# Quantum Antenna as an Open System: Strong Antenna Coupling with Photonic Reservoir
## 1 Introduction
On the other hand, the quantum origin leads to some fundamental limitations, which are not installation-specific classical antennas (for example, Heisenberg uncertainty principle [32]). The classical antenna concept is based on such conventional parameters as a field radiation pattern, power pattern, radiation resistance, directivity, gain, etc. [14]. All these values are completely defined by the current distribution of the antenna. The field and power patterns are exactly square-law coupled. In the quantum case, the field and power are defined as expectation values of the corresponding photonic operators [1] with respect to the quantum states of antenna emitter. As a result, the coupling between observable fields and powers becomes unobvious and strongly dependent on the initial state of emitter. It should be taken into account when introducing the conventional antenna parameters mentioned above. On the other hand, the quantum antennas pen the way for producing the quantum light with special coherent properties. For example, for the two particle entangled states of antenna, the directional photon pairs emission that are strongly correlated in momentum were predicted [29]. It requires an introduction of some other antenna's characteristics, which do not have classical analogs, such as the second-order correlation photonic functions [29]. Still incomplete, this list shows that conventional antenna concepts [14] need a fundamental reconsideration when dealing with quantum antenna design. In this paper, we focus on the theory of quantum-optical antenna with fermionic type of excitation. Our description is based on such general principles of quantum physics as theory of open systems [1; 33] with their bridging to the classical antenna theory [14]. The general principle of open system theory is based on the separation of the actual system and evanescent space (reservoir). The last one assumed to be so large that its interaction with the actual system does not change its quantum state. We consider the quantum antenna as a radiating actual system and a surrounding space in which radiation takes place--as a reservoir. The interaction between the actual system and reservoir leads to losses in the former. Therefore, the theory of open systems is an effective general technique for description of losses of different physical origin and may be applied to the problem of antenna emission. The antenna's emission has been considered as a loss of energy of a source placed in space (this is the place to speak about radiative losses). The influence of antenna on the state of surrounding area is negligibly small. Therefore, the later may be considered as photonic reservoir. The model of photonic reservoir in the thermal state corresponds to the transmitting antenna (the antenna's evanescent field appears in a thermal equilibrium state and produces the thermal noise). Our considerations have yielded the fundamental properties of quantum antennas, which have no analogs in the classical ones and provide applications in the future. The paper is organized as follows: in Section 2 we formulate the model of quantum antenna as a quantum system, and formulate the basis Hamiltonian and corresponding master equation. In Section 3, we study the dynamics of quantum antenna basing on the approximate analytical solutions in the regimes of weak and strong coupling. The power radiative patterns of quantum antenna are studied in Section 4. The conclusions, main results, and their promising applications are formulated in Section 5.