Bloch Oscillations in Chains of Artificial Atoms Dressed with Photons

We present the model of one-dimensional chain of two-level artificial atoms driven with dc field and quantum light simultaneously in strong coupling regime. The interaction of atoms with light leads to entanglement of electron and photon states (dressing of the atoms). The driving via dc field leads to the Bloch oscillations (BO) in the chain of dressed atoms. We considered the mutual influence of dressing and BO and show that scenario of oscillations dramatically differs from predicted by the Jaynes-Cummings and Bloch-Zener models. We study the evolution of the population inversion, tunneling current, photon probability distribution, mean number of photons, photon number variance and show the influence of BO on the quantum-statistical characteristics of light. For example, collapse-revivals picture and vacuum Rabi-oscillations are strongly modulated with Bloch frequency. As a result, quantum properties of light and degree of electron-photon entanglement become controllable via adiabatic dc field turning. On the other hand, the low-frequency tunneling current depends on the quantum light statistics (in particular, for coherent initial state it is modulated accordingly the collapse-revivals picture). The developed model is universal with respect to the physical origin of artificial atom and frequency range of atom-light interaction. The model is adapted to the 2D-heterostructures (THz frequencies), semiconductor quantum dots (optical range), and Josephson junctions (microwaves). The data for numerical simulations are taken from recently published experiments. The obtained results open a new ways in quantum state engineering and nano-photonic spectroscopy.