rus
DOI: 10.22184/1993-7296.FRos.2025.19.3.232.246
This review discusses various development methods for the single-photon sources (SPS).Earlier, the first part of the review (Photonics Russia. 2024; 18(5): 376–396) has discussed the requirements for single-photon sources and their characteristic criteria, and described the single-photon sources based on the single ions and single atoms. The second part of the review (Photonics Russia. 2024; 18(8): 610–620) has considered the SPSs based on the quantum dots and on the color centers in crystals. The third part (Photonics Russia. 2025; 19(1): 28–38) has considered the single-photon sources based on the carbon nanotubes and defects in them (defect engineering in nanotubes), on the nanocrystals and layered nanocrystals. The final section examines the single-photon sources on the collective states in the ensemble systems, on the single molecules and metal ions in a polymer matrix, as well as the sources on nonlinear crystals.
This review discusses various development methods for the single-photon sources (SPS).Earlier, the first part of the review (Photonics Russia. 2024; 18(5): 376–396) has discussed the requirements for single-photon sources and their characteristic criteria, and described the single-photon sources based on the single ions and single atoms. The second part of the review (Photonics Russia. 2024; 18(8): 610–620) has considered the SPSs based on the quantum dots and on the color centers in crystals. The third part (Photonics Russia. 2025; 19(1): 28–38) has considered the single-photon sources based on the carbon nanotubes and defects in them (defect engineering in nanotubes), on the nanocrystals and layered nanocrystals. The final section examines the single-photon sources on the collective states in the ensemble systems, on the single molecules and metal ions in a polymer matrix, as well as the sources on nonlinear crystals.
Теги: ensemble sources ensemble systems four-wave mixing (fwm) single molecules single-photon source (sps) ансамблевые источники ансамблевые системы одиночные молекулы четырехволновое смешение
Single Photon Sources. Review. Part 4
V. G. Krishtop
JSC “InfoTeСS”, Moscow, Russia
Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Moscow region, Russia
Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow region, Russia
This review discusses various development methods for the single-photon sources (SPS).Earlier, the first part of the review (Photonics Russia. 2024; 18(5): 376–396) has discussed the requirements for single-photon sources and their characteristic criteria, and described the single-photon sources based on the single ions and single atoms. The second part of the review (Photonics Russia. 2024; 18(8): 610–620) has considered the SPSs based on the quantum dots and on the color centers in crystals. The third part (Photonics Russia. 2025; 19(1): 28–38) has considered the single-photon sources based on the carbon nanotubes and defects in them (defect engineering in nanotubes), on the nanocrystals and layered nanocrystals. The final section examines the single-photon sources on the collective states in the ensemble systems, on the single molecules and metal ions in a polymer matrix, as well as the sources on nonlinear crystals.
Keywords: single-photon source (SPS), Ensemble systems, Ensemble sources, Single molecules, four-wave mixing (FWM)
The article received on: 01.08.2024
The article accepted on: 16.08.2024
Ensemble systems
The electromagnetic traps allow both single particles and groups of particles, i. e., atom ensembles, to be held and studied [167–169]. The single-photon sources “on demand” have been developed that use collective excitations in the atom ensembles [170–173]. The atom ensembles can theoretically [174, 175] enhance a single photon state due to the superradiance phenomenon, i. e., coherent collective radiation due to the correlation between the atom phases and amplitudes in the ensemble. The atoms in the ensemble obtain a collective coherent state (the so-called Dicke state, for more details please read [176–179]) and emit coherent radiation as united large dipole.
The atoms in the ensemble have the energy levels consisting of two metastable ground states |g and |u and one excited state |e (Fig. 15). All atoms are first optically pumped to the state |u. Then a weak writing pulse that corresponds to the transition |u → |e, probabilistically develops a single collective excitation, thus causing the signal photon emission at the transition |e → |g with a low probability. The registration of a single signal photon indicates successful excitation. The “writing” laser pulse is made weak to reduce the probability of exiting of more than one photon-atom-spin excitation. Then a strong read-out pulse deterministically returns the single excitation to its original state, while generating exactly one photon at the |e → |u transition.
To increase the coherence time and improve the efficiency of single-photon emission of an ensemble of single atoms, the dipole traps or optical lattices are used. Moreover, it is necessary to comply with the momentum conservation law for the writing pulse, the read-out pulse, and the emitted photon.
The main efforts in the field of studying quantum ensembles are related to the hope of developing quantum memory [180–184] and quantum repeaters [185–187]. At present, the experimentally demonstrated coherence time of spin waves in the atom ensembles Cs and Rb is several milliseconds [180–182].
It is interesting that a wide variety of quantum objects can unite into an ensemble, demonstrate coherent effects and produce single-photon radiation. For example, the quantum ensembles of semiconductor quantum dots [188], diamond nanocrystals [189, 190], and core/shell/shell nanocrystals [191] have already been experimentally proven. It has also turned out that the quantum objects with a distance between them significantly greater than the wavelength can be combined into the quantum ensemble [179, 192]. Relatively recently, an ensemble of single atoms in the waveguide with a distance greater than the wavelength has been experimentally demonstrated [193].
Single molecules
A very fleeting analogue of ensemble systems can be the single molecules. For the single-photon emitters, rather comprehensive organic molecules consisting of tens of atoms are used, for example, chromophore-containing polymers. To draw the analogy, it is enough to imagine that the atoms that make up such a molecule formed an ensemble of quantum particles, in which the necessary collective excitations are available that can lead to the emission of single photons. Similarly, in the molecules, two metastable levels and one excited state are used to implement the single-photon emission.
The single-photon emission mode has been achieved for a number of very different molecules [194].
The partial list of organic single molecules that have already demonstrated single-photon emission (Fig. 24) is as follows: Anthracene, Pentacene, Perrylene, Terrylene, 7.8,15.16‑dibenzoterrylene (DBT), Tetra-tert-butylterrylene (TBT), r-Terphenil, 2.3,8.9‑dibenzanthanthrene (DBATT), Terrylenediimide (TDI), ZnPc, Rhodamine 6G (R6G), Oxazine 720, B-phycoerythrin (B-PE), DiIC18(3).
The single-photon emission of single molecules has been widely studied by many groups in the solid and liquid media [195–198]. In particular, the operation of a single-photon source in a single-molecular system at the room temperature [199, 200] as well as under the electrical pumping [201] has been experimentally demonstrated.
This approach requires further improvement for practical applications. The assistance can be provided rather unexpectedly: the “optical tweezers” technology is developing and finding ever wider application in biochemistry and biophysics that allows for the capture, movement and retention of individual molecules for a long period of time. The “optical tweezers” devices for biochemical research are being developed with ever new original technical solutions that leads to their wider distribution and better process efficiency. The optical tweezers are already applied in the cold atom quantum computers to ensure their controlled interaction. Maybe, in the near future we will apply the industrial single-photon sources based on a single molecule held in the “optical tweezers” at room temperature. The concept of obtaining single-photon emitters by any electrochemical methods in the form of a solution or suspension is also rather interesting from a technological point of view.
Metal ions in the polymer matrix
The polymer macromolecules containing a metallic ion with the required energy level structure is of particular interest as a source of single photons. Due to their internal structure, such molecules are capable of self-organizing into the low-dimensional (one-dimensional or two-dimensional) structures where the emitting atoms are located in strictly determined positions and in precisely determined quantities [202]. These structures can be placed on the surface of silicon (and other) chips with the preexisting electrical wiring or an optical system (such as photonic integrated circuits or microlenses). In addition, the application of an active polymer layer with atomic radiation sources can be one of the final microelectronic operations.
Single molecules of phthalocyanines and two-dimensional polymer structures based on them (such as PPc – polyphthalocyanines) are promising materials. The octacyanophthalocyanide molecule has four-beam symmetry and contains a metal atom in the center, while these can be atoms of various metals. During polymerization, such molecules can generate linear chains or a flat monoatomic layer similar to the patterned graphene. However, unlike graphene, the PPcs have four-beam symmetry, rather than hexagonal one. In this monolayer of a flat graphene-like polymer, the metal atoms are embedded in a two-dimensional crystal lattice in a regular square order at a distance of ~1 nm from each other (Fig. 17). Individual excitation of such “metal atoms captured in the polymer traps” can lead to the single-photon emission. In addition, the polyphthalocyanines have semiconductor properties that is very useful for developing the electrically controlled sources.
The single-photon sources on single phthalocyanine molecules doped with various metals have already been shown, including electrically controlled ones [203–204]. In paper [205], the single-photon emission of linear polyphthalocyanines (linear ensembles of phthalocyanine molecules doped with zinc atoms) has been demonstrated.
The synthesis of polyphthalocyanines with erbium, as well as the synthesis of polyphthalocyanines with erbium complexes, is very promising, since erbium allows one to obtain radiation of about 1550 nm. The luminescence near 1550 nm has already been demonstrated using the monophthalocyanine molecules with erbium complexes [206, 207], including at room temperature [208].
Moreover, the polymer matrix can be applied only for the delivery of an optically active ion or atom to a certain point of the microchip or optical system at the production stage, using the self-organization capabilities of the polymer molecules. Subsequently, the organic matrix can be removed chemically, optically or thermally (burned in, burned out, evaporated, dissolved, etc.), thus being a kind of analogue of the so-called “sacrificial layer” that is widely used in microelectronic technologies.
Single-photon sources on the nonlinear crystals. Spontaneous parametric scattering
Spontaneous parametric scattering (SPDC) is a nonlinear optical process in the nonlinear media as a result of which a pumping photon is split into a pair of correlated photons of lower energy [209, 210].
When an intense laser beam passes through the highly nonlinear material, the photons interact with the crystal lattice with nonlinear polarization. Most photons pass through the crystal in an unchanged condition, but some photons are split into the pairs of photons with lower energies (a signal photon and an idler photon) as a result of interaction with the medium. During the SPDC process, the energy and momentum conversation laws are executed: the total energy and momentum of the resulting photons are equal to the energy and momentum of the pumping photons. The SPDC process efficiency is usually low. Therefore, on practical grounds, it can be considered that the photon splitting processes occur strictly one at a time.
The spontaneous parametric scattering of light can be interpreted as a scattering process on quantum fluctuations of the electromagnetic field or a photon scattering process on zero (vacuum) states relevant to the signal and idler photons. The role of the medium is to mix various frequency modes of the electromagnetic field due to its nonlinear susceptibility.
The SPDC process layout is shown in Fig. 26. A pumping photon with a frequency νp falls on the nonlinear crystal. When propagating in a nonlinear medium, it is divided into two photons: a signal photon with a frequency νs and an idler photon with a frequency νi.
From a physical point of view, the signal and idler photons are equivalent. During the physical experiments, the signal photon is usually the one with the higher frequency; in the actual devices, the photons are designated depending on their purpose. The signal and idler photons can have the same or various polarization (such scattering is called, respectively, SPDC type I and type II), and also coincide with the pumping polarization or differ from it.
In general, the signal and idler photons propagate in two different directions, and the photons that pass through the crystal without any changes propagate in a third direction. Thus, all three types of photons can be sorted by directions.
The signal and idler photons produced by the SPDC are entangled with each other. Based on the entangled photon pairs, the heralded single-photon sources are generated: detection of one photon from an entangled pair (e. g. at a detector inside the source device) notifies that the second photon generation from the pair has definitely occurred, and provides information about its state.
By selecting the correct crystal orientation relative to the crystal optical axes, it is possible to arrange the emission of signal and idler photons in such a way that both emitted photons have the same frequency and/or are emitted in the same direction. This is the method for creating the sources of entangled photon pairs.
Until recently, it has been assumed that the pair of emitted photons is produced at a single point, within the constraints of quantum uncertainty. Some time ago, a non-local mechanism for the development of correlated photon pairs in SPDC was discovered. It was shown that the photons constituting an entangled pair could be emitted from the spatially separated points [212, 213].
The crystals required for SPDC
To efficiently implement the downconversion in parametric nonlinear crystals, a high nonlinearity factor is required. This allows generating a large number of entangled photons. The crystal nonlinearity can be significantly changed depending on the temperature and pressure. Therefore, in the operating mode, it is necessary to provide specified conditions with stable temperature and pressure. Moreover, it is possible to control the temperature or pressure to fine-tune the crystal parameters or the domain period.
Optical anisotropy is required. The SPDC is effective in the media without an inversion center, most often these are the crystals without any center of symmetry. A nonlinear crystal has various refractive indices along different crystallographic axes.
For the efficient nonlinear interaction, the crystal shall have high optical quality and be optically transparent (have low absorption) at all three frequencies: at the pumping frequency and at the frequencies of signal and idler photons. To arrange SPDC in a crystal, it is necessary to correctly adjust the experimental conditions, such as the optical pumping wavelength, the phase matching angle and the crystal thickness.
A high-power laser with the sufficient energy to induce nonlinear interactions in the material is used as a pump. Typically, a fairly high pumping power density is required; the crystal shall have a high optical breakdown threshold to withstand the high-power density without being destroyed.
The most commonly used nonlinear crystals include lithium niobate LiNbO3 (NL), lithium triborate LiB3O5 (LBO), potassium dihydrogen orthophosphate KH2PO4 (KDP), barium beta borate BaB2O4 (BBO).
At first glance, it seems that for more efficient photon generation it is sufficient to take larger crystals in order to increase the optical path along which the nonlinear interaction occurs. However, the phase matching condition is violated already at rather short distances due to the dispersion of optical waves in the medium that leads to the destructive interference and decreased conversion efficiency. To avoid destructive interference, a periodic structure made of ferroelectric domains (areas with various polarization and, accordingly, periodic spatial nonlinearity modulation) is generated in the crystal along the pumping beam propagation path so that the phase ratio between the input and generated photons remains constant along the entire crystal length for efficient nonlinear conversion of the input photons. The domain period is calculated to fulfill the phase matching conditions for the wavelengths used that makes it possible to increase the interaction length and arrange the constructive interference [214]. The application of periodically polarized crystals makes it possible to significantly increase the SPDC efficiency. However, at the same time it imposes additional requirements on the temperature and pressure stability in the crystal.
One of the SPDC process disadvantages is the finite (albeit extremely small) probability of multiphoton events, although the situation is much better than with the sources based on the linear attenuation of laser pulses, for which the probabilities of multiphoton events are much higher.
Four-wave mixing (FWM).
The four-wave mixing process is another generation method for single-photon radiation in a nonlinear medium. During the mixing process, two pumping photons are converted into a signal and an idler photons. For this purpose, the medium shall have a cubic nonlinearity. Similar to the SPDC process, the four-wave mixing requires the phase matching conditions. However, unlike SPDC that can occur in both bulk and waveguides, the four-wave mixing process is usually shown only in the waveguides included in the photonic integrated circuits, since the high-power density is required.
The waveguide sources generally demonstrate a higher probability of photon pair generation than the bulk sources due to the smaller number of interacting modes. The four-wave mixing photon sources can achieve brightness at the level of 1 MHz.
The four-wave mixing process in the quantum-optical mode is used in the quantum communications to generate single photons [215], correlated pairs of photons [216, 217], squeezed light [218,219], and entangled photons [220].
Conclusion
In conclusion, it should be noted that there is a wide variety of ways to implement the single-photon sources. All such methods have been studied and developed to the various extent. Many of them have only been implemented as the scientific experiments, although there are already a number of commercially available single-photon sources.
From the current perspective of the growing need for single-photon sources for the commercial QKD systems, the most promising sources are those operating without liquid cooling that allow for electrical pumping and emission “on demand”. Application in the fiber systems imposes an additional requirement for the source to operate at a frequency relevant to the telecommunication transparency windows of the optical fiber (these are the ranges of about 1310 nm and 1550 nm). The development of photonic integrated circuit (PIC) technologies shall make it possible to omit the inconvenient requirement of electrical control, and to supply optical pumping radiation directly to the desired point of the integrated circuit by the integrated photonics methods.
In this sense, various color centers in diamonds and other materials (e. g. silicon, boron nitride, and boron carbide) appear to be the most promising. So far, no color center has been found that efficiently emits in the telecommunications range. The research is underway to convert the frequency of single photons, as well as to search for new color centers in new materials. At present, the QKD systems are being developed for the atmospheric and space segments, and the radiation frequency requirements for them are very different. They are determined, for example, by the transparency windows of the atmosphere or the solar radiation spectrum. The color centers may be useful for application in the free space.
Some semiconductor quantum dots are also capable of operating at room temperature. However, their high-quality production requires some expensive and labor-intensive precision technologies such as molecular-beam epitaxy. Moreover, their noise characteristics at high temperatures still leave much to be desired.
The heralded sources based on the nonlinear materials may also be promising, but there are a number of technical difficulties in application of the nonlinear materials for this purpose. The main difficulty is the very low conversion efficiency. Such low efficiency entails the need to increase the pumping intensity and the crystal size. In the case of large crystal sizes, it is necessary to develop a periodic structure with the “frozen” polarization in the crystal (for example, PPLN – periodically poled lithium niobat) that allows constructive interference to be organized along the optical beam path in the crystal. After this, the problem of significant changes in the local characteristics in the crystal under the influence of intense radiation comes to the fore leading to the frequency offset at which this very constructive interference is implemented, relative to the pumping frequency, and again to the deteriorated conversion efficiency. Despite the extremely attractive scientific results announced, this “vicious circle” is quite difficult to break, and there are still few commercially available sources.
If we consider the broader tasks of the more distant future, for which the single-photon sources may be useful, then the first thing to mention is the fact that the quantum computers based on various physical principles are currently being intensively researched and developed. The priority areas are as follows: the computers based on single ions and atoms, on superconducting qubits, on photonic chips, etc. As an indirect advantage, this development leads to the rapid improvement of experimental techniques for controlling individual quantum objects in various conditions, including at low and ultra-low temperatures, in a vacuum, etc. However, the most important thing is that the need for quantum data exchange within the quantum computers and between different quantum computers, including distant ones, is already looming on the horizon. This issue already needs to be kept in mind. For this purpose, it would probably be most efficient to arrange transportation of the quantum states using the single-photon sources based on the same quantum objects on which this computer is built. Such an interaction arrangement between the quantum computers due to the direct exchange of quantum states for data transmission and transformation is now commonly called the “quantum internet”. Apparently, the cold atom and single ion sources shall play a significant role in the quantum internet implementation, despite all the technical difficulties during the experimental implementation process.
In light of the foregoing, there are some remaining various “dark horses” in this single-photon race, namely the ensemble and electrochemical approaches to the single-photon emission arrangement. The technological maturity in this case is much lower. However, at the same time, there are rather currently distant hopes that the statistical many-particle approaches to the quantum systems may soon bring unexpected and bright breakthroughs in the field of science and technology, and ultimately may prove more effective than the conventional deterministic practices. It should also be noted that the experimental approaches in these areas are also developing rapidly due to the related problems in other scientific areas. The ensemble systems are actively studied to develop the quantum memory and quantum repeaters, and the electrochemical methods for nanocrystal synthesis are developing due to the medical applications, for example, cancer diagnostics using the up-conversion nanoparticles or targeted drug delivery by the transport nanocrystals.
Some researches of single-photon radiation and its sources has already led to many fundamental discoveries and significantly influenced the development of fundamental and applied science, technology, and society. However, the most interesting events in the quantum communications and quantum cryptography are obviously yet to come.
ABOUT AUTHOR
Krishtop Vladimir G.; Cand. of Sciences (Phys.&Math.);
e-mail: vladimir.krishtop@infotecs.ru; Moscow; Moscow Institute of Physics and Technology, (MIPT, Phystech), Dolgoprudny, Moscow region; Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow region, Russia.
ORCID: 0000-0001-6063-2657
V. G. Krishtop
JSC “InfoTeСS”, Moscow, Russia
Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Moscow region, Russia
Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow region, Russia
This review discusses various development methods for the single-photon sources (SPS).Earlier, the first part of the review (Photonics Russia. 2024; 18(5): 376–396) has discussed the requirements for single-photon sources and their characteristic criteria, and described the single-photon sources based on the single ions and single atoms. The second part of the review (Photonics Russia. 2024; 18(8): 610–620) has considered the SPSs based on the quantum dots and on the color centers in crystals. The third part (Photonics Russia. 2025; 19(1): 28–38) has considered the single-photon sources based on the carbon nanotubes and defects in them (defect engineering in nanotubes), on the nanocrystals and layered nanocrystals. The final section examines the single-photon sources on the collective states in the ensemble systems, on the single molecules and metal ions in a polymer matrix, as well as the sources on nonlinear crystals.
Keywords: single-photon source (SPS), Ensemble systems, Ensemble sources, Single molecules, four-wave mixing (FWM)
The article received on: 01.08.2024
The article accepted on: 16.08.2024
Ensemble systems
The electromagnetic traps allow both single particles and groups of particles, i. e., atom ensembles, to be held and studied [167–169]. The single-photon sources “on demand” have been developed that use collective excitations in the atom ensembles [170–173]. The atom ensembles can theoretically [174, 175] enhance a single photon state due to the superradiance phenomenon, i. e., coherent collective radiation due to the correlation between the atom phases and amplitudes in the ensemble. The atoms in the ensemble obtain a collective coherent state (the so-called Dicke state, for more details please read [176–179]) and emit coherent radiation as united large dipole.
The atoms in the ensemble have the energy levels consisting of two metastable ground states |g and |u and one excited state |e (Fig. 15). All atoms are first optically pumped to the state |u. Then a weak writing pulse that corresponds to the transition |u → |e, probabilistically develops a single collective excitation, thus causing the signal photon emission at the transition |e → |g with a low probability. The registration of a single signal photon indicates successful excitation. The “writing” laser pulse is made weak to reduce the probability of exiting of more than one photon-atom-spin excitation. Then a strong read-out pulse deterministically returns the single excitation to its original state, while generating exactly one photon at the |e → |u transition.
To increase the coherence time and improve the efficiency of single-photon emission of an ensemble of single atoms, the dipole traps or optical lattices are used. Moreover, it is necessary to comply with the momentum conservation law for the writing pulse, the read-out pulse, and the emitted photon.
The main efforts in the field of studying quantum ensembles are related to the hope of developing quantum memory [180–184] and quantum repeaters [185–187]. At present, the experimentally demonstrated coherence time of spin waves in the atom ensembles Cs and Rb is several milliseconds [180–182].
It is interesting that a wide variety of quantum objects can unite into an ensemble, demonstrate coherent effects and produce single-photon radiation. For example, the quantum ensembles of semiconductor quantum dots [188], diamond nanocrystals [189, 190], and core/shell/shell nanocrystals [191] have already been experimentally proven. It has also turned out that the quantum objects with a distance between them significantly greater than the wavelength can be combined into the quantum ensemble [179, 192]. Relatively recently, an ensemble of single atoms in the waveguide with a distance greater than the wavelength has been experimentally demonstrated [193].
Single molecules
A very fleeting analogue of ensemble systems can be the single molecules. For the single-photon emitters, rather comprehensive organic molecules consisting of tens of atoms are used, for example, chromophore-containing polymers. To draw the analogy, it is enough to imagine that the atoms that make up such a molecule formed an ensemble of quantum particles, in which the necessary collective excitations are available that can lead to the emission of single photons. Similarly, in the molecules, two metastable levels and one excited state are used to implement the single-photon emission.
The single-photon emission mode has been achieved for a number of very different molecules [194].
The partial list of organic single molecules that have already demonstrated single-photon emission (Fig. 24) is as follows: Anthracene, Pentacene, Perrylene, Terrylene, 7.8,15.16‑dibenzoterrylene (DBT), Tetra-tert-butylterrylene (TBT), r-Terphenil, 2.3,8.9‑dibenzanthanthrene (DBATT), Terrylenediimide (TDI), ZnPc, Rhodamine 6G (R6G), Oxazine 720, B-phycoerythrin (B-PE), DiIC18(3).
The single-photon emission of single molecules has been widely studied by many groups in the solid and liquid media [195–198]. In particular, the operation of a single-photon source in a single-molecular system at the room temperature [199, 200] as well as under the electrical pumping [201] has been experimentally demonstrated.
This approach requires further improvement for practical applications. The assistance can be provided rather unexpectedly: the “optical tweezers” technology is developing and finding ever wider application in biochemistry and biophysics that allows for the capture, movement and retention of individual molecules for a long period of time. The “optical tweezers” devices for biochemical research are being developed with ever new original technical solutions that leads to their wider distribution and better process efficiency. The optical tweezers are already applied in the cold atom quantum computers to ensure their controlled interaction. Maybe, in the near future we will apply the industrial single-photon sources based on a single molecule held in the “optical tweezers” at room temperature. The concept of obtaining single-photon emitters by any electrochemical methods in the form of a solution or suspension is also rather interesting from a technological point of view.
Metal ions in the polymer matrix
The polymer macromolecules containing a metallic ion with the required energy level structure is of particular interest as a source of single photons. Due to their internal structure, such molecules are capable of self-organizing into the low-dimensional (one-dimensional or two-dimensional) structures where the emitting atoms are located in strictly determined positions and in precisely determined quantities [202]. These structures can be placed on the surface of silicon (and other) chips with the preexisting electrical wiring or an optical system (such as photonic integrated circuits or microlenses). In addition, the application of an active polymer layer with atomic radiation sources can be one of the final microelectronic operations.
Single molecules of phthalocyanines and two-dimensional polymer structures based on them (such as PPc – polyphthalocyanines) are promising materials. The octacyanophthalocyanide molecule has four-beam symmetry and contains a metal atom in the center, while these can be atoms of various metals. During polymerization, such molecules can generate linear chains or a flat monoatomic layer similar to the patterned graphene. However, unlike graphene, the PPcs have four-beam symmetry, rather than hexagonal one. In this monolayer of a flat graphene-like polymer, the metal atoms are embedded in a two-dimensional crystal lattice in a regular square order at a distance of ~1 nm from each other (Fig. 17). Individual excitation of such “metal atoms captured in the polymer traps” can lead to the single-photon emission. In addition, the polyphthalocyanines have semiconductor properties that is very useful for developing the electrically controlled sources.
The single-photon sources on single phthalocyanine molecules doped with various metals have already been shown, including electrically controlled ones [203–204]. In paper [205], the single-photon emission of linear polyphthalocyanines (linear ensembles of phthalocyanine molecules doped with zinc atoms) has been demonstrated.
The synthesis of polyphthalocyanines with erbium, as well as the synthesis of polyphthalocyanines with erbium complexes, is very promising, since erbium allows one to obtain radiation of about 1550 nm. The luminescence near 1550 nm has already been demonstrated using the monophthalocyanine molecules with erbium complexes [206, 207], including at room temperature [208].
Moreover, the polymer matrix can be applied only for the delivery of an optically active ion or atom to a certain point of the microchip or optical system at the production stage, using the self-organization capabilities of the polymer molecules. Subsequently, the organic matrix can be removed chemically, optically or thermally (burned in, burned out, evaporated, dissolved, etc.), thus being a kind of analogue of the so-called “sacrificial layer” that is widely used in microelectronic technologies.
Single-photon sources on the nonlinear crystals. Spontaneous parametric scattering
Spontaneous parametric scattering (SPDC) is a nonlinear optical process in the nonlinear media as a result of which a pumping photon is split into a pair of correlated photons of lower energy [209, 210].
When an intense laser beam passes through the highly nonlinear material, the photons interact with the crystal lattice with nonlinear polarization. Most photons pass through the crystal in an unchanged condition, but some photons are split into the pairs of photons with lower energies (a signal photon and an idler photon) as a result of interaction with the medium. During the SPDC process, the energy and momentum conversation laws are executed: the total energy and momentum of the resulting photons are equal to the energy and momentum of the pumping photons. The SPDC process efficiency is usually low. Therefore, on practical grounds, it can be considered that the photon splitting processes occur strictly one at a time.
The spontaneous parametric scattering of light can be interpreted as a scattering process on quantum fluctuations of the electromagnetic field or a photon scattering process on zero (vacuum) states relevant to the signal and idler photons. The role of the medium is to mix various frequency modes of the electromagnetic field due to its nonlinear susceptibility.
The SPDC process layout is shown in Fig. 26. A pumping photon with a frequency νp falls on the nonlinear crystal. When propagating in a nonlinear medium, it is divided into two photons: a signal photon with a frequency νs and an idler photon with a frequency νi.
From a physical point of view, the signal and idler photons are equivalent. During the physical experiments, the signal photon is usually the one with the higher frequency; in the actual devices, the photons are designated depending on their purpose. The signal and idler photons can have the same or various polarization (such scattering is called, respectively, SPDC type I and type II), and also coincide with the pumping polarization or differ from it.
In general, the signal and idler photons propagate in two different directions, and the photons that pass through the crystal without any changes propagate in a third direction. Thus, all three types of photons can be sorted by directions.
The signal and idler photons produced by the SPDC are entangled with each other. Based on the entangled photon pairs, the heralded single-photon sources are generated: detection of one photon from an entangled pair (e. g. at a detector inside the source device) notifies that the second photon generation from the pair has definitely occurred, and provides information about its state.
By selecting the correct crystal orientation relative to the crystal optical axes, it is possible to arrange the emission of signal and idler photons in such a way that both emitted photons have the same frequency and/or are emitted in the same direction. This is the method for creating the sources of entangled photon pairs.
Until recently, it has been assumed that the pair of emitted photons is produced at a single point, within the constraints of quantum uncertainty. Some time ago, a non-local mechanism for the development of correlated photon pairs in SPDC was discovered. It was shown that the photons constituting an entangled pair could be emitted from the spatially separated points [212, 213].
The crystals required for SPDC
To efficiently implement the downconversion in parametric nonlinear crystals, a high nonlinearity factor is required. This allows generating a large number of entangled photons. The crystal nonlinearity can be significantly changed depending on the temperature and pressure. Therefore, in the operating mode, it is necessary to provide specified conditions with stable temperature and pressure. Moreover, it is possible to control the temperature or pressure to fine-tune the crystal parameters or the domain period.
Optical anisotropy is required. The SPDC is effective in the media without an inversion center, most often these are the crystals without any center of symmetry. A nonlinear crystal has various refractive indices along different crystallographic axes.
For the efficient nonlinear interaction, the crystal shall have high optical quality and be optically transparent (have low absorption) at all three frequencies: at the pumping frequency and at the frequencies of signal and idler photons. To arrange SPDC in a crystal, it is necessary to correctly adjust the experimental conditions, such as the optical pumping wavelength, the phase matching angle and the crystal thickness.
A high-power laser with the sufficient energy to induce nonlinear interactions in the material is used as a pump. Typically, a fairly high pumping power density is required; the crystal shall have a high optical breakdown threshold to withstand the high-power density without being destroyed.
The most commonly used nonlinear crystals include lithium niobate LiNbO3 (NL), lithium triborate LiB3O5 (LBO), potassium dihydrogen orthophosphate KH2PO4 (KDP), barium beta borate BaB2O4 (BBO).
At first glance, it seems that for more efficient photon generation it is sufficient to take larger crystals in order to increase the optical path along which the nonlinear interaction occurs. However, the phase matching condition is violated already at rather short distances due to the dispersion of optical waves in the medium that leads to the destructive interference and decreased conversion efficiency. To avoid destructive interference, a periodic structure made of ferroelectric domains (areas with various polarization and, accordingly, periodic spatial nonlinearity modulation) is generated in the crystal along the pumping beam propagation path so that the phase ratio between the input and generated photons remains constant along the entire crystal length for efficient nonlinear conversion of the input photons. The domain period is calculated to fulfill the phase matching conditions for the wavelengths used that makes it possible to increase the interaction length and arrange the constructive interference [214]. The application of periodically polarized crystals makes it possible to significantly increase the SPDC efficiency. However, at the same time it imposes additional requirements on the temperature and pressure stability in the crystal.
One of the SPDC process disadvantages is the finite (albeit extremely small) probability of multiphoton events, although the situation is much better than with the sources based on the linear attenuation of laser pulses, for which the probabilities of multiphoton events are much higher.
Four-wave mixing (FWM).
The four-wave mixing process is another generation method for single-photon radiation in a nonlinear medium. During the mixing process, two pumping photons are converted into a signal and an idler photons. For this purpose, the medium shall have a cubic nonlinearity. Similar to the SPDC process, the four-wave mixing requires the phase matching conditions. However, unlike SPDC that can occur in both bulk and waveguides, the four-wave mixing process is usually shown only in the waveguides included in the photonic integrated circuits, since the high-power density is required.
The waveguide sources generally demonstrate a higher probability of photon pair generation than the bulk sources due to the smaller number of interacting modes. The four-wave mixing photon sources can achieve brightness at the level of 1 MHz.
The four-wave mixing process in the quantum-optical mode is used in the quantum communications to generate single photons [215], correlated pairs of photons [216, 217], squeezed light [218,219], and entangled photons [220].
Conclusion
In conclusion, it should be noted that there is a wide variety of ways to implement the single-photon sources. All such methods have been studied and developed to the various extent. Many of them have only been implemented as the scientific experiments, although there are already a number of commercially available single-photon sources.
From the current perspective of the growing need for single-photon sources for the commercial QKD systems, the most promising sources are those operating without liquid cooling that allow for electrical pumping and emission “on demand”. Application in the fiber systems imposes an additional requirement for the source to operate at a frequency relevant to the telecommunication transparency windows of the optical fiber (these are the ranges of about 1310 nm and 1550 nm). The development of photonic integrated circuit (PIC) technologies shall make it possible to omit the inconvenient requirement of electrical control, and to supply optical pumping radiation directly to the desired point of the integrated circuit by the integrated photonics methods.
In this sense, various color centers in diamonds and other materials (e. g. silicon, boron nitride, and boron carbide) appear to be the most promising. So far, no color center has been found that efficiently emits in the telecommunications range. The research is underway to convert the frequency of single photons, as well as to search for new color centers in new materials. At present, the QKD systems are being developed for the atmospheric and space segments, and the radiation frequency requirements for them are very different. They are determined, for example, by the transparency windows of the atmosphere or the solar radiation spectrum. The color centers may be useful for application in the free space.
Some semiconductor quantum dots are also capable of operating at room temperature. However, their high-quality production requires some expensive and labor-intensive precision technologies such as molecular-beam epitaxy. Moreover, their noise characteristics at high temperatures still leave much to be desired.
The heralded sources based on the nonlinear materials may also be promising, but there are a number of technical difficulties in application of the nonlinear materials for this purpose. The main difficulty is the very low conversion efficiency. Such low efficiency entails the need to increase the pumping intensity and the crystal size. In the case of large crystal sizes, it is necessary to develop a periodic structure with the “frozen” polarization in the crystal (for example, PPLN – periodically poled lithium niobat) that allows constructive interference to be organized along the optical beam path in the crystal. After this, the problem of significant changes in the local characteristics in the crystal under the influence of intense radiation comes to the fore leading to the frequency offset at which this very constructive interference is implemented, relative to the pumping frequency, and again to the deteriorated conversion efficiency. Despite the extremely attractive scientific results announced, this “vicious circle” is quite difficult to break, and there are still few commercially available sources.
If we consider the broader tasks of the more distant future, for which the single-photon sources may be useful, then the first thing to mention is the fact that the quantum computers based on various physical principles are currently being intensively researched and developed. The priority areas are as follows: the computers based on single ions and atoms, on superconducting qubits, on photonic chips, etc. As an indirect advantage, this development leads to the rapid improvement of experimental techniques for controlling individual quantum objects in various conditions, including at low and ultra-low temperatures, in a vacuum, etc. However, the most important thing is that the need for quantum data exchange within the quantum computers and between different quantum computers, including distant ones, is already looming on the horizon. This issue already needs to be kept in mind. For this purpose, it would probably be most efficient to arrange transportation of the quantum states using the single-photon sources based on the same quantum objects on which this computer is built. Such an interaction arrangement between the quantum computers due to the direct exchange of quantum states for data transmission and transformation is now commonly called the “quantum internet”. Apparently, the cold atom and single ion sources shall play a significant role in the quantum internet implementation, despite all the technical difficulties during the experimental implementation process.
In light of the foregoing, there are some remaining various “dark horses” in this single-photon race, namely the ensemble and electrochemical approaches to the single-photon emission arrangement. The technological maturity in this case is much lower. However, at the same time, there are rather currently distant hopes that the statistical many-particle approaches to the quantum systems may soon bring unexpected and bright breakthroughs in the field of science and technology, and ultimately may prove more effective than the conventional deterministic practices. It should also be noted that the experimental approaches in these areas are also developing rapidly due to the related problems in other scientific areas. The ensemble systems are actively studied to develop the quantum memory and quantum repeaters, and the electrochemical methods for nanocrystal synthesis are developing due to the medical applications, for example, cancer diagnostics using the up-conversion nanoparticles or targeted drug delivery by the transport nanocrystals.
Some researches of single-photon radiation and its sources has already led to many fundamental discoveries and significantly influenced the development of fundamental and applied science, technology, and society. However, the most interesting events in the quantum communications and quantum cryptography are obviously yet to come.
ABOUT AUTHOR
Krishtop Vladimir G.; Cand. of Sciences (Phys.&Math.);
e-mail: vladimir.krishtop@infotecs.ru; Moscow; Moscow Institute of Physics and Technology, (MIPT, Phystech), Dolgoprudny, Moscow region; Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow region, Russia.
ORCID: 0000-0001-6063-2657
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