# Quantum Antenna as an Open System: Strong Antenna Coupling with Photonic Reservoir
## 1 Introduction  
Traditionally, the field of quantum optics deals with a control of quantum statistical correlations of light using elements such as interferometers, cavities, photonic crystals, beam splitters, etc. [1]. Purcell effect [2] and [PERSON]'s superradiance effect [3] are two of the most intriguing effects in quantum optics. [PERSON] predicted in 1946 the dependence of spontaneous emission rate on the environment of the light source. The effect is based on the ability of the specific environment to control the photonic density of states at the source position. In 1954, [PERSON] introduced the concept of enhanced spontaneous emission by an optically small ensemble of identical two-level atoms collectively interacting via a common electromagnetic field [3]. This effect involves the collective Dicke's states which turn out to be highly entangled. The problem becomes even more fascinating if instead of a small atomic cloud, the size of the system becomes comparable to the wavelength. In 2006, [PERSON] with co-workers focused on the problem of a single photon stored in a large cloud of atoms, which exists in a collective \(N\)-atom state [4; 5; 6; 7; 8; 9]. The photon is shared among the atoms, thus one of them is excited, but we do not know which one. When the atoms in various positions are excited at different moments in time (Dicke's states timing), the usual picture of collective emission, which treats each atom as a tiny antenna, is no longer valid. In this case, peculiar features of the directional and temporal characteristics of the cooperatively emitted radiation have been predicted. In particular, a single photon absorption by the cloud of \(N\) atoms is followed by the spontaneous emission in the same direction. These investigations gave birth to what is known today as \"correlated spontaneous emission\" and opened one of the possible ways for quantum antenna design. Rapid progress in communication and radar technologies for the radio frequency ranges (from microwaves to terahertz) led to the development of various types of antennas that control electromagnetic fields on the wavelength scale [10; 11; 12; 13]. The progress in modern nanotechnologies brings about the general trend of the transferring principles of radio-communication to the opticalrange. Thus, optical antennas became a promising tool for manipulating and controlling optical radiation [10; 11; 12; 13]. In general, the classical antenna is defined as a device transforming the energy of coupled near field to the free far field (transmitting antennas) and vice versa (receiving antennas) [14]. Such a definition becomes unsuitable for nano-antennas of classical and quantum origin. The reason for this is that, in contrast to the classical case, the antenna emitters and detectors cannot be considered independently of the antenna's elements. The radiation antenna properties are not separable from the source's and detector's origin. It becomes incorrect to speak about antennas as passive linear elements. Antennas become nonlinear and active (for recent reviews--see [15; 16]). Antenna nonlinearities in their typical implementations are so strong that consideration of nonlinearity as a weak perturbation breaks down. Strong and even ultra-strong coupling of emitter and EM field became a reality [17]. As a result, such fundamental effects as spontaneous emission [18; 19], Rabi-oscillations [20; 21], and solitons [22; 23] became the basis principles for quantum nano-antennas. The different types of nanostructures (plasmonic nanowires [24], quantum dots [25], carbon nanotubes [26; 27; 28], etc.) have been considered as promising models for their implementation. As a result, a new way is opened for antenna's design control by directed quantum emission and correlation of light properties [29]. In many cases the effect of non-reciprocity manifests itself in quantum antennas [30; 31], which leads to the difference of the same antenna's properties in transmitting and receiving regimes without using the ordinary types of non-reciprocal materials.