Single-photon sources

In the paper

“The probability of observing n counts for M emitted photons is therefore p x (n) = n M (xT ) n (1 -xT ) M-n . (17”

In the paper

“Adding the variances (or squared standard deviations) of the two signals, we obtain the following variance for the transmission coefficient measured with the coherent source: T 2 C = 1 xM T (T + 1).”

In the paper

“For the transmission measurement, the variance becomes T 2 SP = 1 xM T (T + 1 -2xT ).”

In the paper

“With a similar result for the reference measurement, the ratio of the variances for the squeezed to coherent cases is T 2 SP T 2 C = 1 -2x T 1 + T , (18”

In the paper

“The distribution of the detected counts is also Poissonian, with the average number of detected counts (supposed to be large) S C = xMT and with the shot noise (standard deviation) N C = √ xMT .”

In the paper

“There is a non-zero probability of having more than one photon in a pulse, even for very weak pulses with average photon number n = µ 1.”

In the paper

“Even with resonant-cavity enhancement, the spontaneous emission lifetimes of the emitters discussed in this paper are longer than 100 ps.”

In the paper

“At about the same time, pairs of correlated photons (twin photons) were obtained at high rates by parametric downconversion (Burnham andWeinberg 1970, Hong andMandel 1986).”

What the sources say

• Not checked yetcites Burnham andWeinberg 1970
• Not checked yetcites Hong andMandel 1986

In the paper

“If we send a one-photon state on a beam splitter and place photon-counting detectors on the reflected and transmitted beams, we never observe any coincidence between counts measured by the two detectors, as this would violate energy conservation (see figure 1).”

In the paper

“From the mid-1980s, single ions in traps provided long observation times with one and the same ion (Diedrich and Walther 1987).”

What the sources say

• Not checked yetcites Diedrich and Walther 1987

In the paper

“Singlephoton sources are crucial components in recent proposals for quantum computation by means of linear optics (Knill et al 2001), the only nonlinear step being the detection.”

What the sources say

• Not checked yetcites Knill et al 2001

In the paper

“Sub-Poissonian statistics were first demonstrated in the fluorescence of a very faint atomic beam excited by a continuous laser (Kimble et al 1977).”

What the sources say

• Not checked yetcites Kimble et al 1977

In the paper

“As a consequence, since only emission between the lowest two levels can be detected, the complex system behaves as a two-level emitter.”

In the paper

“For two-level systems such as atoms, the observation of one photon projects the system into the ground state, whence no second photon can be immediately emitted.”

In the paper

“One-photon states present a peculiar anticorrelation effect, which does not exist for a classical wave.”

In the paper

“For perfectly antibunched light, the correlation function therefore cancels for zero time: g (2) (τ = 0) = 0.”

In the paper

“Fearn and Loudon (1987) and Hong et al (1987) pointed out that two photons incident at the same time on the two input ports of a 50%/50% beam splitter interfere in such a way that they both exit from one of the output ports, as illustrated in figure 4.”

What the sources say

• Not checked yetcites Fearn and Loudon (1987)
• Not checked yetcites Hong et al (1987)

In the paper

“Coincidences between the two detectors are then insensitive to dead-times and afterpulses.”

In the paper

“Yet, antibunching alone is by no means sufficient for obtaining single photons on demand.”

In the paper

“Provided the probability of generating two pairs at the same time remains negligible, such correlated pairs can be used as sources of heralded single photons.”

In the paper

“However, dephasing and spectral diffusion, which arise from fast and slow fluctuations of the transition frequency, complicate this picture.”

In the paper

“Those early demonstrations have now been extended to many different systems which could become useful emitters of single photons.”

• Also stated in: § 1. Introduction · hedged

  “They include semiconductor nanocrystals (Lounis et al 2000, Michler et al 2000a, Messin et al 2001), colour centres in diamond (Brouri et al 2000, Kurtsiefer et al 2000), single quantum dots in various geometries (Michler et al 2000b, Santori et al 2001) and several more.”

What the sources say

• Not checked yetcites Lounis et al 2000
• Not checked yetcites Brouri et al 2000 source
• Not checked yetcites Michler et al 2000b

In the paper

“The first successful generation of single photons (Clauser 1974) was based on a cascade transition of calcium atoms.”

What the sources say

• Not checked yetcites Clauser 1974 source

In the paper

“A pulsed excitation gives rise to periodic emission of single photons (d).”

In the paper

“Single emitters usually deliver photons one at a time.”

• Also stated in: § 2.3. Antibunching and second-order correlation function · hedged

  “The photons have a tendency to be emitted one by one, i.e. they are 'antibunched'”

What the sources say

• Not checked yetcites Kimble et al 1977

In the paper

“In order to give rise to a fully destructive interference, the two photons must be completely indistinguishable, i.e. they must be in exactly the same mode.”

In the paper

“In the absence of slow spectral diffusion, the resulting frequency linewidth (full-width at half-maximum),”

In the paper

“If the dipole lies in the focal plane of the collection objective, the polarization is close (but not identical) to linear, parallel to the dipole, for all photons across the whole spatial mode.”

In the paper

“The depth of the two-photon interference effect will no longer be 100% but only T 2 /2T 1 (Bylander et al 2003).”

What the sources say

• Not checked yetcites Bylander et al 2003

In the paper

“which shows that, as expected, the noise with the single-photon source is always less than with the laser.”

In the paper

“In complex geometries, e.g. when the emitter is placed close to an interface (Lukosz and Kunz 1977) or in a particle whose size is comparable with the wavelength, the local field correction depends on details of the structure and must be calculated numerically.”

What the sources say

• Not checked yetcites Lukosz and Kunz 1977

In the paper

“An additional loss of indistinguishability arises from incoherent pumping.”

In the paper

“In many cases, however, the spectrum of a source is broader than the Fourier-transform of the time-profile of the emitted pulse.”

In the paper

“It is determined by the microscopic nature of the emitter and by the way it is coupled to the emission mode.”

In the paper

“The noise reduction is nearly total for high detection quantum yields (x ≈ 1) and for weakly absorbing samples (T ≈ 1).”

In the paper

“If the emitter is placed in a large bulk of dielectric with refractive index n, the emission lifetime is significantly modified.”

What the sources say

• Not checked yetcites Nienhuis and Alkemade (1976)

In the paper

“If the spectrum of a single-photon source is Fourier-transform-limited, i.e. if each photon can be described by the same coherent wavepacket, two photons will be indistinguishable.”

In the paper

“With squeezed light, fluctuations of a given quadrature are reduced with respect to those of coherent light (Kimble andWalls 1987, Drummond 1999).”

What the sources say

• Not checked yetcites Kimble andWalls 1987
• Not checked yetcites Drummond 1999

In the paper

“Photon-counting devices based on III-V semiconductors now become available in the near-IR window (Hiskett et al 2000, Rarity et al 2000, Stucki et al 2001).”

What the sources say

• Not checked yetcites Hiskett et al 2000 source
• Not checked yetcites Rarity et al 2000 source
• Not checked yetcites Stucki et al 2001

In the paper

“If the dipole is perpendicular to the focal plane, the polarization in the collected mode is radial (Fourkas 2001).”

What the sources say

• Not checked yetcites Fourkas 2001 source

In the paper

“A first correction factor arises from the different density of photon modes in the dielectric, as pointed out by Nienhuis and Alkemade (1976), yielding the often-used relation”

What the sources say

• Not checked yetcites Nienhuis and Alkemade (1976)

In the paper

“In the approximation of the spherical Lorentz cavity, and if the polarizability of the object is not too different from that of the surrounding matrix (Schuurmans et al 2000, Vallée et al 2005), the lifetime in a dielectric with index n becomes (Imbusch and Kopelman 1981)”

What the sources say

• Not checked yetcites Schuurmans et al 2000
• Not checked yetcites Vallée et al 2005 source
• Not checked yetcites Imbusch and Kopelman 1981

In the paper

“For example, for a linear dipole emitter such as a single molecule, the polarization pattern of the emitted photons depends on the orientation of the dipole moment (Fourkas 2001, Novotny et al 2001).”

What the sources say

• Not checked yetcites Fourkas 2001 source
• Not checked yetcites Novotny et al 2001

In the paper

“The only way for her to remain unnoticed is to restrict her measurement rate to less than the dark count rate, p dark , of Bob's detectors.”

In the paper

“For low dark count probabilities, it is clear from equations ( 23) and ( 24) that the single-photon source permits more attenuation, i.e. a longer fibre, than an attenuated laser source.”

In the paper

“In this way, Eve has obtained full information on Bob's bits without introducing any error.”

In the paper

“The condition for security of the communication will be that the rate of bits received by Bob, T AB η det , be larger than his detectors' dark counts probability, p dark , which may hide Eve's measurements (Brassard et al 2000):”

What the sources say

• Not checked yetcites Brassard et al 2000

In the paper

“There, the contradiction between the Einstein-Podolsky-Rosen assumptions and quantum mechanics arises even for an individual event.”

What the sources say

• Not checked yetcites Greenberger et al 1989 source

In the paper

“Rarity and collaborators (Rarity et al 1994) proposed a physical quantummechanical random generator based on the 50 : 50 splitting of a beam of single photons.”

What the sources say

• Not checked yetcites Rarity et al 1994 source

In the paper

“Quantum theory predicts that, for each photon, the 'which-way' decision is truly random and independent of history or other experimental parameters.”

In the paper

“Each individual photon coming from the light source and going through the 50 : 50 beam splitter has an equal probability of being reflected or transmitted.”

In the paper

“As shown by Brassard et al (2000), in order to eschew a PNS-attack in the presence of dark counts, the transmission efficiency, T AB , of the line from Alice to Bob should obey the following criterion:”

What the sources say

• Not checked yetcites Brassard et al (2000)

In the paper

“A single measurement (of either three vertically polarized photons or of a horizontal polarization for two photons and a vertical polarization for the third one) will discriminate with certainty between quantum mechanics and a local hidden-variable theory.”

In the paper

“If we endow Eve with unlimited technological power within the laws of physics, the following photon number splitting attack (PNS attack) is in principle possible (Brassard et al 2000, Lütkenhaus 2000):”

What the sources say

• Not checked yetcites Brassard et al 2000
• Not checked yetcites Lütkenhaus 2000

In the paper

“A continuous stream of random numbers at a rate of 1 Mbit s -1 could be produced with no correlations between the generated numbers (Jennewein et al 2000, Stefanov et al 2000) using attenuated LED light sources.”

What the sources say

• Not checked yetcites Jennewein et al 2000
• Not checked yetcites Stefanov et al 2000

In the paper

“All these experiments have confirmed the predictions of quantum mechanics.”

In the paper

“In such a way, the violation of Bell's inequality was demonstrated with pairs of independent photons (Fattal et al 2004b).”

What the sources say

• Not checked yetcites Fattal et al 2004b

In the paper

“The reliability and secrecy of the key transmission can be improved by applying errorcorrecting and privacy-amplifying algorithms to the transmitted bits (Bennett et al 1995).”

What the sources say

• Not checked yetcites Bennett et al 1995

In the paper

“A perfect single-photon source associated with a perfect detection thus would give access to arbitrary small absorptions, impossible to measure with a laser source because of photon noise.”

In the paper

“She thus necessarily induces an additional error rate.”

In the paper

“The detector's after-pulses and dead-times may introduce strong correlations or anticorrelations between successive bits.”

In the paper

“A first step in that direction is the recent generation of polarization-entangled photon pairs with a quantum-dot source (section 6.6).”

In the paper

“Spontaneous emission is not an intrinsic property of an isolated emitter but rather a property of the coupled system of the emitter and the electromagnetic modes in its environment.”

In the paper

“If the Purcell factor is much greater than 1, the emitter will radiate much faster in the cavity than in free space.”

In the paper

“Michler et al (2000) embedded self-assembled InAs and InGaAs quantum dots in microdisc cavities to generate single photons.”

What the sources say

• Not checked yetcites Michler et al 2000

In the paper

“Assuming a normalized Lorentzian mode density with a width of ω 0 /Q for the cavity, ρ cav (ω) ≈ 2Q/π ω 0 , we deduce the following spontaneous emission enhancement:”

In the paper

“Both experiments show that single-photon devices can provide completely secure communication in conditions under which this would be impossible with attenuated laser pulses.”

What the sources say

• Not checked yetcites Waks et al 2002
• Not checked yetcites Beveratos et al 2002

In the paper

“In the weak-coupling regime, the atomic excitation is irreversibly lost to the continuum of all available photon states, including the vacuum modes still accessible (leak modes) and those of the cavity (cavity modes).”

In the paper

“To date, two groups have used a single-photon source in a QKD link which includes sifting, error-correction and privacy amplification.”

What the sources say

• Not checked yetcites Waks et al 2002
• Not checked yetcites Beveratos et al 2002

In the paper

“The radiative transition rate, γ , of an atom from an excited, initial state |e to a lower energy, final state |g depends on the density of available photon states, ρ(ω), at the transition frequency, ω, and on the atom-vacuum field dipole interaction Hamiltonian.”

In the paper

“Efficient cavity-coupled single-photon sources were demonstrated with single quantum dots embedded in microcavities (Ohnesorge et al 1997, Gérard et al 1998, Solomon et al 2001).”

What the sources say

• Not checked yetcites Ohnesorge et al 1997
• Not checked yetcites Gérard et al 1998
• Not checked yetcites Solomon et al 2001

In the paper

“The Purcell factor increases with Q/V only as long as the coupling parameter, g, is less than the decay rates of the system (γ and γ cav ).”

In the paper

“In this case β ≈ 80% of the emitted light was coupled into a single cavity mode.”

What the sources say

• Not checked yetcites Pelton et al 2002
• Not checked yetcites Vuckovic et al 2003

In the paper

“Thus, by altering ρ(ω) (placing the atom in a cavity or near an interface), the spontaneous emission rate can be enhanced or suppressed (Purcell 1946, Drexhage 1974).”

What the sources say

• Not checked yetcites Purcell 1946
• Not checked yetcites Drexhage 1974

In the paper

“The atom-cavity system, in particular, must be able to transfer quantum information between atoms and photons in a coherent manner (Maître et al 1997, Brattke et al 2001).”

What the sources say

• Not checked yetcites Maître et al 1997
• Not checked yetcites Brattke et al 2001

In the paper

“This photon-pair creation process is very inefficient (efficiency ≈ 10 -7 -10 -11 ).”

In the paper

“To circumvent this problem, Kimble's group employed a single Cs atom trapped in the optical cavity.”

What the sources say

• Not checked yetcites McKeever et al 2004

In the paper

“The stimulated emission process requires a strong coupling to a single mode of a high-finesse optical cavity (Law and Kimble 1997).”

What the sources say

• Not checked yetcites Law and Kimble 1997

In the paper

“Photon pairs can be generated by SPDC in non-centrosymmetric crystals such as KDP, BBO, LBO or LiNbO 3 .”

What the sources say

• Not checked yetcites Shen 1984

In the paper

“p multi = p n 2 p n 1 = 1 -p(0) -p(1) 1 -p(0) ≈ n 2 , (30”

In the paper

“In contrast to solid-state single-photon sources, this source operates under non-stationary conditions because atoms enter and leave the cavity randomly.”

In the paper

“The reversible transfer of quantum information between the emitter and the photons opens the way for quantum networks.”

In the paper

“Entangled photon pairs can be obtained in certain atomic cascades (j = 0 → j = 1 → j = 0, j being the total angular momentum of the atomic states) because of the polarization correlation between the successive emitted photons.”

In the paper

“Along the two directions ('1' and '2'), where the cones overlap, the light is described by a Bell entangled state:”

In the paper

“For example, Aspect's experiment used the 4p 2 1 S 0 → 4s 4p 1 P 1 → 4s 2 1 S 0 cascade in a calcium atom beam, which yields two polarization-correlated photons (λ 1 = 551 nm and λ 2 = 423 nm) upon two-photon excitation from 4s 2 1 S 0 to 4p 2 1 S 0 .”

What the sources say

• Not checked yetcites Aspect et al 1982b

In the paper

“Single-photon number-states may be approximated by coherent states with a very low average photon number n .”

In the paper

“When n is small, most pulses are empty: p(n = 0) ≈ 1n .”

In the paper

“When the output beams of the beam splitter were recombined on a second beam splitter to form a Mach-Zehnder interferometer, interferences with a visibility of over 98% were observed when the optical path between the two arms of the interferometer was varied.”

What the sources say

• Not checked yetcites Grangier et al 1986 source

In the paper

“Nonlinear interaction of a pump laser pulse with the crystal occasionally splits one highfrequency pump photon into two lower-frequency, signal and idler photons (Shen 1984).”

What the sources say

• Not checked yetcites Shen 1984

In the paper

“For quantum cryptography, the reliability of the source is related to the probability, p multi , that a non-empty weak coherent pulse contains more than one photon.”

In the paper

“In 1986, Aspect and co-workers (Grangier et al 1986) used this atomic cascade source to demonstrate the wave-particle duality of a photon by sending single photons on a beam splitter.”

What the sources say

• Not checked yetcites Grangier et al 1986 source

In the paper

“The photon production step is based on a stimulated Raman process driven by an adiabatic passage (STIRAP) (Parkins et al 1993, Vitanov et al 2001) between two ground states of a single atom.”

What the sources say

• Not checked yetcites Parkins et al 1993
• Not checked yetcites Vitanov et al 2001 source

In the paper

“Recently, single-photon sources using single atoms strongly interacting with cavities have been demonstrated by the groups of Rempe and Kimble (Kuhn et al 2002, McKeever et al 2004).”

What the sources say

• Not checked yetcites Kuhn et al 2002
• Not checked yetcites McKeever et al 2004

In the paper

“The value of p multi can be made arbitrarily small.”

In the paper

“Sources based on incoherent excitation of the emitting state of a quantum emitter do not meet this essential requirement.”

In the paper

“Furthermore, the complexity and flexibility of the environment at room temperature allows the existence of metastable dark states, leading to extended dark periods, during which emission stops (Zondervan et al 2003(Zondervan et al , 2004)).”

What the sources say

• Not checked yetcites Zondervan et al 2003 source
• Not checked yetcites Zondervan et al 2004

In the paper

“For systems presenting a high photo-stability, for example terrylene in a p-terphenyl crystal (see figure 15), single molecules can operate as single-photon sources (Lounis andMoerner 2000, Treussart et al 2002).”

What the sources say

• Not checked yetcites Lounis and Moerner 2000
• Not checked yetcites Treussart et al 2002

In the paper

“Depending on the molecular compound and host crystal, excursions to a triplet lifetime can in some cases limit the molecular brightness (Bernard et al 1993).”

What the sources say

• Not checked yetcites Bernard et al 1993

In the paper

“As a consequence of fast dephasing, the emission is very far from lifetime-limited, by a factor of at least 10 000!”

In the paper

“As a consequence, a transition to an excited electronic state, even if it starts from the ground state of the solid at zero temperature, is distributed over a broad range of frequencies, corresponding to the creation of additional vibrations and phonons.”

In the paper

“Aromatic molecules were used for an early demonstration of a single-photon source in condensed matter (Brunel et al 1999), as shown in figure 14.”

What the sources say

• Not checked yetcites Brunel et al 1999

In the paper

“They are nearly ideal for the demonstration of quantum-optics experiments.”

In the paper

“After emission of a photon by an isolated atom or ion, no information is left in the matter system (except for a possible recoil, which is usually negligible).”

In the paper

“This observational fact is summarized by Kasha's rule: only the lowest excited state of a given spin multiplicity can efficiently emit light (Birks 1970).”

What the sources say

• Not checked yetcites Birks 1970

In the paper

“Therefore, even in crystalline environments, lines of single organic molecules at room temperature are never much narrower.”

In the paper

“In summary, atom-or ion-based sources of single photons present many advantages as standard sources of pure and indistinguishable photons.”

In the paper

“This process, called singlet-singlet annihilation, is a consequence of Kasha's rule and of the fast relaxation of high excited states.”

In the paper

“At very low temperatures, however, the lowest-frequency transition connecting the ground vibrational states of the ground and excited electronic states is a very narrow line, called the zero-phonon line (ZPL) (Sild and Haller 1988).”

What the sources say

• Not checked yetcites Sild and Haller 1988

In the paper

“Single polymer molecules have been in operation for as long as hours on a glass surface before photobleaching eventually stopped the emission (Lee et al 2004).”

What the sources say

• Not checked yetcites Lee et al 2004

In the paper

“Their main disadvantage is their complexity of operation.”

In the paper

“Multiple excitations therefore cannot lead to emission of two or more photons.”

In the paper

“When one fluorophore is bleached, and provided the product of the reaction is no quencher for neighbouring sites, a new fluorophore becomes the lowest-energy trap and can resume emission.”

In the paper

“However, if the molecules can be protected from atmospheric oxygen and are rigidly held in a crystalline matrix, the stability can sometimes be extended to minutes or hours (Fleury et al 1998, Kulzer et al 1999), even under intense pulsed illumination, as has been shown for terrylene in p-terphenyl crystals (Lounis and Moerner 2000).”

What the sources say

• Not checked yetcites Fleury et al 1998
• Not checked yetcites Kulzer et al 1999
• Not checked yetcites Lounis and Moerner 2000

In the paper

“One of the essential features of a single-photon emitter is that it should be strongly anharmonic, i.e. two-or multi-excitation states should have very different emission properties from the singly excited state.”

In the paper

“For such large assemblies, however, the operation time is lengthened because of the large number of available fluorophores in the assembly.”

In the paper

“Simultaneous emission of two photons in general indicates that two atoms are present in the detection volume (McKeever et al 2004).”

What the sources say

• Not checked yetcites McKeever et al 2004

In the paper

“However, blinking limits their practical applications as sources of single photons.”

In the paper

“However, all multi-excited states are nearly dark because of very efficient exciton-exciton annihilation (also called Auger processes (Klimov et al 2000)) similar to the singlet-singlet and singlet-triplet annihilation in multi-chromophoric molecules and polymers.”

What the sources say

• Not checked yetcites Klimov et al 2000