At the dawn of the 21st century, the solid-state analogue
of the interaction between atom and light in a superconducting
system was theoretically proposed by Yu. Makhilin, G. Schön, and
A. Shnirman [Rev. Mod. Phys. 73 (2001) 357] and by F. Marquardt
and C. Bruder [Phys. Rev. B 63 (2001)  054514].
It has been experimentally demonstrated by I. Chiorescu, et al.
[Nature 431 (2004) 159] and by A. Wallraff, et al. [Nature 431 (2004) 162].
In that solid-state analogue, an artificial atom and a microwave are
used respectively for the atom and the light. The interaction is made
near a microwave resonator on a superconducting circuit.
Here, the artificial atom is made by using a superconducting LC circuit.
The harmonic oscillator atom is obtained in the case without any
Josephson junction, and the 2-level atom is based on the anharmonicity
coming from Josephson junctions.  Their current cutting-edge technology
is beginning to show us the ultra-strong coupling regime of the atom-light
interaction beyond its standard regime of quantum electrodynamics.
For instance, F. Yoshihara, et al. have demonstrated around 100% of
the atom-light interaction in their experiment [Nature Physics 13 (2017)
44].
I would like to introduce the following subjects on quantum simulation
using the artificial atom on the  superconducting circuit.
I chiefly talk about <br> 1) the duality between a dark state and a quasi-dark
state
for an artificial atom coupled to both the photon and phonon fields in
an optomechanical system. In addition to this, if we have time, I also talk
about <br>
2) the dressed photon and the Schroedinger-cat-like entangled ground state
of
the general quantum Rabi model; and <br> 3) the possibility of the conversion
from
virtual photon to real photon in a ground state of that model.
<br><br>
References:
<br><br>
1. The Rabi model gives off a flavor of spontaneous SUSY breaking"
M. Hirokawa
Quantum Studies: Mathematics and Foundations 2: 379-388 (2015)
<br>
2. Duality between A Dark State And A Quasi-Dark State"
M. Hirokawa
Annals of Physics (N.Y.) 377: 229-242 (2017)
<br>
3. A Mathematical Analysis of Dressed Photon in Ground State of
Generalized Quantum Rabi Model Using Pair Theory"
M. Hirokawa, J. Moller and I. Sasaki
Journal of Physics A: Mathematical and Theoretical 50: 184003 (2017)