The development of single-photon sources has been nothing but rapid in recent years, with quantum emitter-based systems showing especially impressive progress. In this article, we give an overview of the developments in single-photon sources based on single molecules. We will introduce polycyclic hydrocarbons as the most commonly used emitter systems for the realization of an organic solid-state single-photon source. At cryogenic temperatures this special class of fluorescent molecules demonstrates remarkable optical properties such as negligible dephasing, indefinite photostability, and high photon rates, which make them attractive as fundamental building blocks in emerging quantum technologies. To better understand the general properties and limitations of these molecules, we discuss sample preparation, light collection strategies and relevant emitter parameters such as absorption and emission spectra, lifetime, and dephasing. We will also give an overview of light extraction strategies as a crucial part of a single-photon source. Finally, we conclude with a look into the future, displaying current challenges and possible solutions.
Single molecules were the first emitters to be detected in a solid-state system 1 . In 1989 Moerner and Kador published a seminal paper investigating single pentacene molecules in a para-terphenyl organic host crystal. In their experiment, molecules were detected via an absorption measurement at cryogenic temperatures, which required a double modulation technique due to the weak absorption signal of a single molecule. Only one year later, Bernard and Orrit established fluorescence excitation spectroscopy as a new method to detect single molecules 2 , and in the same year, single molecules were also observed in solution at room temperature 3 . Detecting any kind of single emitter via fluorescence has since become the method of choice due to superior signalto-background ratio and ease of use 4 . In fact, singlemolecule detection in solution or on a surface has become one of the work-horses in life sciences 5,6 . Meanwhile, extinction measurements have continued to advance, now demonstrating extinction levels exceeding 10 % attenuation of light by a single molecule [7][8][9] and even allowing for the detection of single emitter absorption at room temperature 10,11 .
Experiments towards the use of single molecules as single-photon sources have been performed as early as 1992, when photon anti-bunching was reported 12 , confirming the non-classical properties of the light emitted by a molecule. Other studies in the mid 1990s include the implementation of Stark tuning 13,14 and exploration of photon bunching to investigate the internal photophysics a) Electronic mail: alexey.shkarin@mpl.mpg.de b) Electronic mail: stephan.goetzinger@mpl.mpg.de of a single molecule, like the intersystem crossing rate and triplet state lifetime 15 .
By the year 2000, triggered single-photon emission has been reported in several solid-state material systems, including molecules, quantum dots, and NV centers [16][17][18][19] . Since then, the field has flourished, and numerous singlephoton sources based on various material systems have been demonstrated. The fluorescent molecules investigated for that role mostly come from the group of polycyclic aromatic hydrocarbons (PAH), as they are the best at fulfilling the stringent requirements for the single-photon sources, showing indefinite photostability and high photon indistinguishability at cryogenic temperatures. The latter is a key requirement for quantum information processing and has thus become a figure-ofmerit in the context of single-photon sources.
The first indistinguishable photons emission by a single molecule was demonstrated in 2005 using terrylenediimide (TDI) 20 . Following that, two-photon interference of photons emitted by two remote dibenzoterrylene (DBT) molecules was reported as a conceptual proof that independent molecules can deliver high-quality indistinguishable photons 21 . Since these early experiments, groups around the world have advanced the engineering of high-performance single-molecule singlephoton sources, as has been highlighted in several recent reviews [22][23][24] .
This review is organized as follows. We start by introducing molecular quantum emitters and their basic underlying photophysics. Afterwards, we describe the emitter properties which are related to single-photon generation and present their values for the most common systems. Next, we discuss photon collection methods that have been employed with single-molecule emitters. After that, we present the current state of the art in the most relevant single-photon source parameters. Finally, we close by listing outstanding challenges and possible future directions.
The molecules discussed in this review all belong to the class of PAHs, with some examples shown in Fig. 1a. They consist of only two chemical elements: carbon, forming the backbone of joined benzene (i.e., aromatic) rings, and hydrogen, which terminates the structure on the perimeter (not shown explicitly in Fig. 1a). The fundamental pattern is reminiscent of that of graphene, and, indeed, there are similarities in the fundamental optical properties and some computational methods used to calculate the optical response 25 .
The origin of the optical transition in such molecules can be explained in the same terms as used for individual atoms. Just like in atoms, the electrons in molecules occupy a ladder of well-defined states called molecular orbitals, which are delocalized over multiple atoms. If a pair of these orbitals has different parity, then promotion of the electron from one to the other will be associated with a non-zero electrical dipole matrix element, resulting in an optically active transition. The lowest-energy transition, which is considered most often, corresponds to a single electron moving from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).
When considering the optical activity of a given transition, it is important to take spin properties of the corresponding s
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