ERICE 2012

1. Single photon sources M.Bertolotti Dipartimento di Scienze di Base ed Applicate per l’Ingegneria – Sapienza Università di Roma Via A. Scarpa 16, I-00161 Roma, ITALY. Email: mario.betrtolotti@uniroma1.it ERICE 2012 1

2. Introduction The generation of quantum states of the radiation field has been a topic of growing interest in recent years. This is because of possible applications in quantum communication, information processing and quantum computing, such as quantum networks, secure quantum communications, and quantum cryptography ERICE 2012 2

3. An ideal single-photon source would produce exactly one photon in a definite quantum state, in contrast with a “classical” source, such as attenuated laser pulses, for which the photon number follows a Poisson distribution. A more stringent request would be to have the single photon generation on demand, that is a determinate time. More stringent requests could be high repetition frequency, high efficient extraction into free space or fibre, good coherence. ERICE 2012 3

4. We may divide the single photon sources into three main categories: 1. Random sources so much attenuated that one may assume photons arrive one at the time 2. Real single photon sources that however emit at random 3. Single photon sources ondemand ERICE 2012 4

5. 1.Strongly attenuated sources G.I.Taylor [Proc. Cambridge Phil.Soc. 15(1909)114] could be the first to be mentioned to have performed an interference experiment with a single photon obtained by a strongly attenuated classical source. The result was the same as in the classical case. ERICE 2012 5

6. Strongly attenuated sources Faint laser pulses deliver Poisson distributions of photons from which multi-photon events can never be entirely suppressed. Nevertheless, such sources are much easier to build and operate than single-photon sources. ERICE 2012 6

7. Strongly attenuated sources With an attenuated pulsed laser source, the probability of having 0,1,2,3, or more photons present at a time is controllede by Poisson statistics p(m) = <n>m e<n> /m! where <n> is the mean photon number Single-photon number-states may be approximated by coherent states with a very low average photon number. ERICE 2012 7

8. Strongly attenuated sources One may introduce a probability pm that a non-empty weak coherent pulse contains more than one photon pm = p2 /p1 = [1-p(0)-p(1)]/[1-p(0)] = <n>/2 Where p1 and p2 are the probabilities that a pulse contains at least one and at least two photons, respectively ERICE 2012 8

9. Strongly attenuated sources The value of pm could therefore be made arbitrary small by decreasing <n>. However when <n> is small most pulses are empty. The probability to find no photon is p(0) = 1 - <n> To overcome this difficulty one may increase the pulsed laser rate, but in this way also dark counts increase and the ratio of detected photons to dark counts decreases with <n> ERICE 2012 9

10. 2.Real single-photon sources emitting at random These sources are built around a single emitting nanometric object, producing photon distributions which are far from Poissonian. In most cases, for ex., the probability density of emitting two photons at the same time can be completely neglected, whereas it is still high for an attenuated Poisson source with the same brightness. In most cases, the emission process is spontaneous and takes place after a rapid excitation of the emitter. ERICE 2012 10

11. Single photon sources • Much progress has been made recently towards such devices, especially in suppressing the probability of emitting two photons in the same pulse. Large two-photon suppression has been observed using single-quantum emitters such as molecules [1], diamond colour centres [2], atoms [3], impurities in semiconductors [4] and quantum dots [5]. Significant progress has also been made in increasing the purity of the quantum states produced [6]. • (1)C.Brunel et al. PRL 83 (1999) 2722; B.Lounis and W.E.Moerner, Nature 407 (2000) 491 (2)C.Kurtsiefer et al. PRL 85 (2000) 290; A.Beveratos et al. Eur.Phys. J. D18 (2002) 191 (3)A.Kuhn et al. PRL 89 (2002)67901 (4)S.Strauf PRL 89 (2002) 177403 (5)P.Michler et al. Science 290 (2000) 2282 C.Santori et al. PRL 86 (2001) 1502 V.Zwiller et al. APL 78 (2001) 2476 Z.Yuan et al. Science 295 (2002) 102 J. Vuckovic APL 82 (2003) 3596 (6)C.Santori et al. Nature 419 (2002) 594

12. 2.Real single-photon sources emitting at random Quantum dots (QDs) are the ideal sources. The emission can be controlled by putting the QDs in a cavity and changing the density of states. However, the emission process is spontaneous and takes place after a rapid excitation of the emitter. ERICE 2012 12

13. 2.Real single-photon sources emitting at random Semiconductor quantum dots (QDs) have already produced promising results as single photon emitters. The main difficulty with QDs is that they interact with a solid state environment, necessitating cryogenic operation temperatures, and yet environment induced decoherence is still a problem. However these difficulties are offset by advantages such as being fixed in place, large dipole moments, and the possibility of integration into monolithic optical microcavity structures ERICE 2012 13

14. Control of spontaneous emission from atoms or molecules In 1946, Purcell [1] first predicted that nontrivial boundary conditions of an electromagnetic field in the vicinity of an excited atom could alter its decay rate. The rate  for spontaneous transitions from an initial state |i > with no photons to a final state |f > with one photon is given by the well-known Fermi golden rule [2] where H is the interaction Hamiltonian and ρ(νc) is the density of states at the transition frequency νc, that for radiation in free space is The rule applies also to photonic crystals [3] [1] E.M. Purcell, Phys. Rev. 69, 681 (1946). [2] R. Loudon, The Quantum Theory of Light, Oxford Univ. Press (2000). [3] S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, A. Menna, Phys. Rev. E70, 56614 (2004).

15. History The application to a small cavity for which the density of modes may be modified was considered by Klepper [1]. In particular, when the transition frequency νcis near resonance with a mode eigenfrequency, the spontaneous emission rate can be considerably increased. The effect was experimentally observed [2] with a sodium Rydberg atom set through a resonant superconducting cavity. Also inhibited spontaneous emission was observed by studying the cyclotron motion of a single electron [3]. [1] D. Klepper, Phys. Rev. Lett. 47, 233, (1981). [2] P. Goy, J.M. Raimond, M. Gross, S. Haroche, Phys. Rev. Lett. 50, 1903 (1983). [3] G. Gabrielse, H. Dehmelt, Phys. Rev. Lett. 55, 67 (1985).

16. Photonic crystals may influence atomic emission The decay rate could be suppressed for atoms located inside a PBG when their resonant emission frequency is in the PBG gap. In this frequency range, the electromagnetic density of modes is very small. Resonance enhancement of the decay rate is on the contrary expected at the photonic band edges where the DOM is anomalously large [1,2]. Computer simulations have confirmed changes in the rate of emission in photonic structures [3]. [1] V. Bykov, Phys. Rev. Lett. 58, 2486 (1987). S. John, Phys. Rev. Lett. 58, 2486 (1987). S. John, T. Quang, Phys. Rev. A50, 1764 (1994). [2] E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987). E. Yablonovitch, T. Gmitter, Phys. Rev. Lett. 63, 1950 (1989). [3] Dowling J P 1999 J. Lightwave Technol. 17 2142. Dowling J P and Bowden C M 1992 Phys. Rev. A 46 612. Bendickson J M, Dowling J P and Scalora M 1996 Phys. Rev.E 53 4107. Fogel I S, Bendickson J M, Tocci M D, Bloemer M J, Scalora M, Bowden C M and Dowling J P 1998 Pure Appl. Opt. 7 393. Scalora M, Dowling J P, Tocci M, Bloemer M J, Bowden C M and Haus J W 1995 Appl. Phys. B 60 557. Pereira S and Sipe J E 2000 Phys. Rev. E 62 5745.

17. Density of modes and group velocity in PBG

18. The effect may be seen as a modification of the exponential decaying emission with respect to an atom in free space and can be generated by embedding the atom in photonic crystals Erice 2012

19. The effect may be seen as a modification of the exponentially decaying emission with respect to an atom in free space and can be generated by embedding the atom in photonic crystals [2]. Spontaneous emission of CdSe quantum dots embedded in a 3D photonic crystal consisting of air spheres in titanium dioxide has shown changes in the fluorescence decay curves of the quantum dots inside photonic crystals with different lattice parameters [3–5]. [2] Sprik R, Von Tiggelen B A and Lagendijk A 1996 Europhys. Lett. 35 265. Yang Y, Fleischhaner M and Zhu S Y 2003 Phys. Rev. A 68 43805. Zhu S Y, Li G X, Yang Y P and Li F L 2003 Europhys. Lett. 62 210. Yu Zhang J, Wang X Y and Xiao M 2003 Opt. Photon. News 14 (December) 33. [3] Busch K and John S 1998 Phys. Rev. E 58 3896. Nikolaev I, Lodahl P, Vos W and van Driel F 2005 ECLEO (Munich 2005). [4] Lodahl P, von Driel A F, Nikolaev I S, Irman A, Overgaag K, Vanmalkelberg D and Vos W 2004 Nature 430 654. [5] Nikolaev I S, Lodahl P and Vos W L 2005 Phys. Rev. A 71 53813.

20. An example. Spontaneous emission of CdSe quantum dots embedded in a 3D photonic crystal consisting of air spheres in titanium dioxide shows changes in the fluorescence decay curves of the quantum dots inside photonic crystals with different lattice parameters. Lodahl P, von Driel A F, Nikolaev I S, Irman A, Overgaag K, Vanmalkelberg D and Vos W 2004 Nature 430 654.

21. Using quantum dots embedded in pillar microcavities, one may have two-photon suppression factors as large as 40 [1], improved efficiencies [2] and photon state purities such that the mean wavepacket overlap between consecutive photons is as high as 0.8 [3]. We show an example from the work of Santori [3]. (1) J.Vuckovic et al. APL 82 (2003) 3596 (2) M.Pelton et al. PRL 89 (2002) 233602 (3) C.Santori et al. Nature 419 (2002) 594-

22. Santori realized a single-photon device embedding a quantum dot in a distributed Bragg structure[fig 1(a)]. One or more InAs quantum dots, surrounded by a GaAs matrix, are embedded in a micropillar optical cavity. The QDs serve as the single-photon emitters. The optical microcavity serves to modify the spontaneous emission properties of the QD through the Purcell effects. When a radiative transition of the QD is on resonance with a cavity mode, if the QD couples much more strongly with this mode than to the background “leaky” modes, the spontaneous emission rate can increase substantially and light is emitted mainly into the cavity mode. C.Santori et al. New J.Phys. 6(2004)89

23. The operation scheme is shown in figure 1(c). A short (2-3 ps) optical pulse generated by a tunable Ti-sapphire laser raises the quantum dot into an excited state containing one electron-hole pair. The QD then quickly relaxes (with a timescale of the order of 10 ps) to a lowest excited state. This state then decays through a much slower spontaneous emission process (100-300 ps) to emit a single photon. The spontaneous emission is collected and sent through a narrow-band (0.1 nm) spectral filter. This not only removes background emission from the sample, but also protects against events in which the quantum dot receives multiple excitations. In these events, multiple photons are emitted, but each photon has a unique wavelength, as a result of the electrostatic interactions between particles inside the quantum dot, leading to energy shifts of the order of meV.

24. The sample needs to be cooled to temperatures ranging from 3 to 10 K. The efficiency can be studied through photon correlation with a Hanbury-Brown and Twiss-type set-up.

25. A single photon state is one that should exihbit antibunching. This property was already found by Mandel and Wolf measuring the conditional probability g2(τ) that having detected a photon at time t another photon comes at time t + τ.

26. single-photon sources on demand In the nanosecond time regime the emitted photons from a single quantum system are expected to show antibuching, that is the probability for two photons to arrive at the same time is zero To observe antibunching correlations, the second-order correlation function g2(t) is generally measured by determining the distribution of time delays N(τ) between the arrival of successive photons in a dual beam detector. ERICE 2012 26

27. Single photon generation is examined by measuring the second-order intensity autocorrelation function (g(2)(τ)) using the Hanbury-Brown and Twiss arrangement.

28. Cahotic, laser, and nonclassical light The behaviour of the g(2)(τ) as a function of the time delay τ

29. g(2) (τ) for different Fock states A Fock state with 9 photons B Fock state with 5 photons C Fock state with 1 photon g2(τ ) = 1 – 1/n where n is the number of Fock states ERICE 2012 29

30. Antibunching for a single photon • From A.Beveratos PR A64(2001)061802

31. In the Santori experiment the emission from the QD is spectrally filtered and split into two paths by a beamsplitter, each path leading to a photon counter. Coincidence-counting electronics generates a histogram of the relative delay  = t2 – t1 between photon detection events at counters 1 and 2. The peak at  = 0 corresponds to events in which two photons were detected in the same pulse, and thus the first goal in developing a single-photon source is to make the area of this peak as small as possible. The peaks at times nTrep where Trep = 13 ns is the laser repetition period, correspond to events in which one photon was detected from each of two different pulses.

32. 3.single-photon sources on demand A particularly novel non-classical source of light is a deterministic (or triggered) single-photon source: a source that has the property to emit with a high degree of certainty one (and only one) photon at a user specific time. ERICE 2012 32

33. One method for preparing an approximation to a single-photon state is by generating a pair of photons. This can be achieved using the creation of two photons by a parametric downconversion process ERICE 2012 33

34. Parametric down conversion is a second order nonlinear process where a wave impinging on a nonlinear crystal creates two new light beams obeying energy and momentum conservation ω1 k1 ωo ko ω2 k2 ωo = ω1 + ω2 ko = k1 + k2 ERICE 2012 34

35. Essentially the process is one of conditional preparation: given that either two photons exist or no photon exists, the detection of one photon acts as a signal that a second photon is present in the field. The frequency and direction of propagation of the second photon are related to those of the first by conservation laws, and can be determined by analysing the first “gate” photon. The second photon field can then be regarded as being in a one-photon Fock state ERICE 2012 35

36. Luminescent centres in diamond have recently emerged as an alternative . T.M.Babinec et al. Nature Nanotechnology 5 (2010)195Single photon sources ERICE 2012 36

37. A schematic of the SEM/FIB with nickel-ion source. The yellow cubes represent diamond uninplanted diamond crystals while the blue one is the only crystal which was implanted with nickel. B is SEM image from I.Aharonovich et al. PRB79, 235316 (2009)