single-photon sources (original) (raw)

Acronym: SPS

Definition: light sources the output of which approximates a single-photon state

Alternative term: single-photon emitters

Categories: photonic devices, quantum photonics

• light sources
  • quantum light sources
    * squeezed light sources
    * single-photon sources
    * deterministic photon sources
    * heralded photon sources
    * photon pair sources

Related: photonsFock statesphoton pair sourcesquantum photonicsquantum optics

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DOI: 10.61835/gdy Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

What is a Single-photon Source?

A single-photon source (or single-photon emitter) is a light source with special quantum properties: Its output approximates a quantum state with a single photon (a 1-photon Fock state) in a specific mode.

For a closed optical resonator (cavity), the concept of a single‑photon state is straightforward: It corresponds to a single quantum of energy stored in a discrete, stationary cavity mode. For a propagating beam (e.g. in free space or in an optical fiber), the single‑photon state is instead defined with respect to a traveling‑wave mode — for example, the guided mode of a single-mode fiber. In this case, the quantum state also includes the temporal envelope and spectral distribution of the photon: The photon’s wave packet is localized within a certain time window (typically with a single-sided exponential decay profile) and spectral window. Of course, the widths of temporal and spectral window are related to each other; their product is in the best case Fourier-limited.

As two such non‑overlapping temporal modes are orthogonal, multiple single‑photon states can propagate one after another in the same spatial mode, provided their pulses are sufficiently separated in time.

There are two fundamentally different kinds of single-photon sources:

On-demand Single-photon Sources

On-demand sources (also called deterministic sources) deliver a single photon when receiving some kind of trigger signal — for example, an incoming light pulse or an electrical pulse. The ideal result is a one-photon Fock state in a well-defined spatial–temporal mode, but practically, purity, brightness and indistinguishability (see below) can be limited by multi-photon emission, imperfect coupling, and background noise, for example.

Most designs use some kind of quantum emitters with two or more energy levels — for example:

• a trapped atom or ion
• a color center, e.g. a nitrogen vacancy in diamond
• a single molecule
• a self-assembled or colloidal semiconductor quantum dot

Excitation is achieved with tailored optical or electrical pump pulses. While electrical pumping is simpler and may be suitable for higher repetition rates, optical pumping often leads to better quantum state fidelity. There are sophisticated techniques of coherent population transfer, such as STIRAP = Stimulated Raman Adiabatic Passage using two pump lasers, which results in a particularly high quantum purity and indistinguishability.

Suppressing multi-photon events and scattered pump light often involves spectral and/or polarization filtering. For example, a quantum dot may emit multiple photons (after absorbing multiple pump photons), but these have somewhat different wavelengths; spectral filtering allows one to obtain single photons. Bi-excitonic and excitonic transitions are the most commonly used. One also must safely avoid photons of pump light to be scattered into the output.

Obtaining emission into a single spatial mode is a fundamental challenge. Typically, one achieves that by placing the emitter in a high-Q optical resonator, leveraging the Purcell effect (known from cavity quantum electro-dynamics) to get emission preferentially into the fundamental resonator mode. Various kinds of microcavities, including micropillar Fabry-Perot resonators, photonic crystal cavities and plasmonic devices, are used. They are usually coupled to some kind of waveguides, e.g. nanofibers or photonic crystal waveguides. There are also quantum dots directly coupled to a waveguide.

Note that coupling to a high-Q cavity can not only bring improved coupling efficiency and thus brightness, but also bring additional benefits: It can enhance photon indistinguishability by reducing influences of dephasing effects (see below) in a shorter emission time. Also, higher repetition rates may be enabled.

Heralded Single-photon Sources

Heralded sources, also called probabilistic single-photon sources, do not allow one to control when a photon is emitted: Emission times are random. However, in the ideal case every emitted photon is “heralded” (indicated) by a generated signal. Heralded sources may be used in experiments such that measurements are triggered only when a photon emission is heralded.

The heralding involves the creation of separable photon pairs, where one photon is detected. Different processes can be used for photon pair generation; the most common choice is non-degenerate parametric fluorescence (SPDC = spontaneous parametric downconversion) in nonlinear processes:

• This can be based on a ($\chi^{(2)}$) nonlinear crystal, where a pump photon can (with a low probability) be converted into a signal and idler photon pair, but not e.g. into a signal photon alone. Through their different wavelengths (or possibly through different polarizations), signal and idler photons can easily be separated.
• Four-wave mixing (FWM) is similar, but uses a ($\chi^{(3)}$) nonlinearity. Two pump photons (rather than one) can be converted to a pump and signal photon pair, having a higher and lower optical frequency, respectively, which again allows their easy separation from the pump light.

A very helpful property of such parametric processes is the directed emission. Ideally, one utilizes such processes in nonlinear waveguides, e.g. in periodically poled LiNbO3 devices, to directly obtain a single-mode output. Quasi-phase matching is an essential tool for such devices.

In any case, a real-world source is never perfect. In particular, some emitted photons may not be heralded due to a non-perfect quantum efficiency of the photodetector, or the produced photon is lost.

Unfortunately, the conversion efficiency from pump to signal and idler photons is low due to a trade-off with quantum state fidelity: Increasing pump intensity increases the efficiency, but decreases quantum state fidelity. Nevertheless, high photon generation rates can be achieved, e.g. millions of photons per second. However, the brightness (see below) is low, and the power conversion efficiency is unsatisfactory. The optical bandwidth, which is often substantial, is usually determined by phase matching. The pump bandwidth can also play a role in the optimization.

Quantum dot sources (optically or electrically pumped) have also been used to produce photon pairs with multi-megahertz emission rates, using a biexciton-exciton cascade. Key advantages of that technological approach are a more compact setup with better conversion efficiency, which can also be much cheaper to fabricate. However, cavity coupling is needed as for on-demand sources, and various imperfections introduce challenges for achieving high performance.

Multiplexed Heralded Single-photon Sources

Heralded sources have a fundamental limitation of brightness, as explained above. However, the concept can be further enhanced with multiplexing. Various multiplexing strategies offer unique advantages and limitations for boosting the single-photon generation probability while maintaining high purity and indistinguishability.

In one variant of this approach, multiple heralded sources are connected to a responsive multiplexer capable of routing the output from any successful source to a common single-mode output channel. Each time a heralding detector registers an emission event, the multiplexer swiftly reconfigures to direct the corresponding single photon from the successful emitter. As a result, the brightness can be far higher than achievable with a single source, while the other quantum qualities are largely preserved.

Another method uses a single source and temporal multiplexing. Here, the generated photons are sent into an active temporal delay network, where optical switches are used to direct generated photons to the output. This results in a lower repetition rate, but with increased probability of obtaining photons at the expected times.

Applications of Single-photon Sources

Single-photon sources are widely used in quantum photonics, both for fundamental physics experiments and for applications in quantum technology:

• As examples of fundamental physics applications, single-photon sources can be used for tests of photon statistics, wave–particle duality, delayed-choice experiments, tests of Bell inequality violations and quantum teleportation.
• Quantum key distribution for quantum-secure communications (quantum cryptography) can utilize single-photon sources, e.g. when using the Bennett–Brassard protocol [1]. However, many systems still use weak laser pulses as a simpler, although not perfect solution.
• Quantum random number generation can be implemented using single-photon sources.
• Quantum computing can employ different technologies, where photonics provides some options. For example, one generates single photons as carriers of “flying qubits”, i.e., qubits which can be transported, e.g. via optical fibers. Multiphoton Boson sampling can be performed with single photons, and may find applications in quantum machine learning.
• Quantum metrology can also use single-photon sources in various ways, e.g. for some types of quantum-enhanced measurements and as quantum radiometric standards for the characterization of single-photon detectors.

Applications differ a lot in terms of their requirements on single-photon sources, which makes the suitability of specific technologies substantially application-dependent. The following section discusses key properties which are often relevant.

Properties of Single-photon Sources

The most essential performance aspects of single-photon sources, describing details of quantum state fidelity, can be described with three dimensionless parameters for brightness, purity and indistinguishability, as explained in the following. Various other aspects can also be relevant for applications.

Brightness

For deterministic (on-demand) sources, the brightness ($B$) is understood as the probability that an applied trigger event indeed produces a photon. For probabilistic sources, it is the probability that after a photon is heralded one indeed obtains a photon.

Brightness is a product of various factors: the efficiencies of emission (the emitter’s intrinsic quantum efficiency), collection and possibly coupling to the desired output channel (e.g. to an output waveguide). Sometimes, brightness values are specified which exclude certain factors — for example, brightness based on emission without considering collection and coupling.

Ideally, one has ($B = 1$). A high brightness is generally desirable for applications, but some applications can indeed still work reasonably well with a low-brightness source ($B$) far below 1, possibly at the cost of longer measurement times.

Purity of Single-photon State

Ideally, a single-photon source would never generate more than a single photon, but this can happen based on various mechanisms, depending on the type of source. The hallmark quantum statistical property of single-photon sources is photon antibunching: Following the detection of one photon, it is unlikely to detect another in a short time window.

Photon antibunching can be quantitatively described with a second-order correlation function ($g^{(2)}(\tau)$): Perfect antibunching means that ($g^{(2)}(0) = 0$); in practice, one can at least have a small ($g^{(2)}(\tau)$) (far below 1) for small arguments ($\tau$). This is called the Hanbury Brown and Twiss effect. The second-order correlation function is measured by sending the light to a 50:50 beam splitter with two following single-photon photodetectors with high quantum efficiency; the detector signals are processed with correlation electronics.

A common metric for single-photon purity is ($P = 1 - g^{(2)}(0)$). Values close to ($P = 1$) (above 0.9 or even 0.98) are attained using advanced emitter technologies and are generally required for quantum optical applications.

Classic light sources such as fluorescent lamps and thermal radiators do not show antibunching: Fluorescence typically yields Poissonian statistics with ($g^{(2)}(\tau) = 1$), indicating uncorrelated photon arrival times, while thermal sources even display photon bunching with ($g^{(2)}(0) = 2$). Strongly attenuated laser beams (coherent states) also have Poissonian statistics and ($P = 0$); they are not considered true single-photon sources, although they can be used in some quantum experiments and in quantum key distribution.

Propagation losses degrade the observed purity by mixing in vacuum states. Careful optical engineering is thus needed to preserve quantum statistical properties from source to application.

Photon Indistinguishability

Ideal single-photon sources emit photons that are indistinguishable in all quantum degrees of freedom: optical frequency, polarization, spatial–temporal mode, and arrival time. This indistinguishability underlies quantum interference effects. For example, in a Hong–Ou–Mandel (HOM) interferometer, two identical photons are sent into a beam splitter and will exhibit perfect coalescence, suppressing coincident detections. The contrast of this HOM “dip” quantifies the indistinguishability parameter ($I$), providing a direct performance metric for photon sources.

Indistinguishability of photons from one source is compromised by dephasing processes, such as phonon interactions in solid-state emitters, which broaden the optical spectrum beyond its transform limit and disrupt quantum coherence. Cryogenic operation, advanced material engineering and optimized cavity enhancement are often used to minimize these effects.

If photons are generated in multiple quantum dots, their indistinguishability is also easily compromised by variations in the properties of the quantum dots, in particular in their spectral properties. Therefore, there are attempts to tune their emission spectra to the same value. That problem is avoided when using single atoms or ions, which are clearly indistinguishable, assuming that only one isotope occurs.

While high photon indistinguishability is essential for quantum computing, quantum teleportation, and multi-photon interference experiments, some quantum key distribution protocols are robust even with moderate or poor III values.

Other Properties

In addition to brightness, purity, and indistinguishability, several other source properties can be critical:

• Deterministic vs. heralded: Some applications (e.g., clocked photonic quantum gates) require on‑demand sources, while others can accommodate heralded, probabilistic sources.
• Single spatial mode: Efficient use generally requires photons in a well‑defined mode, such as the fundamental mode of a single‑mode fiber. Emission into random directions reduces collection efficiency and usability.
• Wavelength and bandwidth: The emission wavelength should match the spectral sensitivity of efficient detectors (e.g., avalanche photodiodes) and/or align with low‑loss transmission windows (e.g., telecom C‑band) of telecom fibers. The spectral bandwidth influences compatibility with filtering, interference visibility, and quantum memories.
• Polarization: Applications differ in their tolerance for polarization fluctuations. Fixed, well‑defined polarization can be essential when involving interference effects.
• Integration potential: Some emitter platforms are naturally compatible with photonic integrated circuits (e.g., based on silicon photonics), facilitating on‑chip quantum processing.
• Scalability: To enable practical quantum computing and networking, single-photon sources must be scalable — meaning they can be well reproducibly integrated into large arrays or photonic chips with high efficiency, purity, and indistinguishability. Challenges like uniform photon generation, loss minimization and real-time reconfigurability must be addressed towards that goal. Overcoming scalability hurdles directly impacts the feasibility of error-corrected multi-photon quantum technologies.
• Operating conditions: Operational temperature requirements range from room‑temperature devices to those needing cryogenic cooling. Sensitivity to mechanical vibrations, magnetic fields, and electrical noise also varies.

Methods of quantum‑state tomography can be used to fully characterize a source’s output state — capturing its optical spectrum, polarization, and inter‑modal correlations. Such comprehensive validation is essential for demanding applications, though it is experimentally complex.

The specific combination of these properties required depends strongly on the target application; for example, quantum networking and computing demand stricter control over all mode parameters than basic quantum key distribution.

Currently available single-photon sources are generally exhibiting non-ideal performance and/or substantial technical complexity. Their further optimization is a crucial element for the general development of quantum technology.

Various other types of devices are often used in conjunction with single-photon sources:

• Single-photon detectors with high quantum efficiency and low noise are often needed in this context. Different technologies can be used:
  • Avalanche photodiodes operated in Geiger mode are a common choice.
  • Superconducting nanowire single-photon detectors (SNSPDs) offerer superior timing resolution, high quantum efficiency and ultra-low dark count rate.
  • Photomultiplier tubes (PMTs) are another option.
• Quantum memories store and retrieve single-photon quantum states on demand.
• Optical modulators and optical switches of various types can be essential for quantum processing.
• Waveguides, photonic lanterns and photonic integrated circuits enable scalable photonic architectures, complex quantum circuits, and robust photon routing.
• Various types of optical components and devices are often employed:
  • Beam splitters are essential for superimposing quantum states of light, e.g. in interferometers.
  • Optical delay lines are employed for timing adjustments, e.g. when interfering subsequently emitted photons.
  • Spectral and polarization filters are important parts of some single-photon sources, and also used together with them.
  • Optical resonators, e.g. in the form of microcavities, are parts of many single-photon sources and may be used in further quantum processing.

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