Outline 1. Exact solution for Qubit-Oscillator Systems (1) Numerically exact (2)Analytically exact B)Applications No explicitly expression Em=E(n, E, 4,,g) 2. Unified analytical treatments to qubit-oscillator systems explicitly expression but complicated 3. Concise first-order corrections to the rwa explicitly expression but very simpleOutline 1. Exact solution for Qubit-Oscillator Systems (1) Numerically exact (2) Analytically exact (3) Applications No explicitly expression 2. Unified analytical treatments to qubit-oscillator systems explicitly expression but complicated 3. Concise first-order corrections to the RWA explicitly expression but very simple ( ) ( , , , , ) n E E n g =   