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10.22184/1993-7296.FRos.2024.18.5.376.396
The review discusses various ways to create single-photon sources (SPS). The task of generating single photons can be solved in various ways, and at the moment there is no one among them that would be significantly preferable. An extensive list of literature makes it possible to analyze the prospects for the development of single-photon sources.
The review discusses various ways to create single-photon sources (SPS). The task of generating single photons can be solved in various ways, and at the moment there is no one among them that would be significantly preferable. An extensive list of literature makes it possible to analyze the prospects for the development of single-photon sources.
Теги: группировка и антигруппировка фотонов квантовое распределение ключей (крк) кубиты однофотонный источник (иоф) основные платформы для изготовления иоф расщепление по числу фотонов состояния-«ловушки»
Single-Photon Sources. Review
Part 1
V. G. Krishtop
Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow region.
JSC “InfoTeСS”, Moscow.
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region.
The review discusses various ways to create single-photon sources (SPS). The task of generating single photons can be solved in various ways, and at the moment there is no one among them that would be significantly preferable. An extensive list of literature makes it possible to analyze the prospects for the development of single-photon sources.
Keywords: single-photon source (SPS), qubits, bunching and antibunching, QKD – quantum key distribution, decoy states, photon number splitting, the main platforms for the manufacture of SPS
The article received on:01.08.2024
The article accepted on: 16.08.2024
Introduction
Research in the field of single photon generation methods has led to significant development of methods for manipulating quantum objects, to a deeper understanding of quantum physics, and in addition, has yielded in a significant number of Nobel prizes. The results of these studies are being implemented both in experimental and applied physics, in some fields of chemistry and biology, as well as in instrumentation and cryptography.
The first part of the review discusses the necessary and desirable requirements for single-photon sources and criteria for characterizing sources. And then, as broadly as possible, but relatively briefly, scientific articles on the development of single-photon sources in various ways are reviewed. The first part of the review includes single-photons sources based on single ions and based on single atoms.
The second and third parts reviews SPS on quantum dots, on color centers in crystals, on carbon nanotubes and defects in them, on nanocrystals and layered nanocrystals, on single molecules, in low-dimensional structures, and metal ions in a polymer matrix, as well as ensemble systems, and sources on nonlinear crystals.
The review is intended for a wide range of readers who have basic knowledge in the field of quantum physics and want to get an idea of the state of research and development in the field of SPS. Materials from several previous reviews were used. An extensive list of literature is of particular value, which one can rely on when proceeding to studies of the required sections.
What single-photon sources are intended for [1]
Single-photon sources are used in quantum cryptography to create quantum key distribution systems (QKD systems). Using single-photon states, it is possible to guarantee the confidentiality of communication and the detection of any interference attempts.
Single-photon sources provide the ability to create and manipulate individual quantum bits (qubits). This is necessary for the development of quantum computers and other devices capable of performing quantum computing. It is assumed that the computer performance of quantum computers in a number of specific tasks will be significantly higher than the currently available classical computer performance of even the most powerful supercomputers currently available (Quantum Threat).
Besides, single-photon sources are used to conduct fundamental physical experiments aimed at verifying and studying the basic principles of quantum physics. Single-photon sources have also found application in quantum sensors and medicine.
Ideally, any single quantum particle – an atom, molecule, ion, quantum dot, etc., capable of absorbing and emitting photons in a narrow band of optical frequencies – can serve as a single-photon source. The main problem is to increase the efficiency of collecting single-photon radiation. It is also necessary to develop simple methods of electrical control of the single photon emission [2].
Accordingly, to implement a single-photon source, it is necessary to organize a relatively isolated stable quantum system having an atom-like energy structure and a permitted radiative transition between energy levels, to ensure its controlled (electrical or optical) excitation and subsequent radiative relaxation from the excited state, and then be able to effectively collect and redirect the resulting single-photon radiation.
Ideally, the source of quantum states should simultaneously provide true single-photon statistics, be deterministic, fast, and must work outside laboratory conditions.
The second-order correlation function g(2)(τ)
The Hanbury Brown-Twiss interferometer (HBT interferometer) is used to characterize photon sources.
Single-photon radiation from the output of the QKD system is fed to a symmetrical fiber-optic splitter. Identical single-photon detectors are connected to each of the outputs of the splitter. The detector readings are processed by a time interval measurement system (correlation scheme). Since a single photon cannot be absorbed by two detectors at the same time, it is detected by only one of the detectors with a probability determined by the quantum efficiency of the detector.
Thus, in the presence of ideal single-photon radiation at the output of the QKD system, the detectors would register the emitted single photons strictly singly, but would never be triggered synchronously. If the source is not ideal, and emits multiphoton pulses, among other things, there is a possibility that the first detector will detect one part of the photons of this pulse, and the second detector will detect the other part simultaneously. As a result, the detectors will be triggered synchronously.
The closer the single-photon source is to the ideal one, the lower the proportion of multiphoton pulses, the less likely synchronous triggering of the HBT interferometer photodetectors will occur.
Using a time interval meter, Grangier parameter, or second-order Glauber autocorrelation function g(2)(τ) is constructed. The function g(2)(τ) shows with what probability the photon will be detected by the second detector in the time interval τ after the first detector is triggered. The value of the second-order autocorrelation function g(2)(τ) at zero time characterizes the “single-photon quality” of the signal.
I(t) I(t + τ)
g(2)(τ) =––.
I(t)2
The form g(2)(τ) can be used to characterize the statistics of the source [3, 4].
So, to confirm the single-photon mode of a source, the second-order Glauber autocorrelation function g(2)(τ) is measured. It is the results of the experimental measurement of g(2)(τ) that scientists show in scientific articles as proof of the single-photon nature of the sources under study. For a true single-photon source, g(2)(0) = 0, for real sources, a value of g(2)(0) less than 1 / 2 is considered sufficient confirmation of the single-photon mode. Real experiments have demonstrated very small values of the g(2)(0) value, up to 7.5 × 10–5 [5].
Bunching, antibunching
and coherent source
The attenuated laser (faint laser, weak laser) is a coherent source and has a Poisson probability distribution P(n) of emission of n photons in an attenuated optical pulse.
The value of g(2)(0) for a source with Poisson distribution is equal to one g(2)(0) = 1 (there is no bunching of photons). If the radiation has sub-Poisson statistics, then g(2)(0) < 1, if super-Poisson, then g(2)(0) > 1.
Single-photon sources demonstrate antibunching. g(2)(0) = 0 for a true single-photon source. In quantum cryptography, it is precisely the antibunching of photons that is desirable. Since photons are emitted one at a time, the probability of simultaneous observation of two photons for an ideal source is 0. The photon source is antibunched, if g(2)(0) < g(2)(τ) [6].
The specifics of coherent states should be taken into account in the development and implementation of QKD protocols [7].
Photon bunching can occur in sources with resonators when the photon lifetime in the resonator is comparable to the pulse repetition period.
By measuring the probabilities included in the expression of the correlation function, it is possible to estimate the value of the correlation function and show how true the hypothesis of Poisson statistics is.
Attenuated laser as a single-photon source for QKD
The existing single-photon CRT systems overwhelmingly use a quasi-single-photon source based on a weakened laser [8]. Typically, in QKD systems, the laser intensity is attenuated to such an extent that, on average, each pulse contains less than one photon. A thick silicon wafer is often used as an attenuator, and with it a controlled attenuator for precise adjustment. Micromechanical controlled mirrors mounted in a fiber gap are also sometimes used, which redirect radiation completely or partially.
The number of photons in the pulse of a weakened laser obeys Poisson distribution. When the laser radiation is attenuated to an intensity of 0.1–0.2 photons per pulse, the vast majority of pulses that have overcome the attenuator contain only one photon (Fig.4). In attenuated laser radiation, along with single-photon pulses, there is inevitably a fraction of multiphoton pulses corresponding to the Poisson distribution. For example, the average value of the number of photons in a pulse of μ = 0.1 leads to a probability of 90% for zero photons, 9% for one photon and 1% for more than one photon [9].
The single photon emission purity of a quasi-single-photon source is a critically important characteristic for QKD systems. To keep the QKD-protocol secure, it is necessary to take into account the proportion of multiphoton pulses in the physical implementation of the quantum key distribution system. All protocol security proofs suggests that the attacker has full access to the quantum line and is not limited in technical means, and all information that is fundamentally possible to extract from the line will be fully extracted and used by him. In this case, this means that all multiphoton pulses can be “eavesdropped”. Therefore, in the technical implementation of the quantum protocol, in order to ensure mathematical security, it is necessary to take into account all multiphoton pulses as information leakage to an attacker.
This means that in real QKD systems, it is necessary to carefully ensure that the permitted single-photon mode is initially set and strictly maintained in real operating conditions. All elements providing a single-photon mode of optical radiation must be calibrated at the wavelength of the emitter, and the single-photon mode must be confirmed under all possible operating modes. To confirm the single-photon mode of a source, it is necessary to measure the average number of photons used in transmitting a single quantum state observed at the output of the system and confirm the Poisson statistics of the photons number distribution in optical pulses at the system output.
To do this, it is necessary to measure:
Measurement of the average number of photons per pulse
If the probability P(n) of emission of n photons in one optical pulse entering the quantum channel from the QKD system obeys the Poisson distribution, then it is sufficient to control the average number of photons in optical pulse to ensure a “sufficiently single-photon” operating mode of the QKD system emitter, and carefully take into account the proportion of non-single-photon pulses to ensure security of the protocol [10].
The methods for determining the average number of photons in one optical pulse of the QKD system are described in detail in the ETSI Group Specification QKD [11] (ETSI – European Telecommunications Standards Institute).
The average number of photons in one optical pulse n is calculated by the value of the average radiation power. Knowing the average energy of one optical pulse and the repetition rate of the unattenuated optical pulses, and the wavelength of the laser, we can calculate the average number of photons in one pulse:
p · λ
μ =–, (2)
f · c · h
where P is the average radiation power [W];
f is the pulse repetition rate [Hz];
λ is the average radiation wavelength [nm];
h is Planck’s constant (h ≈ 6.63∙10–34 [J ∙ s]),
c is the speed of light in vacuum (c ≈ 2.99 ∙ 108 m/s).
Knowledge of the quantum efficiency, the probability of dark counts and after pulses, as well as the pulse repetition rate (it is necessary to synchronize the calibrated photodetector and the output of the QKD system) makes it possible to recalculate the frequency of the photodetector under the influence of radiation from the output of the QKD system to the average number of photons. In real QKD systems, the average number of photons per pulse is constantly monitored so that the proportion of multiphoton pulses does not exceed the threshold value at which the quantum protocol ceases to be secret.
Decoy-states for countering a photon number splitting attack [12]
In stable attenuated laser radiation, the number of photons in a pulse is described by Poisson statistics, which inevitably leads to a known share of multiphoton pulses. On the one hand, this fact imposes additional restrictions on the technical implementation of the quantum protocol, but on the other hand, knowledge of statistics provides a relatively simple and elegant opportunity to detect outside interference in the process of quantum key distribution.
This is used in the Decoy-state method [7, 13, 14], which consists in preparing and transmitting, specially prepared decoy states, along with information states. In addition to information states with an average number of photons μ, Alice prepares some share of decoy states with other average numbers of photons: ν1 and ν2. At the same time, which of the states will be sent is randomly selected each time. Electro-optical intensity modulators are used to prepare information states and decoy states in Decoy-state protocols.
Eve does not know in advance the state with what average number of photons is in the channel, so it acts the same with each parcel. Her intervention distorts the statistics of Bob’s counts in different ways for each set of states with an average number of photons per pulse μ, ν1 and ν2.
After basis announcement and discarding mismatched bases, Bob finds out which set of states each click answered, and can calculate statistics separately for each set with the numbers μ, ν1 and ν2. According to the statistics of detector triggers for decoy states, Bob calculate the proportion of a single-photon component in information pulses. If this proportion remains within the required limits, then the protocol will remain secure, Alice and Bob start information reconciliation and privacy amplification procedures, considering that the key is formed only on a single-photon component.
And if the proportion of a single-photon component turns out to be different than it is predetermined by Poisson statistics for three sets of states with photon numbers μ, ν1 and ν2, then it can be assumed that the attacker intervened and launched a Photon Number Splitting attack (PNS) [12].
Of course, it would be much more convenient to have an ideal single-photon source – a source with exactly one photon per pulse. Such a source would simplify the technical implementation of quantum protocols and weaken the mathematical requirements for protocol security. There are a number of requirements that an ideal single-photon source must meet.
What are the requirements for an ideal single-photon source? [15]
one photon can be emitted at any arbitrarily determined time by the user (that is, the source is deterministic or “on demand” – single photon on demand),
the probability of emitting one photon is 100%,
the probability of multiphoton emission is 0%,
the emitted photons are indistinguishable,
the repetition rate is maximum (limited only by the time duration of a single-photon pulse).
Deviations from these ideal characteristics, which are always present in the real world, should be taken into account when setting up experiments and developing encryption systems.
For commercial QKD systems, there are additional requirements for an ideal single-photon source:
the wavelength in the telecommunication C-band range (usually, 1550 nm);
photon repetition rate over 100 MHz:
high brightness;
high quantum yield.
electrical excitation.
Working at room temperature
Most traditional single-photon sources require low temperatures to achieve optimal performance. From a practical point of view, the most interesting sources are those that operate at room temperature. Research is being conducted in the field of single-photon sources based on A3B5 semiconductors, such as gallium nitride (GaN) and indium nitride (InN), for example, quantum dots based on gallium nitride (GaN) can provide single-photon radiation at room temperature. Also promising objects for creating single-photon sources at room temperature are color defects in diamond, for example, NV centers (nitrogen vacancy). To date, the development of stable and efficient single-photon sources at room temperature is an active area of research. Technologies and materials continue to evolve, and significant breakthroughs in this area may be achieved in the future.
Work in the telecommunications range
Quantum communications and quantum networks require single-photon sources designed for the telecommunication wavelength range (about 1550 nm). Sources emitting in other optical fiber transparency windows are also interesting, – 1310 nm and about 850 nm, – but losses in optical fiber at these wavelengths are much higher.
These can be single-photon sources based on spontaneous parametric down-conversion (SPDC) in nonlinear crystals that generate a pair of photons with different energies, including one (or both) photon in the telecommunications range. InAs-based quantum dots have the potential to generate single-photon signals in the near infrared range. Some ions in the crystal matrix, such as erbium (Er3+) and praseodymium (Pr3+) ions, can generate single photons in the telecommunications range.
Superconducting nanowires, superconducting monatomic contacts, carbon nanotubes and graphene nanostructures, nanocrystals and quantum dots in a liquid or polymer matrix may also be promising.
Another area of scientific research in the field of developing single-photon sources for the telecommunication wavelength range is the development of methods for converting single photons of submicron wavelengths into photons of the telecommunication range. This can be done, for example, using cascade Raman scattering in a stepwise Bregg resonator in a single-mode optical fiber [16], or using four-wave mixing in a periodically poled lithium niobate waveguide [17]. Very attractive in this context is the idea of integrating single synthetic nanodiamonds containing a single color center directly into an optical fiber or into the structure of a photonic integrated circuit, after which frequency conversion can be implemented using well-developed fiber or integrated technologies.
At the same time, optical communication systems and quantum key distribution systems in open space (in the atmosphere, earth-satellite or in space between two spacecraft) are being actively developed, where different wavelengths can be used, and for these tasks there is no a requirement of a strictly defined wavelength for the source.
Indistinguishability
of emitted photons
For practical use, photons emitted from a single-photon source must be indistinguishable. Indistinguishable photons must have the same wavelength, polarization, and temporal and spatial extent. The Hong-Ou-Mandel effect is used to characterize indistinguishability.
The Hong-Ou-Mandel (HOM) effect is a two-photons interference phenomenon, wherein two indistinguishable photons are interfered on a symmetrical beam splitter, and the photons always emerge on the same, but random output port.
Two photons from one source are prepared so that they arrive simultaneously at the two inputs of a symmetrical beam splitter. Detectors are placed at both outputs of the beam splitter, and the coincidence between the two detectors is measured. If the photons are indistinguishable, there should be no coincidences[18]. Almost perfect indistinguishability has been experimentally realized [19, 20].
Electrical or optical pumping.
One of the requirements of practical implementation is the use of electric pumping. It is generally believed that electric pumping is more technically simple to implement than optical or microwave, and this opinion is justified by a completely reasonable desire to use standard microelectronic technologies for the production of single-photon sources. The implementation of electrical control in microelectronic technology is not a problem, while the implementation of optical components in an integrated design is not yet a generally accepted practice.
At the same time, we should not forget about the rapid development of photonic integrated circuit technologies, as well as the growing desire of microelectronics manufacturers to integrate optical data buses to connect blocks of modern silicon chips. Sooner or later, this will lead to the creation of microelectronic transceivers and receivers as elements of an integrated circuit of a next-generation processor, or as elements of a photonic integrated circuit, and the technological issues of optical pumping distribution to a single-photon emitter will be largely resolved. Currently, it is impossible to go without mentioning the desire for electrical control of a single-photon source, but in the near future this issue will turn out to be unprincipled.
Key parameters of single-photon sources for QKD systems
Table 1 lists the parameters that are monitored during metrological measurements of single-photon sources in an accredited testing laboratory.
The main types of single photon sources
So, the use of an attenuated laser is a compromise temporary technical solution, which is used due to the lack of commercially available true single-photon sources. True single-photon sources could mitigate the protocol implementation requirements and increase the speed of quantum key generation. Currently, active scientific research is underway, and a large number of scientific articles on the topic of single-photon sources are being published. Single-photon sources for other wavelengths are already being sold. The emergence of commercial single-photon sources for QKD by optical fiber is not far off.
Probabilistic (non-deterministic) sources are based on photon pairs that are created using parametric downconversion (PDC) in bulk crystals [21, 22] and waveguides [23, 24] and four-wave mixing (FWM) processes in optical fibers [25, 26].
Deterministic sources (allowing to emit a single photon “on demand”) use color centers [27, 28], quantum dots [29–31], single atoms [32, 33], single ions [34], single molecules [35] and atomic ensembles [36].
The clear distinction between the two types of sources is blurred in real applications, because, for example, a truly deterministic source based on the color center becomes probabilistic, provided that losses associated with radiation output from the material area where the color center is located are taken into account.
Heralded single-photon sources [37–40]
Heralded single-photon sources provide an opportunity to accurately determine the moment of generation of a single photon. Heralded single-photon sources generate single photons and simultaneously send a heralding that a photon has been successfully generated. This allows us to know exactly when and where a single photon was generated.
Heralded single-photon sources provide certainty of the presence of a single photon by pre-detection or notification of its generation. A typical implementation of such a source uses a nonlinear optical process known as spontaneous parametric scattering using nonlinear crystals. In this process, under certain conditions of interaction of photons with matter, one photon decomposes into two – a signal photon and a heralding photon. A heralding photon, which is information about the generation of a photon signal, can be detected and registered using a photodetector or other light detector. This heralding allows you to know for sure that the generation of a single photon has occurred, and provides information about its status.
Such sources operate on the basis of certain quantum mechanical processes, such as spontaneous parametric scattering, emission of fluorescent glow from a single-molecular crystalline dye or a high-intensity fluorescent lamp. Nonlinear optical processes in nonlinear crystals are often used. The most widely used heralded single-photon sources based on spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (FWM).
The main platforms used
for the manufacture of SPS [41]
Single-photon sources based on single ions [42–46]
To create a single photon source based on single ions for a wavelength of 1550 nanometers, the most suitable ions are ions of rare earth elements such as erbium (Er), thulium (Tm) or Praseodymium (Pr) operating in the infrared region of the spectrum. This is due to the fact that ions of rare earth elements have energy transitions between energy levels corresponding to the telecom wavelength. In particular, erbium (Er) ions are widely used to generate single photons at 1550 nm. For a wavelength of 1310 nanometers, cerium (Ce3+), praseodymium (Pr3+), ytterbium (Yb3+) or erbium (Er3+) ions are best suited.
Special magnetostatic traps are used to hold ions (Penning trap, Paul trap, radio frequency trap, trap with a rotating electric field, etc.) (Fig.5.). Ions can be formed directly by ionizing gas near or inside the trap (for example, by an electron beam or corona discharge) and held in the trap for a sufficient time to excite energy levels and spontaneous or stimulated photon emission. Buffer gas or laser cooling is used to cool the particles. Due to the Coulomb repulsion of charged particles, it is possible to organize a trap in such a way that exactly one ion is held in a certain area of space, and exactly one photon is emitted at each exposure.
The ions used as single-photon emitters [48–50] have a configuration of energy levels with two ground states and one excited state. With the help of a radio frequency ion trap, it is possible to stably localize a single ion in the center of an optical resonator, and limit the ion wave packet to a length much shorter than the optical wavelength, as well as fix the position of the wave packet with an accuracy of several nanometers. This ensures the continuous production of single-photon pulses. Since there is only one ion inside the resonator, the possibility of multiphoton events is excluded [49, 51].
Single ions as the basis of a single-photon source have the advantage that they are all identical, and demonstrate indistinguishability between different sources and different pulses from the same source.
The difficulty lies in the fact that resonant ion transitions occur in the ultraviolet region and excited states have high rates of spontaneous decay. Radiation in the resonant mode is accompanied by spontaneous radiation. In addition, the ion can remain in the ground state at the end of the excitation pulse without emitting a single photon. These factors can seriously reduce the probability of emitting single photon during each pump cycle. Another problem concerns how efficiently light can be collected, since the usual solution for neutral atoms – using strongly coupled resonators – is difficult for charged particles.
The improvement of experimental techniques in the manipulation of individual ions is due to the fact that one of the priorities in the development of quantum computers is the development of a quantum computer based on trapped ions [52–54]. Demonstrators of a quantum computer based on several hundred trapped ions have already been developed. It should be noted that the same applies to individual atoms; diffraction methods for creating three-dimensional optical atomic traps have made it possible to capture and hold more than ten thousand individual atoms.
Single-photon sources based on ultracold atoms
In traps, due to electromagnetic forces, it is possible to retain not only ions or charged elementary particles, but also neutral atoms if they have of nonzero dipole moments or magnetic moments.
Sources of single photons based on individual atoms typically operate at low temperatures and/or in vacuum conditions. Today, alkali metals atoms such as Cs and Rb are used [55–60].
First, you need to prepare a system in which individual atoms will be present. This can be achieved, for example, by laser cooling of a beam of atoms and placing atoms in optical traps.
To stop an atom, it needs to be cooled, i. e., to reduce its speed to less than a few centimeters per second. There are various ways to do this, but the most convenient method turned out to be laser cooling. Laser beams create a series of standing waves of polarized light, whose electric fields resemble a kind of comb. When an atom passes through it, bursts of electric field alternately “reset” the atom to an increasingly lower energy state and cool it down more and more [61].
Various traps have been developed to hold single atoms. One of the most common ways to hold single atoms is using optical gratings. Focused laser beams are used, which create an electromagnetic field with periodic potential wells for atoms. There are also magnetic, electrostatic, magneto-optical and microdipole traps [61, 62]. Historically, the Pauli trap and the Penning trap were invented first. Holographic traps are very interesting from a technical point of view, where the three-dimensional structure of potential wells in space is formed as a result of projecting a hologram through a holographic mask [63].
After capturing single atoms inside the trap, the atoms are excited by a laser. The laser system must be tuned to a certain energy corresponding to the transition of the selected atom from the ground state to the excited state. As a result of the excitation of a single atom, its electron transitions to an excited state. Relaxation from the excited state to the ground state is accompanied by the emission of a single photon. In each such process, a single photon is generated on a single atom. The emission of single photons can occur spontaneously or through a stimulated process, depending on the experimental conditions. As in the case of single ions, individual neutral atoms are identical, and different impulses from the same source and from different sources are indistinguishable. Ultracold atoms have a long coherence length, which means that the photons emitted by these atoms can maintain phase correlation over long time intervals.
Monatomic emitter
Another approach may be as follows: single atoms are first captured and cooled inside an open magneto-optical trap. Then the trap is turned off (or periodically turned off and on, or the amplitude of the field in the trap is periodically modulated) and the cooled atoms alternately fall freely under the influence of gravity and one by one pass through a high-precision optical resonator tuned to the frequency of the radiative optical transition of atoms. The probability of photon emission in a resonator with a suitable frequency is significantly higher than in free space, due to the Purcell effect. The efficiency of single photon generation for this approach may be close to 1, but the implementation of a monatomic emitter requires serious experimental efforts. Narrow beams of atoms are also used, irradiation of which with a laser yields single-photon radiation.
Single photon sources based on ultracold atoms have significant disadvantages: high complexity of implementation in comparison with other methods of generating single photons, limited operating conditions, low generation rate, poor scalability. The creation of single photon sources based on ultracold atoms requires a complex experimental arrangement. The implementation of a single-photon source on ultracold atoms requires high stability of the system, precise adjustment and control of experimental conditions. Creating large arrays of single-photon sources based on ultracold atoms is becoming technically difficult and requires significant costs and efforts. The rate of generation of single photons based on ultracold atoms may be low, especially in comparison with some other methods such as spontaneous parametric scattering or generation through quantum dots.
Part 1
V. G. Krishtop
Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow region.
JSC “InfoTeСS”, Moscow.
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region.
The review discusses various ways to create single-photon sources (SPS). The task of generating single photons can be solved in various ways, and at the moment there is no one among them that would be significantly preferable. An extensive list of literature makes it possible to analyze the prospects for the development of single-photon sources.
Keywords: single-photon source (SPS), qubits, bunching and antibunching, QKD – quantum key distribution, decoy states, photon number splitting, the main platforms for the manufacture of SPS
The article received on:01.08.2024
The article accepted on: 16.08.2024
Introduction
Research in the field of single photon generation methods has led to significant development of methods for manipulating quantum objects, to a deeper understanding of quantum physics, and in addition, has yielded in a significant number of Nobel prizes. The results of these studies are being implemented both in experimental and applied physics, in some fields of chemistry and biology, as well as in instrumentation and cryptography.
The first part of the review discusses the necessary and desirable requirements for single-photon sources and criteria for characterizing sources. And then, as broadly as possible, but relatively briefly, scientific articles on the development of single-photon sources in various ways are reviewed. The first part of the review includes single-photons sources based on single ions and based on single atoms.
The second and third parts reviews SPS on quantum dots, on color centers in crystals, on carbon nanotubes and defects in them, on nanocrystals and layered nanocrystals, on single molecules, in low-dimensional structures, and metal ions in a polymer matrix, as well as ensemble systems, and sources on nonlinear crystals.
The review is intended for a wide range of readers who have basic knowledge in the field of quantum physics and want to get an idea of the state of research and development in the field of SPS. Materials from several previous reviews were used. An extensive list of literature is of particular value, which one can rely on when proceeding to studies of the required sections.
What single-photon sources are intended for [1]
Single-photon sources are used in quantum cryptography to create quantum key distribution systems (QKD systems). Using single-photon states, it is possible to guarantee the confidentiality of communication and the detection of any interference attempts.
Single-photon sources provide the ability to create and manipulate individual quantum bits (qubits). This is necessary for the development of quantum computers and other devices capable of performing quantum computing. It is assumed that the computer performance of quantum computers in a number of specific tasks will be significantly higher than the currently available classical computer performance of even the most powerful supercomputers currently available (Quantum Threat).
Besides, single-photon sources are used to conduct fundamental physical experiments aimed at verifying and studying the basic principles of quantum physics. Single-photon sources have also found application in quantum sensors and medicine.
Ideally, any single quantum particle – an atom, molecule, ion, quantum dot, etc., capable of absorbing and emitting photons in a narrow band of optical frequencies – can serve as a single-photon source. The main problem is to increase the efficiency of collecting single-photon radiation. It is also necessary to develop simple methods of electrical control of the single photon emission [2].
Accordingly, to implement a single-photon source, it is necessary to organize a relatively isolated stable quantum system having an atom-like energy structure and a permitted radiative transition between energy levels, to ensure its controlled (electrical or optical) excitation and subsequent radiative relaxation from the excited state, and then be able to effectively collect and redirect the resulting single-photon radiation.
Ideally, the source of quantum states should simultaneously provide true single-photon statistics, be deterministic, fast, and must work outside laboratory conditions.
The second-order correlation function g(2)(τ)
The Hanbury Brown-Twiss interferometer (HBT interferometer) is used to characterize photon sources.
Single-photon radiation from the output of the QKD system is fed to a symmetrical fiber-optic splitter. Identical single-photon detectors are connected to each of the outputs of the splitter. The detector readings are processed by a time interval measurement system (correlation scheme). Since a single photon cannot be absorbed by two detectors at the same time, it is detected by only one of the detectors with a probability determined by the quantum efficiency of the detector.
Thus, in the presence of ideal single-photon radiation at the output of the QKD system, the detectors would register the emitted single photons strictly singly, but would never be triggered synchronously. If the source is not ideal, and emits multiphoton pulses, among other things, there is a possibility that the first detector will detect one part of the photons of this pulse, and the second detector will detect the other part simultaneously. As a result, the detectors will be triggered synchronously.
The closer the single-photon source is to the ideal one, the lower the proportion of multiphoton pulses, the less likely synchronous triggering of the HBT interferometer photodetectors will occur.
Using a time interval meter, Grangier parameter, or second-order Glauber autocorrelation function g(2)(τ) is constructed. The function g(2)(τ) shows with what probability the photon will be detected by the second detector in the time interval τ after the first detector is triggered. The value of the second-order autocorrelation function g(2)(τ) at zero time characterizes the “single-photon quality” of the signal.
I(t) I(t + τ)
g(2)(τ) =––.
I(t)2
The form g(2)(τ) can be used to characterize the statistics of the source [3, 4].
So, to confirm the single-photon mode of a source, the second-order Glauber autocorrelation function g(2)(τ) is measured. It is the results of the experimental measurement of g(2)(τ) that scientists show in scientific articles as proof of the single-photon nature of the sources under study. For a true single-photon source, g(2)(0) = 0, for real sources, a value of g(2)(0) less than 1 / 2 is considered sufficient confirmation of the single-photon mode. Real experiments have demonstrated very small values of the g(2)(0) value, up to 7.5 × 10–5 [5].
Bunching, antibunching
and coherent source
The attenuated laser (faint laser, weak laser) is a coherent source and has a Poisson probability distribution P(n) of emission of n photons in an attenuated optical pulse.
The value of g(2)(0) for a source with Poisson distribution is equal to one g(2)(0) = 1 (there is no bunching of photons). If the radiation has sub-Poisson statistics, then g(2)(0) < 1, if super-Poisson, then g(2)(0) > 1.
Single-photon sources demonstrate antibunching. g(2)(0) = 0 for a true single-photon source. In quantum cryptography, it is precisely the antibunching of photons that is desirable. Since photons are emitted one at a time, the probability of simultaneous observation of two photons for an ideal source is 0. The photon source is antibunched, if g(2)(0) < g(2)(τ) [6].
The specifics of coherent states should be taken into account in the development and implementation of QKD protocols [7].
Photon bunching can occur in sources with resonators when the photon lifetime in the resonator is comparable to the pulse repetition period.
By measuring the probabilities included in the expression of the correlation function, it is possible to estimate the value of the correlation function and show how true the hypothesis of Poisson statistics is.
Attenuated laser as a single-photon source for QKD
The existing single-photon CRT systems overwhelmingly use a quasi-single-photon source based on a weakened laser [8]. Typically, in QKD systems, the laser intensity is attenuated to such an extent that, on average, each pulse contains less than one photon. A thick silicon wafer is often used as an attenuator, and with it a controlled attenuator for precise adjustment. Micromechanical controlled mirrors mounted in a fiber gap are also sometimes used, which redirect radiation completely or partially.
The number of photons in the pulse of a weakened laser obeys Poisson distribution. When the laser radiation is attenuated to an intensity of 0.1–0.2 photons per pulse, the vast majority of pulses that have overcome the attenuator contain only one photon (Fig.4). In attenuated laser radiation, along with single-photon pulses, there is inevitably a fraction of multiphoton pulses corresponding to the Poisson distribution. For example, the average value of the number of photons in a pulse of μ = 0.1 leads to a probability of 90% for zero photons, 9% for one photon and 1% for more than one photon [9].
The single photon emission purity of a quasi-single-photon source is a critically important characteristic for QKD systems. To keep the QKD-protocol secure, it is necessary to take into account the proportion of multiphoton pulses in the physical implementation of the quantum key distribution system. All protocol security proofs suggests that the attacker has full access to the quantum line and is not limited in technical means, and all information that is fundamentally possible to extract from the line will be fully extracted and used by him. In this case, this means that all multiphoton pulses can be “eavesdropped”. Therefore, in the technical implementation of the quantum protocol, in order to ensure mathematical security, it is necessary to take into account all multiphoton pulses as information leakage to an attacker.
This means that in real QKD systems, it is necessary to carefully ensure that the permitted single-photon mode is initially set and strictly maintained in real operating conditions. All elements providing a single-photon mode of optical radiation must be calibrated at the wavelength of the emitter, and the single-photon mode must be confirmed under all possible operating modes. To confirm the single-photon mode of a source, it is necessary to measure the average number of photons used in transmitting a single quantum state observed at the output of the system and confirm the Poisson statistics of the photons number distribution in optical pulses at the system output.
To do this, it is necessary to measure:
- the transmission frequency of single-photon quantum states;
- average radiation power;
- the average wavelength of photons emitted into the quantum channel;
- the second-order correlation function, characterizing the single photon emission purity of the signal transmitted over the quantum channel.
Measurement of the average number of photons per pulse
If the probability P(n) of emission of n photons in one optical pulse entering the quantum channel from the QKD system obeys the Poisson distribution, then it is sufficient to control the average number of photons in optical pulse to ensure a “sufficiently single-photon” operating mode of the QKD system emitter, and carefully take into account the proportion of non-single-photon pulses to ensure security of the protocol [10].
The methods for determining the average number of photons in one optical pulse of the QKD system are described in detail in the ETSI Group Specification QKD [11] (ETSI – European Telecommunications Standards Institute).
The average number of photons in one optical pulse n is calculated by the value of the average radiation power. Knowing the average energy of one optical pulse and the repetition rate of the unattenuated optical pulses, and the wavelength of the laser, we can calculate the average number of photons in one pulse:
p · λ
μ =–, (2)
f · c · h
where P is the average radiation power [W];
f is the pulse repetition rate [Hz];
λ is the average radiation wavelength [nm];
h is Planck’s constant (h ≈ 6.63∙10–34 [J ∙ s]),
c is the speed of light in vacuum (c ≈ 2.99 ∙ 108 m/s).
Knowledge of the quantum efficiency, the probability of dark counts and after pulses, as well as the pulse repetition rate (it is necessary to synchronize the calibrated photodetector and the output of the QKD system) makes it possible to recalculate the frequency of the photodetector under the influence of radiation from the output of the QKD system to the average number of photons. In real QKD systems, the average number of photons per pulse is constantly monitored so that the proportion of multiphoton pulses does not exceed the threshold value at which the quantum protocol ceases to be secret.
Decoy-states for countering a photon number splitting attack [12]
In stable attenuated laser radiation, the number of photons in a pulse is described by Poisson statistics, which inevitably leads to a known share of multiphoton pulses. On the one hand, this fact imposes additional restrictions on the technical implementation of the quantum protocol, but on the other hand, knowledge of statistics provides a relatively simple and elegant opportunity to detect outside interference in the process of quantum key distribution.
This is used in the Decoy-state method [7, 13, 14], which consists in preparing and transmitting, specially prepared decoy states, along with information states. In addition to information states with an average number of photons μ, Alice prepares some share of decoy states with other average numbers of photons: ν1 and ν2. At the same time, which of the states will be sent is randomly selected each time. Electro-optical intensity modulators are used to prepare information states and decoy states in Decoy-state protocols.
Eve does not know in advance the state with what average number of photons is in the channel, so it acts the same with each parcel. Her intervention distorts the statistics of Bob’s counts in different ways for each set of states with an average number of photons per pulse μ, ν1 and ν2.
After basis announcement and discarding mismatched bases, Bob finds out which set of states each click answered, and can calculate statistics separately for each set with the numbers μ, ν1 and ν2. According to the statistics of detector triggers for decoy states, Bob calculate the proportion of a single-photon component in information pulses. If this proportion remains within the required limits, then the protocol will remain secure, Alice and Bob start information reconciliation and privacy amplification procedures, considering that the key is formed only on a single-photon component.
And if the proportion of a single-photon component turns out to be different than it is predetermined by Poisson statistics for three sets of states with photon numbers μ, ν1 and ν2, then it can be assumed that the attacker intervened and launched a Photon Number Splitting attack (PNS) [12].
Of course, it would be much more convenient to have an ideal single-photon source – a source with exactly one photon per pulse. Such a source would simplify the technical implementation of quantum protocols and weaken the mathematical requirements for protocol security. There are a number of requirements that an ideal single-photon source must meet.
What are the requirements for an ideal single-photon source? [15]
one photon can be emitted at any arbitrarily determined time by the user (that is, the source is deterministic or “on demand” – single photon on demand),
the probability of emitting one photon is 100%,
the probability of multiphoton emission is 0%,
the emitted photons are indistinguishable,
the repetition rate is maximum (limited only by the time duration of a single-photon pulse).
Deviations from these ideal characteristics, which are always present in the real world, should be taken into account when setting up experiments and developing encryption systems.
For commercial QKD systems, there are additional requirements for an ideal single-photon source:
the wavelength in the telecommunication C-band range (usually, 1550 nm);
photon repetition rate over 100 MHz:
high brightness;
high quantum yield.
electrical excitation.
Working at room temperature
Most traditional single-photon sources require low temperatures to achieve optimal performance. From a practical point of view, the most interesting sources are those that operate at room temperature. Research is being conducted in the field of single-photon sources based on A3B5 semiconductors, such as gallium nitride (GaN) and indium nitride (InN), for example, quantum dots based on gallium nitride (GaN) can provide single-photon radiation at room temperature. Also promising objects for creating single-photon sources at room temperature are color defects in diamond, for example, NV centers (nitrogen vacancy). To date, the development of stable and efficient single-photon sources at room temperature is an active area of research. Technologies and materials continue to evolve, and significant breakthroughs in this area may be achieved in the future.
Work in the telecommunications range
Quantum communications and quantum networks require single-photon sources designed for the telecommunication wavelength range (about 1550 nm). Sources emitting in other optical fiber transparency windows are also interesting, – 1310 nm and about 850 nm, – but losses in optical fiber at these wavelengths are much higher.
These can be single-photon sources based on spontaneous parametric down-conversion (SPDC) in nonlinear crystals that generate a pair of photons with different energies, including one (or both) photon in the telecommunications range. InAs-based quantum dots have the potential to generate single-photon signals in the near infrared range. Some ions in the crystal matrix, such as erbium (Er3+) and praseodymium (Pr3+) ions, can generate single photons in the telecommunications range.
Superconducting nanowires, superconducting monatomic contacts, carbon nanotubes and graphene nanostructures, nanocrystals and quantum dots in a liquid or polymer matrix may also be promising.
Another area of scientific research in the field of developing single-photon sources for the telecommunication wavelength range is the development of methods for converting single photons of submicron wavelengths into photons of the telecommunication range. This can be done, for example, using cascade Raman scattering in a stepwise Bregg resonator in a single-mode optical fiber [16], or using four-wave mixing in a periodically poled lithium niobate waveguide [17]. Very attractive in this context is the idea of integrating single synthetic nanodiamonds containing a single color center directly into an optical fiber or into the structure of a photonic integrated circuit, after which frequency conversion can be implemented using well-developed fiber or integrated technologies.
At the same time, optical communication systems and quantum key distribution systems in open space (in the atmosphere, earth-satellite or in space between two spacecraft) are being actively developed, where different wavelengths can be used, and for these tasks there is no a requirement of a strictly defined wavelength for the source.
Indistinguishability
of emitted photons
For practical use, photons emitted from a single-photon source must be indistinguishable. Indistinguishable photons must have the same wavelength, polarization, and temporal and spatial extent. The Hong-Ou-Mandel effect is used to characterize indistinguishability.
The Hong-Ou-Mandel (HOM) effect is a two-photons interference phenomenon, wherein two indistinguishable photons are interfered on a symmetrical beam splitter, and the photons always emerge on the same, but random output port.
Two photons from one source are prepared so that they arrive simultaneously at the two inputs of a symmetrical beam splitter. Detectors are placed at both outputs of the beam splitter, and the coincidence between the two detectors is measured. If the photons are indistinguishable, there should be no coincidences[18]. Almost perfect indistinguishability has been experimentally realized [19, 20].
Electrical or optical pumping.
One of the requirements of practical implementation is the use of electric pumping. It is generally believed that electric pumping is more technically simple to implement than optical or microwave, and this opinion is justified by a completely reasonable desire to use standard microelectronic technologies for the production of single-photon sources. The implementation of electrical control in microelectronic technology is not a problem, while the implementation of optical components in an integrated design is not yet a generally accepted practice.
At the same time, we should not forget about the rapid development of photonic integrated circuit technologies, as well as the growing desire of microelectronics manufacturers to integrate optical data buses to connect blocks of modern silicon chips. Sooner or later, this will lead to the creation of microelectronic transceivers and receivers as elements of an integrated circuit of a next-generation processor, or as elements of a photonic integrated circuit, and the technological issues of optical pumping distribution to a single-photon emitter will be largely resolved. Currently, it is impossible to go without mentioning the desire for electrical control of a single-photon source, but in the near future this issue will turn out to be unprincipled.
Key parameters of single-photon sources for QKD systems
Table 1 lists the parameters that are monitored during metrological measurements of single-photon sources in an accredited testing laboratory.
The main types of single photon sources
So, the use of an attenuated laser is a compromise temporary technical solution, which is used due to the lack of commercially available true single-photon sources. True single-photon sources could mitigate the protocol implementation requirements and increase the speed of quantum key generation. Currently, active scientific research is underway, and a large number of scientific articles on the topic of single-photon sources are being published. Single-photon sources for other wavelengths are already being sold. The emergence of commercial single-photon sources for QKD by optical fiber is not far off.
Probabilistic (non-deterministic) sources are based on photon pairs that are created using parametric downconversion (PDC) in bulk crystals [21, 22] and waveguides [23, 24] and four-wave mixing (FWM) processes in optical fibers [25, 26].
Deterministic sources (allowing to emit a single photon “on demand”) use color centers [27, 28], quantum dots [29–31], single atoms [32, 33], single ions [34], single molecules [35] and atomic ensembles [36].
The clear distinction between the two types of sources is blurred in real applications, because, for example, a truly deterministic source based on the color center becomes probabilistic, provided that losses associated with radiation output from the material area where the color center is located are taken into account.
Heralded single-photon sources [37–40]
Heralded single-photon sources provide an opportunity to accurately determine the moment of generation of a single photon. Heralded single-photon sources generate single photons and simultaneously send a heralding that a photon has been successfully generated. This allows us to know exactly when and where a single photon was generated.
Heralded single-photon sources provide certainty of the presence of a single photon by pre-detection or notification of its generation. A typical implementation of such a source uses a nonlinear optical process known as spontaneous parametric scattering using nonlinear crystals. In this process, under certain conditions of interaction of photons with matter, one photon decomposes into two – a signal photon and a heralding photon. A heralding photon, which is information about the generation of a photon signal, can be detected and registered using a photodetector or other light detector. This heralding allows you to know for sure that the generation of a single photon has occurred, and provides information about its status.
Such sources operate on the basis of certain quantum mechanical processes, such as spontaneous parametric scattering, emission of fluorescent glow from a single-molecular crystalline dye or a high-intensity fluorescent lamp. Nonlinear optical processes in nonlinear crystals are often used. The most widely used heralded single-photon sources based on spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (FWM).
The main platforms used
for the manufacture of SPS [41]
- SPS on single atoms and ions;
- SPS on nonlinear effects in crystals: spontaneous parametric down-conversion (SPDC) or four-wave mixing (FWM);
- SPS on quantum dots;
- SPS on NV-centers in diamond and color centers in nanocrystals;
- SPS on carbon nanotubes.
Single-photon sources based on single ions [42–46]
To create a single photon source based on single ions for a wavelength of 1550 nanometers, the most suitable ions are ions of rare earth elements such as erbium (Er), thulium (Tm) or Praseodymium (Pr) operating in the infrared region of the spectrum. This is due to the fact that ions of rare earth elements have energy transitions between energy levels corresponding to the telecom wavelength. In particular, erbium (Er) ions are widely used to generate single photons at 1550 nm. For a wavelength of 1310 nanometers, cerium (Ce3+), praseodymium (Pr3+), ytterbium (Yb3+) or erbium (Er3+) ions are best suited.
Special magnetostatic traps are used to hold ions (Penning trap, Paul trap, radio frequency trap, trap with a rotating electric field, etc.) (Fig.5.). Ions can be formed directly by ionizing gas near or inside the trap (for example, by an electron beam or corona discharge) and held in the trap for a sufficient time to excite energy levels and spontaneous or stimulated photon emission. Buffer gas or laser cooling is used to cool the particles. Due to the Coulomb repulsion of charged particles, it is possible to organize a trap in such a way that exactly one ion is held in a certain area of space, and exactly one photon is emitted at each exposure.
The ions used as single-photon emitters [48–50] have a configuration of energy levels with two ground states and one excited state. With the help of a radio frequency ion trap, it is possible to stably localize a single ion in the center of an optical resonator, and limit the ion wave packet to a length much shorter than the optical wavelength, as well as fix the position of the wave packet with an accuracy of several nanometers. This ensures the continuous production of single-photon pulses. Since there is only one ion inside the resonator, the possibility of multiphoton events is excluded [49, 51].
Single ions as the basis of a single-photon source have the advantage that they are all identical, and demonstrate indistinguishability between different sources and different pulses from the same source.
The difficulty lies in the fact that resonant ion transitions occur in the ultraviolet region and excited states have high rates of spontaneous decay. Radiation in the resonant mode is accompanied by spontaneous radiation. In addition, the ion can remain in the ground state at the end of the excitation pulse without emitting a single photon. These factors can seriously reduce the probability of emitting single photon during each pump cycle. Another problem concerns how efficiently light can be collected, since the usual solution for neutral atoms – using strongly coupled resonators – is difficult for charged particles.
The improvement of experimental techniques in the manipulation of individual ions is due to the fact that one of the priorities in the development of quantum computers is the development of a quantum computer based on trapped ions [52–54]. Demonstrators of a quantum computer based on several hundred trapped ions have already been developed. It should be noted that the same applies to individual atoms; diffraction methods for creating three-dimensional optical atomic traps have made it possible to capture and hold more than ten thousand individual atoms.
Single-photon sources based on ultracold atoms
In traps, due to electromagnetic forces, it is possible to retain not only ions or charged elementary particles, but also neutral atoms if they have of nonzero dipole moments or magnetic moments.
Sources of single photons based on individual atoms typically operate at low temperatures and/or in vacuum conditions. Today, alkali metals atoms such as Cs and Rb are used [55–60].
First, you need to prepare a system in which individual atoms will be present. This can be achieved, for example, by laser cooling of a beam of atoms and placing atoms in optical traps.
To stop an atom, it needs to be cooled, i. e., to reduce its speed to less than a few centimeters per second. There are various ways to do this, but the most convenient method turned out to be laser cooling. Laser beams create a series of standing waves of polarized light, whose electric fields resemble a kind of comb. When an atom passes through it, bursts of electric field alternately “reset” the atom to an increasingly lower energy state and cool it down more and more [61].
Various traps have been developed to hold single atoms. One of the most common ways to hold single atoms is using optical gratings. Focused laser beams are used, which create an electromagnetic field with periodic potential wells for atoms. There are also magnetic, electrostatic, magneto-optical and microdipole traps [61, 62]. Historically, the Pauli trap and the Penning trap were invented first. Holographic traps are very interesting from a technical point of view, where the three-dimensional structure of potential wells in space is formed as a result of projecting a hologram through a holographic mask [63].
After capturing single atoms inside the trap, the atoms are excited by a laser. The laser system must be tuned to a certain energy corresponding to the transition of the selected atom from the ground state to the excited state. As a result of the excitation of a single atom, its electron transitions to an excited state. Relaxation from the excited state to the ground state is accompanied by the emission of a single photon. In each such process, a single photon is generated on a single atom. The emission of single photons can occur spontaneously or through a stimulated process, depending on the experimental conditions. As in the case of single ions, individual neutral atoms are identical, and different impulses from the same source and from different sources are indistinguishable. Ultracold atoms have a long coherence length, which means that the photons emitted by these atoms can maintain phase correlation over long time intervals.
Monatomic emitter
Another approach may be as follows: single atoms are first captured and cooled inside an open magneto-optical trap. Then the trap is turned off (or periodically turned off and on, or the amplitude of the field in the trap is periodically modulated) and the cooled atoms alternately fall freely under the influence of gravity and one by one pass through a high-precision optical resonator tuned to the frequency of the radiative optical transition of atoms. The probability of photon emission in a resonator with a suitable frequency is significantly higher than in free space, due to the Purcell effect. The efficiency of single photon generation for this approach may be close to 1, but the implementation of a monatomic emitter requires serious experimental efforts. Narrow beams of atoms are also used, irradiation of which with a laser yields single-photon radiation.
Single photon sources based on ultracold atoms have significant disadvantages: high complexity of implementation in comparison with other methods of generating single photons, limited operating conditions, low generation rate, poor scalability. The creation of single photon sources based on ultracold atoms requires a complex experimental arrangement. The implementation of a single-photon source on ultracold atoms requires high stability of the system, precise adjustment and control of experimental conditions. Creating large arrays of single-photon sources based on ultracold atoms is becoming technically difficult and requires significant costs and efforts. The rate of generation of single photons based on ultracold atoms may be low, especially in comparison with some other methods such as spontaneous parametric scattering or generation through quantum dots.
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