Classical light, such as light from incandescent light bulbs (thermal light, Fig-ure 2.1 (a)) and lasers (coherent light, FigFig-ure 2.1 (b)), is easily available and used in everyday life. For non-classical light this is not the case, since the required
2.5. Single Photon Emitters
a
|g>
|e>
Excitation Emission
b
E E
Generation Heralding
t
Figure 2.6.: Single photon emission. (a) Sketch of a deterministic single pho-ton emitter. It is excited, what, for example due to Coulomb interaction or the Pauli principle [45], leads to one single excitation in the system. This excitation subsequently spontaneously decays and a single photon is emitted. (b) Sketch of a probabilistic source. A correlated photon pair is generated, e.g., by parametric fluorescence [36]. One of the photons is detected to herald the remaining single photon.
technology is still in its infancy. Also, generation (and measurement) of single pho-tons today often requires special equipment and is in most cases only feasible in a laboratory environment. Figure 2.6 sketches the basic working principle of single photon sources. Either a single excitation is used to create a single photon (Fig-ure 2.6 (a)) or correlated photons are created, with one being detected to herald the other (Figure 2.6 (b)) [44]. Note that the so called heralded single photons are not single photons in a strict sense, since they are never in the corresponding pure Fock state.
In the following, an overview of the most common single photon emitters is given.
More detailed description of single photon emitters are given by Lounis et al. [46]
and Eisaman et al. [47].
2.5.1. Atoms
Neutral atoms can be used as single photon emitters [48, 49] and antibunching has been observed for the first time on a beam of Na atoms [48]. In more advanced schemes aiming at high rates of single photon generation, the atoms are cooled by a laser [50, 51] in a magneto optical trap [52]. Subsequently they fall through a high finesse cavity so one can get single photons out, but only when there is exactly one atom inside the cavity. This is a statistical process resulting in time spans with single photon emission (one atom present), without emission (no atom present) or multiphoton emission (more than one atom). This can be overcome by trapping a single atom in a dipole trap [53–55], where it is possible to hold the atom on the timescale of several seconds.
-31.8 -21.2 -10.6 0.0 10.6 21.2 31.8
Figure 2.7.: Indistinguishable photons from atoms. (a) shows the setup used by Legero et al. [56] to produce and analyse indistinguishable photons from atoms.
Atoms are first trapped in a magneto optical trap. Then, they fall through an optical cavity, where laser light triggers the emission of single photons, if there is only one atom in the cavity. Subsequently, the single photons are sent through an interferometer with single photon detectors at both output ports. (b) shows the measured coincidences with one interferometer arm blocked (solid line), where a pronounced antibunching dip is visible. If the arm is open, but the arms are polarised differently (dotted line), the depth of the dip is reduced to about 0.5 (cf. Equation 2.17). (c) shows the coincidences for both arms open for parallel and perpendicular polarisations. For parallel polarization, the coincidences are suppressed at zero time delay due to the Hong-Ou-Mandel effect (see Section 2.3).
(adapted from [56])
2.5. Single Photon Emitters
Figure 2.8.: Single photons from molecules. (a) setup used by Lounis et al. [59]
to measure single photon emission from molecules at room temperature. A con-focal microscope (see Section 4.1) is used to excite the molecules and collect the light, which is analysed by a HBT correlator. (b) is a 10µm by 10µm confocal micrograph of single terrylene molecules. (c) shows a lifetime histogram of such a molecule acquired by TCSPC. In (d), the autocorrelation function as acquired with the HBT correlator is shown. The peak at zero time delay is heavily suppressed, indicating single photon emission from the molecule. (adapted from [59])
Ionised atoms have the advantage that they can be held in radio frequency traps due to their charge [57]. In this way, it can be assured that there is always one single ion emitting single photons. Also, it is possible to implement various miniaturised ion traps on a semiconductor chip [58]. With today’s semiconductor fabrication techniques, this could open a way for implementing many (interacting) single pho-ton emitters in a small volume.
Photons emitted by atoms usually have small linewidths and are indistinguish-able [56] – very useful features for most quantum optics applications. A measure-ment on the indistinguishability of photons emitted by atoms is shown in Figure 2.7.
Major disadvantaged of atoms as single photon emitters are the complicated laser systems and ultra-high vacuum apparatuses needed, which easily can fill up a whole laboratory. Also, for many ions the optical transitions lie in the ultraviolet spectral range [47]. This makes the optical elements expensive and hinders effective use of optical fibres due to their high absorption at these wavelengths.
2.5.2. Molecules
Single molecules are capable of emitting single photons at cryogenic tempera-tures [60] as well as at room temperature [59, 61]. Single photon emission was first demonstrated by molecules embedded in a solid [60], but is also possible for molecules in solution [62]. An optical measurement of single terrylene molecules is shown in Figure 2.8. The level structure of fluorescent molecules can be described by a three level system with a singlet ground state |S0i, an exited singlet state
|S1i, and an intermediate triplet state |T1i. Single photons are emitted when the
a
Energy
b
Ex c
e
h
Figure 2.9.: Quantum dot level structure. (a) shows a particle in an infinite potential well. Discrete energy levels (vertical lines) arise from the confinement.
Also, the corresponding wave functions are indicated. (b) shows the level structure of a quantum dot. Electron e and hole h are separated by the energy difference Ex. (c) shows the recombination of electron and hole, which leads to emission of a single photon.
molecule is pumped from |S0ito|S1iand then relaxes to |S0i. With a small prob-ability it can also enter the triplet state |T1i, which is a dark state, i.e., no photon is emitted [47].
Besides many advantages of single molecules as single photon emitters like nar-row, at cryogenic temperatures even Fourier limited, zero phonon lines (ZPLs) [63], their main drawback is their lack of stability. They show a blinking behaviour and there is always a chance of destroying the molecule irreversibly via photo bleach-ing [64].
2.5.3. Quantum Dots
Quantum dots are semiconductor structures so small, that their radius abecomes comparable to the exciton Bohr radius ab [65]. In the case a ab, the so called strong confinement regime, electron and hole behave like particles in a box, and therefore have discrete energies (see Figure 2.9 (a)) [66]. Because of this, the energy of an electron hole pair inside the quantum dot is also discretised (Figure 2.9 (b)).
When electron and hole recombine, this energy can be released as a single photon (Figure 2.9 (c)). Coulomb interaction between electron and hole gives rise to addi-tional terms when calculating the energy. Further corrections are introduced when dealing with more complicated states like the biexciton (a state of two excitons [67]) or the trion (a state of an exciton together with an additional electron or hole [68]).
A measurement indicating single photon emission from colloidal CdSe/ZnS quan-tum dots is shown in Figure 2.10 [69]. Besides single photon emission, a pronounced blinking behaviour is visible.
2.5. Single Photon Emitters
Figure 2.10.: Single photons from CdSe/ZnS quantum dots. (a) shows a confocal microscopy image of CdSe/ZnS quantum dots on glass as measured by Michler et al. [69]. Blinking of the quantum dots is visible as bright or dark lines along the scanning direction. (b) is an antibunching measurement from a single quantum dot indicating single photon emission. The red line is a fit to the data. (c) shows the blinking behaviour of a CdSe/ZnS quantum dot. The quantum dot switches from bright states to dark states and vice versa. (adapted from [69])
2.5.4. Defect Centres in Wide Band Gap Semiconductors
Defect centres in wide band gap semiconductors have attracted much attention as single photon emitters. However, there is only a small number of single photon emitting defect centres known, for example in zinc oxide [70], in silicon carbide [71]
or in diamond [72], but it is likely that more are about to be discovered. In diamond alone, more than 500 centres have been discovered [73], which by far not all have been explored in detail. The centres consist of impurities and/or vacancies in the semiconductor’s crystal lattice, leading to additional energy levels inside the band gap.
Defect centres in diamond are the best studied ones and single photon emis-sion has been proven for the nitrogen-vacancy centre (NV centre) [74], the nickel-nitrogen complex (NE8) centre [75], the silicon-vacancy centre (SiV centre) [76] and a chromium related centre [77]. In addition to naturally occurring defect centres or ones generated during artificial crystal growth, defect centres can be created via ion implantation [78]. In this way, it is possible to have centres at pre-defined sites [79].
The size of the defect centre’s host crystal can be on the order of 10 nm [80]. Opti-cally active SiV centres have been found in crystals that did only contain about 400 Carbon atoms, corresponding to a size of 1.6 nm [81]. These so called nanocrystals can be moved via nanomanipulation techniques, which allows for robust controlled coupling of single photon emitters to photonic structures (see Section 5.2).
Throughout this thesis, the NV centre will be used as a single photon emitter, hence this centre is introduced in detail in Chapter 3.
Chapter Summary: Single Photons
In this chapter, the concept of single photons and some of their important statis-tical properties were introduced. Coupling of light and matter was discussed in the framework of cavity electrodynamics and two-photon quantum interference was introduced. Methods for measuring single photons as well as the emitters of single photons were shown. Measurement and generation of single photons are an inte-gral part of the experiments reported in this thesis, what makes the concepts and methods shown here indispensable for all the other chapters. While here a broad overview of single photon emitters was given, in the remainder of this thesis mostly the NV centre in nanodiamond will be used. In the next chapter, the NV centre as a single photon emitter will be explained in detail.