second SiV" center 152 = 0) equals 0.35. This confirms single photon emission for both the first SiV" center 151 and the second SiV" center 152. (T) is used to measure the correlation functions including background noise, while the calligraphic g-2)(r) is used for the modeled correlation function without background. The index i equals 1 for the first SiV" center 151 and 2 for the second SiV" center 152. The measured data was fitted with where S(is the signal from the first SiV" center 151 or the second SiV" center 152, It = Si + Bi is the total signal including background counts BLand g = 1 +

[0156] [-(1 + a) ■ exp (-7^) + a ■ exp (-7^)] is a three level model of the correlation function. TXand T2correspond to the lifetimes of the two optical transitions of the three-level scheme, where T is the resonant lifetime, T2is the shelving time, and “a” is a free fit parameter. From the fit the signal to noise ratio 4 for either the first SiV" center 151 or the second SiV" center 152 can be determined, which will give a lower bound for the HOM dip. To measure the two-photon interference, both the first SiV" center 151 and the second SiV" center 152 are independently off-resonantly excited and the emitted photons 160 interfere on the 50:50 beam splitter 367 after the polarization of the photons 160 was matched by half-wave plates 362. The resulting correlation function is shown in Figure 20. Data 440 for parallel polarization are shown in dots, data 442 for perpendicular polarization are shown in triangles. A fit 441 to the data 440 for parallel polarization has a dashed curve. A fit 443 to the data 442 for perpendicular polarization has a solid curve.

[0157] Both for data 440 and for data 442, the data 440, 442 was fit with where ct 9^ C is a first order correlation function of the respective SiV" centers 151, 152, is the homogeneous linewidth of the respective SiV" centers 151 , 152, and A is the detuning. The equation of S'HOMW 'Scalled equation 1.

[0158] The signal and noise for each quantum emitter 140 were fixed with the previously determined signal to noise ratio of the individual correlation measurements of both SiV" centers 151, 152. The variable g in front of the interference term can be interpreted as an efficiency coefficient, where a value of 0 means no two-photon-interference and 1 means maximum interference. A value of 0.61 ±0.16 for g was determined for the case of parallel polarization. As an additional figure-of-merit a coalescence time window (CTW) can be calculated.

[0159] It gives a time-window for which coalescence can occur on the beam-splitter 367. By integrating over the visibility function VH0M= 1 - g^^ / g^ (T), it follows CTW = f VH0Md = (0.35 ± 0.20) ns, which is below the limit of 2Tltwhere T±« 1.9 ns is the excited state lifetime. The visibility function VH0Mis shown as curve 444 in Figure 20.

[0160] To determine the long-time dynamics of the first SiV" center 151 and the second SiV" center 152 the correlation functions of both emitters are analyzed. A three-level model for the correlation function is fit to them. We find a shelving time of around 25 ns for both the first SiV" center 151 and the second SiV" center 152. Therefore, the correlation functions #® (T) andarenormalized to 1 with the averaged value of #® (T) and S'HOMW with 75 ns < T < 100 ns as shown in Figures 21, 22 and 23.

Claims

Claims1. Coherent single photon source (100) comprising: a nanodiamond (120) having a quantum emitter (140), wherein the nanodiamond (120) and the quantum emitter (140) are designed and configured such that the quantum emitter (140) emits coherent, indistinguishable photons (160).

2. Coherent single photon source (100) according to claim 1 , characterized in that a size of the nanodiamond (120) is smaller than a wavelength of the emitted photons (160).

3. Coherent single photon source (100) according to claim 1 or 2, characterized in that a second order correlation function at zero-time delay of the emitted photons (160) is smaller than 0.5, wherein a first input component of a correlation measurement comprises photons (160) emitted from the quantum emitter (140) and a second input component of the correlation measurement comprises photons (160) from the quantum emitter (140) which is time delayed relative to the first component by a time difference which is larger than 1 second.

4. Coherent single photon source (100) according to any of the preceding claims, characterized in that the quantum emitter (140) is a group IV color center, in particular a single negatively charged silicon vacancy Si " center (150).

5. Coherent single photon source (100) according to any of the preceding claims, characterized in that a surface of the nanodiamond (120) is hydrogen-terminated.

6. Coherent single photon source (100) according to any of the preceding claims, further comprising:a filter (352, 361, 364) which is designed and configured to filter the photons (160) which are emitted from the quantum emitter (140) of the coherent single photon source (100).

7. Coherent single photon source (100) according to any of the preceding claims, characterized in that the nanodiamond (120) is selected from a sample of produced nanodiamonds (120) such that a homogeneous linewidth of an atomic transition (C, A, B, D) of the quantum emitter (140) of the nanodiamond (120) is smaller than two times a Fourier-Transform limit of this atomic transition (C, A, B, D); and that for a time scale larger than 1 minute a difference between a maximum of a frequency of the atomic transition (C, A, B, D) and a minimum of the frequency of the atomic transition (C, A, B, D) is smaller than two times the Fourier-Transform limit of this atomic transition (C, A, B, D).

8. Coherent single photon source (100) according to any of the preceding claims, further comprising: a cavity (280, 282) which is designed and configured such that an atomic transition (C, A, B, D) of the quantum emitter (140) is coupled to a mode of the cavity (280, 282).

9. Coherent single photon source (100) according to the preceding claim, characterized in that a Purcell factor for the cavity (282), and the atomic transition (C, A, B, D) of the quantum emitter (140) is larger than 1.

10. System (300) comprising: a first coherent single photon source (101) according to any of the preceding claims; and a second coherent single photon source (102) according to any of the preceding claims; wherein the first coherent single photon source (101) and the second coherent single photon source (102) are designed and configured suchthat photons (160) emitted from a first quantum emitter (151) of a first nanodiamond (121) of the first coherent single photon source (101) are indistinguishable from photons (160) emitted from a second quantum emitter (152) of a second nanodiamond (122) of the second coherent single photon source (102).

11. System (300) according to the preceding claim characterized in that the first nanodiamond (121) of the first coherent single photon source (101) and the second nanodiamond (122) of the second coherent single photon source (102) are selected from a common sample of produced nanodiamonds (120) such that a difference between a first frequency of an atomic transition (C, A, B, D) of the first quantum emitter (151) of the first nanodiamond (121) and a second frequency of the atomic transition (C, A, B, D) of the second quantum emitter (152) of the second nanodiamond (122) is smaller than two times a Fourier-Transform limit of this atomic transition (C, A, B, D); and that both the first homogeneous linewidth of the atomic transition (C, A, B, D) of the first quantum emitter (151) of the first nanodiamond (121) and the second homogeneous linewidth of the atomic transition (C, A, B, D) of the second quantum emitter (152) of the second nanodiamond (122) are smaller than two times the Fourier-T ransform limit of this atomic transition (C, A, B, D); and that for a time scale larger than 1 minute both a first difference between a maximum of the first frequency and a minimum of the first frequency and a second difference between a maximum of the second frequency and a minimum of the second frequency is smaller than two times the Fourier- Transform limit of this atomic transition (C, A, B, D).

12. System according to claim 10 or 11, characterized in that a second order correlation function at zero-time delay of the emitted photons (160) is smaller than 0.5, wherein a first input component of a correlation measurement comprises photons (160) emitted from the first quantum emitter (151) and a secondinput component of the correlation measurement comprises photons (160) emitted from the second quantum emitter (152).

13. System (300) according to claim 10, 11 or 12, characterized in that a distance between the first nanodiamond (120) of the first coherent single photon source (101) and the second nanodiamond (120) of the second coherent single photon source (100) is larger than 1 meter.

14. System (300) according to claim 10, 11 , or 12, characterized in that a distance between the first nanodiamond (121) of the first coherent single photon source (101) and the second nanodiamond (122) of the second coherent single photon source (102) is smaller than a wavelength of an emitted photon (160) or an atomic transition (C, A, B, D) of the first quantum emitter (151) and an atomic transition (C, A, B, D) of the second quantum emitter (152) are coupled to a mode of a common cavity (280, 282).

15. Use of a nanodiamond (120) having a quantum emitter (140) or two nanodiamonds (120) each having a quantum emitter (140) as a coherent single photon source (100) or a system having a first coherent single photon source (101) and a second coherent single photon source (102).

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