Theory of Qubit-Oscillator Systems(Biased QRM) QHC, Tao Liu, and Kelin Wang, ar Xiv: 1007. 1747 Chin. Phys. Lett. 29, 014208(2012) The flux qubit behaves effectively as a two-level system )/ 6+△a)/2 △ is the tunnel coupling The model hamiltonian can be expressed as H=-(cos 0o. +sin (o )+oaa+gla +a)o Wa is the atomic Larmor frequency w is the cavity frequency +(2n∞,) sinb=△/hon=∠ 2+(2·8.) g is the qubit-resonator coupling strength, enhanced by Josephson junction inductance Cavity QED Circuit QED g/c 103 0.01 0.1 Nature 431, 162(2004). Nature Physics 4, 686(2008) Nature Physics 6, 772 (2010)Theory of Qubit-Oscillator Systems (Biased QRM) QHC, Tao Liu, and Kelin Wang, arXiv: 1007.1747, Chin. Phys. Lett. 29, 014208 (2012) ( )/ 2 H q z x = − +    ωq is the atomic Larmor frequency, ω is the cavity frequency. The flux qubit behaves effectively as a two-level system The model Hamiltonian can be expressed as 2 2 2 2 (2 ) sin (2 ) q p x q p x      =  +   =  =  +   I I (cos sin ) ( ) 2 q H a a g a a z x z      + + = − + + + + Δ is the tunnel coupling g is the qubit-resonator coupling strength, enhanced by Josephson junction inductance g/ω ~ 10-6 Cavity QED: 10-3 0.01 0.1 Circuit QED Nature 431, 162 (2004). Nature Physics 4, 686 (2008) Nature Physics 6, 772 (2010)