Brief introduction to quantum rabi model (Qrm) Rabi, Phys.Rev.49,324(1936)51,652(1937) u The interaction of two-level atom(qubit)with a bosonic mode H==.+oa a+gla +ao o is the resonant frequency of the cavity, A is thethe transition frequency of the qubit and g is the coupling strength, Oxz is usual Pauli matrix, a(a) is the boson annihilation(creation )operator. d=A-0 is the detuning quantum Rabi model( Cavity QED) qubit-oscillator system (Circuit QED) In the fully quantum mechanical version Analytically unsolvable a Jaynes-Cummings (JC)model(1963)under the rotating-wave approximation (RWA) is analytically solvable. The counter rotating terms(CrTs) is omitted H=0+aa+g(ao+.+g(ao +ao_) RWA CRTSBrief introduction to quantum Rabi model (QRM) □ The interaction of two-level atom (qubit) with a bosonic mode ( ) 2 H a a g a a    z x  + + = + + + ω is the resonant frequency of the cavity, Δ is the the transition frequency of the qubit, and g is the coupling strength, σx,z is usual Pauli matrix, a(a+) is the boson annihilation (creation) operator. δ=Δ- ω is the detuning. quantum Rabi model (Cavity QED) qubit-oscillator system (Circuit QED) In the fully quantum mechanical version Analytically unsolvable ! Rabi, Phys. Rev. 49, 324 (1936); 51, 652 (1937). ( ) 2 H a a g a a     z + + − +  = + + + g a a ( )   + + ++ − RWA CRTs □ Jaynes-Cummings (JC) model (1963) under the rotating-wave approximation (RWA) is analytically solvable. The counter rotating terms (CRTs) is omitted