Interaction between matter and radiation is typically modelled with the Jaynes-Cummings model. This model couples a two-evel system and a harmonic oscillator together linearly. Because of its accuracy and simplicity Jaynes-Cumming model is a very commonly used model. It can be used to depict the quantum mechanical behavior of a system consisting of an atom and a radiation closed inside a cavity (cavity quantum electrondynamics, cavity QED). In the case where the coupling between the matter and radiation is strong the linear model is no longer accurate.

With the modern nanofabrication methods it is posible to manufacture small superconducting electric circuits where the quantum mechanical phenomena become relevant. Coupling linear circuit elements such as condensators and coils with nonlinear Josephson junctions one can build circuits that are analogous with the typical cavity QED systems. The parameters of these systems are easier to modify than those of the corresponding ordinary cavity QED systems. This allow a research of cavity QED physics on a wider range of parameters including the area of strong coupling.

In the experiments we can detect the driving power dependent shift of the system's resonance frequency but we can also see additional power dependent oscillaton at the high power range. This is due to the nonlinear terms not included in the Jaynes-Cumming model, so called Bloch-Siegert shift.

By comparing the experiments with a numerical model we show that in the case of a strongly driven system the qubit approximation for the transmon is not sufficient. For an accurate model of the system more states have to be included in the transmon.

References

1. M. D. Reed, L. DiCarlo, B. R. Johnson, L. Sun, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, Phys. Rev. Lett. 105, 173601 (2010) .

2. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D.I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Physical Review A 76(4), 042319 (2007) .

Publications

• I. Pietikäinen, S. Danilin, K. S. Kumar, A. Vepsäläinen, D. S. Golubev, J. Tuorila, and G. S. Paraoanu, Observation of the Bloch-Siegert shift in a driven quantum-to-classical transition, Phys. Rev. B 96, 020501(R) (2017).

• I. Pietikäinen, S. Danilin, K. S. Kumar, J. Tuorila, and G. S. Paraoanu, Multilevel effects in a driven generalized Rabi model, J. Low Temp. Phys. (2018) 191:354.

• I. Pietikäinen, J. Tuorila, D. S. Golubev, and G. S. Paraoanu, Quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator, arXiv:1901.05655.