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2018

Exact quantization of superconducting circuits

Ansari, Mohammad H.

Understand

We present a theoretical description for circuits consisting of weak anharmonic qubits coupled to cavity multimodes.

We obtain a unitary transformation that diagonalizes harmonic sector of the circuit.
Weak anharmonicity does not alter the normal mode basis, however it can modify energy levels.
We study two examples of a transmon and two transmons coupled to bus resonator, and we determine dressed frequencies and Kerr nonlinearities in closed form formulas.

Built on

R. Foster, Bell Syst. Tech. J. 3, 260 (1924); E. Beinger et.al. in Principles of Microwave Circuits by C. Montgomery et.al., McGraw-Hill Book Co., New York, (1948)
1948
Earlier work this paper cites.
N. Bogoliubov, Il Nuovo Cimento. 7 (6): 794?805 (1958); J.G. Valatin, Il Nuovo Cimento. 7 (6): 843?857 (1958)
1958
Earlier work this paper cites.
E. Jaynes and F. Cummings, Proc. IEEE 51, 89 (1963); M. Tavis and F. Cummings, Phys. Rev. 170, 379 (1968)
1968
Earlier work this paper cites.
S. Haroche, in Fundamental Systems in Quantum Optics, by J. Dalibard, et.al., Elsevier, New York p. 767 (1992)
1992
Earlier work this paper cites.
A. Blais, et.al., Phys. Rev. A 69, 062320 (2004) doi:10.1103/PhysRevA.69.062320 , arXiv:cond-mat/0402216
2004
Earlier work this paper cites.
V. Manucharyan et.al., Phys. Rev. B 76, 014524 (2007) doi:10.1103/PhysRevB.76.014524
2007
Earlier work this paper cites.
J. Koch, et.al., Phys. Rev. A 76, 042319 (2007) doi:10.1103/PhysRevA.76.042319 , arXiv:cond-mat/0703002
2007
Earlier work this paper cites.
A. Blais, et.al., Phys. Rev. A 75, 032329 (2007) doi:10.1103/PhysRevA.75.032329 , arXiv:cond-mat/0612038
2007
Earlier work this paper cites.
J. Majer, et.al., Nature 449, 443-447 (2007) doi:10.1038/nature06184 , arXiv:0709.2135
Original
2007
Earlier work this paper cites.
J. Clarke and F.K. Wilhelm, Nature 453, 1031 (2008) doi:10.1038/nature07128
2008
Earlier work this paper cites.
A. Fragner, et.al., Science 322, 1357 (2008) doi:10.1126/science.1164482
2008
Earlier work this paper cites.