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A single photon source is a device in which quantum mechanical properties of the quantized radiation field are employed to allow for an accurate control of emitted photons on demand. This class of device enables the encoding of information on a single photon level, which generates particular interest for applications in quantum computing and quantum cryptology.

The requirement for an effective single photon source is that an active emitter possess a high quantum efficiency of ? ˜ 1, and is able to emit one photon after another. It has been demonstrated that individual self-assembled quantum dots are apt for the generation of single photons due to their ability to be produced in large numbers, integrated into complex systems, and be pumped either optically or electrically. Additionally, a self-assembled quantum dot can be easily embedded in an appropriate microcavity in order to achieve a high photon collection efficiency[3]. In fact, it has been argued that the most promising application for quantum dots is in single photon generation[4].

History

The first successful generation of single photons was performed in 1974 by J. F. Clauser[5], and was based on a cascade transition of calcium atoms. In these experiments, each excited atom delivered a couple of photons with different wavelengths. One of the photons was detected after spectral filtering and was used for the conditional detection of the companion photon. These one-photon states produced an anticorrelation effect, which does not exist for a classical wave. It was observed that upon interaction with a beam splitter, there was no coincidence between the reflected and transmitted photons. This phenomenon was dubbed “antibunching”.

Unfortunately, the brightness from these early sources was very low, so throughout the 1980s a great deal of research was performed on trapping single ions. These traps provided long observation times with one and the same ion. This long series of antibunched photons came closer to an ideal device that could emit photons on demand. Around the same time, pairs of correlated photons were obtained at high rates by parametric down-conversion. This process involves sending a short laser pulse into a nonlinear crystal to generate pairs of signal and idler photons, and remains a cornerstone of quantum optics experiments[6].

In the 1990s, sensitive detection of fluorescence led to the detection of single organic molecules and later, single semiconductor heterostructures. This caused some of the quantum optics experiments that were previously conducted on atoms and ions in gas to be reproduced in condensed matter. It was not long before nano-structures were proposed as possible sources for single photon generation[6]. Ever since the late 1990s, a variety of nano-structures were experimented with, and now the majority of single photon emitters are making use of the quantum dot structure.

Photon optics

When dealing with the interaction of light and matter in the quantum regime, the electromagnetic field can be represented in terms of a quantized harmonic oscillator. Each quanta of this representation of the electromagnetic field is a photon. Additionally, every observable of the field (amplitude, phase, etc.) becomes an operator.

Some of these operators commute, and some do not. In fact, since the field is represented by a harmonic oscillator, and electromagnetic mode can be described by two non-commuting operators analogous to position and momentum for a one-dimensional particle. These operators can either be regarded as the electric field and the vector potential, or the amplitude and the phase. All non-commuting operators imply an uncertainty relation, in which a precise measurement of the observable is limited. However, one of the uniqe traits of the electromagnetic field in the quantum regime is the possibility to squeeze light. When the light is squeezed, a very precise measurement of one observable can be measured at the cost of precision in the other observable. This property allows for the measurement of very weak absorption.

Quantum dots

Main article: Quantum dot

A quantum dot is a semiconductor nano-structure that is confined in all three spatial dimensions. Quantum dots are often referred to as “artificial atoms” due to the atom-like discrete energy level spectrum that arises as a result of their confinement. Quantum dots provide a quantum system which can be grown within a variety of semiconductor devices, and can be engineering to have a wide range of desired properties [7].

There are a variety of methods to effectively produce quantum dots. The two categories of quantum dot formation are the top-down and bottom-up approach. In the top-down approach, quantum dots are formed using fabrication methods. An active layer is patterned lithographically and etched, so that only the dots remain. The bottom-up approach is a growth process using either synthesized precursor compounds (forming colloidal nanocrystals), or epitaxial growth of strained semiconductor layers. In the strained layer approach, one material will be deposited onto a lattice mismatched substrate, and islands will form instead of a uniform layer in an effort to minimize surface strain. This effect is known as Stranski-Krastanov (SK) growth. These islands form quantum dots, which depending on the material system can produce good optical qualities.

Optical properties of quantum dots

If the quantum dot material has a lower bandgap energy than the substrate material, the quantum dot forms a potential trap for electrons and holes. If the dot is sufficiently small, only a few quantized states are confined within the dot. Both the valence band and conduction band holds two electrons or holes of opposite spin. Therefore, if the quantum dot is excited with a picosecond laser pulse, the carriers become excited and rapidly relax to the lowest energy state. This quantum dot has captured two electrons and two holes that form a biexciton state, which decays by a radiative cascade. One of the trapped electron-hole pair produces a photon (the biexciton photon), and the second electron hole pair produces a second photon (the exciton photon) [7].

Multiple excitations can coexist in self-assembled quantum dots and can also coexist with charge carriers. This leads to characteristic bi or multi-exciton lines and to trion or even multi-charged lines when an exciton is combined with an electron or a hole. The advantages for quantum dots over other photonic crystals are the higher purity and crystalline quality, less defect sites to promote non-radiative recombination, and the smaller size and larger quantum confinement[6].

Because of the multi-exciton lines, a quantum dot single photon source must work at a low temperature (~5-10°K), and the mono-excitonic emission must be filtered out spectrally. At higher temperatures, the excitons escape towards the wetting layers or the substrate, and the luminescence efficiency of the dot decreases[6].

Devices

In order for a quantum dot single photon emitter to be practical, it is beneficial to be electrically driven. Ideally, these devices should be small, robust, efficient, and have a low probability of emitting more than one photon[4]. Extensive research and development has been put into the development of quantum dot single photon sources that meet these criteria.

Electrically injected single photon emitting diodes (SPED) were reported as early as 2000, and development has continued since. A simple SPED consists of a vertical p-i-n junction with a layer of low density quantum dots within the intrinsic region. An opaque metallic film patterned with micron-sized apertures on the surface of the device allowed emission to be collected from only one dot[4]. As the voltage increases, carriers are injected into the device and some result in emission from the dot directly beneath the aperture.

A wide variety of devices that utilize a quantum dot for single photon emission have been developed. Below is a brief description of several specific devices collected from literature that have been fabricated.

Self-assembled InAs quantum dots embedded in GaAs disks

InAs quantum dots are grown on a GaAs substrate using molecular beam epitaxy (MBE). The quantum dot region is located within a GaAs disk that is suspended above the substrate surface. Optical pumping of this device is performed using a mode-locked femptosecond laser. The electron-hole pairs are generated in the GaAs barrier region and then captured by the InAs quantum dots. The emitted photons were split by a 50/50 beam splitter, and the resulting beams were measured using single-photon-counting avalanche diodes (SPAD) .

Self-assembled CdSe quantum dots embedded in ZnSe mesas

Self-assembled CdSe quantum dots were deposited on a GaAs substrate, and surrounded by ZnSe barriers. This structure was then etched to form mesas containing around 10 quantum dots on average. The sample was then excited using a continuous-wave (cw) laser, while photon correlation measurements were performed by excitation with a frequency-doubled mode-locked femptosecond laser. The photon collection mechanism is similar to that of the InAs quantum dot device, in that the beam of photons impinges upon a 50/50 beam splitter, and is measured on two SPADs[3].

Electrically driven InAs quantum dots

InAs quantum dots are confined within the intrinsic region of an MBE-grown GaAs p-i-n diode, as a metallic contact supplies electric excitation. At low injection currents, the dot electroluminescence spectrum reveals a single sharp line due to the exciton recombination, with another line due to the biexciton recombination[8]. This demonstrates that electrically-driven quantum dot single photon sources are possible, which is a significant step towards wide scale adoption.

Applications

Quantum cryptography

Being able to control the flow of light on a single photon level supports a relatively straightforward method of encoding and manipulating quantum information. Carrying information on a single photon provides a means to test the secrecy of optical communications, which can be applied to the problem of sharing digital cryptographic keys[7]. In this application of quantum key distribution (QKD), the well-defined character of the single photon state is exploited to detect and prevent any spying on the transmission of information.

In a statistical representation of number states, like in a traditional LED or laser, an eavesdropper can escape detection while attempting to extract information from an encrypted signal. However, in a well-prepared number state as generated by a single photon source, this is impossible, due to the inability to measure a quantum state without modifying it. Therefore, any attempt to access the information while the photon is en route introduces detectable errors in the communication[6].

Random number generation

Most common random number generators rely on one of two approaches. The first, pseudorandom generators use a mathematical computer algorithm to pick numbers at random. The second, physical random generators rely on the inherent randomness of noise of a physical observable. Both of these approaches suffer from systematic errors and perturbations that cause the system to deviate from a truly random distribution of numbers.

Quantum mechanics provides a truly physical source of randomness. If a photon impacts a 50/50 beam splitter, there is an equal probability of being either reflected or transmitted. The outcome of the photon is truly random and independent of history or other experimental parameters. A stream of precisely controlled photons whose outcomes are completely independent of each other can lead to an ideal random number generator[6].

Measurement of weak absorptions

Using traditional light sources, the measurement of weak absorption signals is hampered by the fluctuations in the number of photons. The low noise level of a single photon source is very valuable for these measurements. A single photon source produces amplitude-squeezed light which implies reduced noise for amplitude measurements when compared to the coherent states that follow a Poisson distribution. In fact, a perfect single photon source should be associated with perfect detection, allowing for arbitrarily small absorption measurements, which would be impossible to accomplish with a laser source[6].

Other applications

Due to the complex nature of the quantum system, a variety of exotic theoretical applications are being considered. These include (but are most certainly not limited to) using photons as “flying qubits” in quantum computing[6], quantum optical logic gates[9], and communications applications such as quantum teleportation[7].