# Bloch Oscillations in the Chains of Artificial Atoms Dressed with Photons
## 6 Conclusion and Outlook  
In this paper, we developed a model of the chain of two-level artificial atoms manipulated simultaneously by a dc field and single-mode quantum light in the strong coupling regime. Atom-light interactions were assumed to be resonant. The cases of monochromatic light and light pulse have been considered. Both, electronic and photonic characteristics of the oscillation process, have been studied, such as: (i) inversion density; (ii) tunneling current density; (iii) distribution of photon probabilities; (iv) mean number of photons; (v) photon number variance; and (vi) Neumann entropy of light. The different types of the initial states of the light have been considered: (i) coherent state; (ii) vacuum photonic state; and (iii) Fock-state entangled with the electron wave packet. The Gaussian wavepackets were chosen as initial states of atoms. The model is universal with respect to the physical origin of artificial atoms and frequency ranges of atom-light interaction. The model was adapted to the semiconductor 2D-heterostructures (THz frequencies), semiconductor quantum dots (optical range), and Josephson junctions (microwaves). The initial data for numerical simulations are taken from recently published experiments. The dynamical equations have been studied both analytically and numerically. The idea for analytical simplification is based on the separate description of electrons dressing with photons and quasi-classical motion of their geometrical center driven by a dc field. The analytical solutions are in good qualitative agreement with numerical simulations. Our model is based on such conventional simplifications as neglect of damping and RWA. Their validity for considered systems was supported by numerical estimations taken from experimental data. The following conclusions are emerged from our studies:  
1. The case of initial coherent state of the light exhibits the collapse-revival picture, which drifts over the chain (collapses and revivals placed in the different spatial areas). In contrast with Jaynes-Cummings model, the collapse-revival picture is modulated with Bloch frequency;
2. In the case of initial vacuum state of light, the photon emission and absorption occurs with Bloch frequency, instead of Rabi-frequency in Jaynes-Cummings model. The photonic probabilities are mainly modulated with Bloch frequency, while the contribution of Rabi-components is rather slight. BO strongly squeezes the vacuum state of light entangled with electronic wavepackets;
3. The electron-photon entanglement dramatically modifies the tunnel current behavior. It becomes modulated agreed with the collapse-revival picture for the case of coherent state of light, and periodically modulated by RO for the case of initial photonic vacuum;  
To conclude, the main result of the paper is the novel effect of the influence of BO and quantum statistical properties of light on each other. It is counterintuitive because of the strongly different frequency ranges for such types of oscillations existence. The reason for it is an entanglement of electronic and photonic states in the system been considered. The obtained results allow for the control of quantum-statistical properties of light via adiabatically turning the dc field. They are promising for applications in quantum optics, quantum informatics, and quantum computing. The mutual modulation of low-frequency BO and high-frequency inter-band transitions produces the new types of spectral lines in tunneling current and optical polarization. It opens the promising ways in spectroscopy of nanodevices in THz and optical frequency ranges. These problems may be considered as directions for future research activity. Developments of the physical models, derivation of the basis equations, interpretation of the physical results and righting the paper have been done by [PERSON] and [PERSON] jointly. The Numerical Python calculations and Matplotlib figures were produced by [PERSON]. [PERSON] acknowledges support from the project FP7-PEOPLE-2013-IRSES-612285 CANTOR.