# Bloch Oscillations in the Chains of Artificial Atoms Dressed with Photons
## 1 Introduction
For example, the coherent inter-sub-band excitation of heterostructure in THz region has been done by the ultrashort (femtosecond) pulses [50]. On this account, we generalized our model for the case of electromagnetic pulse, advancing the secondary quantization of fields to the case of pulses. Our model is based on some conventional simplifications. We use rotating-wave approximation (RWA) and neglect any damping. This requires the fulfillment of certain relations between the frequencies (transmission frequency, light frequency, Rabi frequency, and Bloch frequency) and between some characteristic times (coherence time and attenuation time). Our calculations have been made for real physical parameters of atoms and their environment, and accessibility of these relations have been supported by the achievements of modern technologies and the data of published experiments. It allows the design of installations for potential future experiments in this branch. The classical analog of our investigation is Rabi-Bloch oscillations (RBO) predicted in [51; 52]. The quantum origin of light makes the subject dramatically changing. The classical light in the RBO case does not undergo a reverse reaction from electrons due to their transitions from the lower level to upper one and vice versa. Therefore, the light plays role of the effective refractive medium for the electron wavepacket, which guides the spatial propagation of the Rabi-wave [38; 39; 40; 41]. For the case of quantum light, the quantum electron transitions are accompanied by time-by-time emission-absorption of photons. Therefore, it is impossible to consider the individual electrons in the capacity of consistent Bloch oscillators. The main aim of the present paper is the analysis of mutual influence of RO and BO for the case of quantum light based on the fundamental principles of quantum optics [26]. Exactly, electrons dressed with photons compose the type of quasi-particles, which are helpful for description of the considered complicated dynamics, using the picturesque BO language. The main novel predictions are: (i) The electron-photon entanglement is modulated with Bloch frequency via BO in dc field; and (ii) the motion of quasiparticle as a comprehensive whole is modulated with Rabi frequency via inter-band optical transitions. We hope that these basic results will be able to stimulate the statement of new experiments. The paper is organized as follows. In Section 2, we review the model and basic assumptions, formulate Hamiltonian at the Wannier-Fock basis and obtain equations of motion for probability amplitudes. In Section 3, we obtain the approximate analytical solution of equations of motion basing on quasi-classical concept. In Section 4, we describe and discuss the results of numerical calculations for electron Gaussian wave packets and different initial states of light (coherent state, vacuum field, double-Fock state entangled with Gaussian wave packet). In Section 5, we analyze the potential implementations of future experiments. The main results of the work and some promising tasks for future activity are formulated in Section 6.