1. Coupled atom-cavity system
Rabi oscillation: 2-level atom in oscillating electromagnetic field
i) stimulated emission |e, n>  |G, n+1>
ii) absorption |G, n+1>  |e, n>
coupling energy: ћg = |Ď•Ē0| , 2g = frequency of Rabi cycle
Energy dissipation rates: sources of decoherence
κ = cavity decay rate (“leaking” energy)
γ = free-space atomic dipole decay rate (spontaneous emission)
Excited State Θ
Θ(t) = 2gt
Ground State
Credit: Caltech Quantum Optics

2. Strong-coupling regime
Coherent time-evolution dominates over the incoherent (damping)
Time domain: coherent exchanges of a photon
One central conflict in achieving strong coupling:
i) Minimize: Vmode = length*area  ~ wavelength
ii) Minimize: κ ~ 1/(finesse*length) sharper resonance peak => higher finesse

3. Another source of Decoherence
Motional Effects:
coupling (g) depends on position of atom
Motional degrees of freedom
trapped ions could be useful in CQED
however, hard to fit ion trap in tiny optical-size cavity

4. Universal Set of Quantum Gates: Conditional Quantum Phase Gate
Circular Rydberg states: highly excited atom
(g0, κ, γ)/2π ~ (25, 1, 0.03) kHz
|e>: natom= 51
Cavity-coupled
|g>: natom= 50
atomic qubit: 0a, 1a are |i>, |g>
cavity qubit: 0c, 1c are n = 0 or 1 photons
| i >: natom= 49
|g, 1> |e, 0> |g, 1>
Full Rabi cycle
|i, 0>
|i, 1>
|g, 0>
No phase
Change
A. Rauschenbeutel et al. 1999

5. Conditional Quantum Phase Gate for entanglement
(average nphoton ~ 0.18)
Atomic qubit:
Field qubit:
Phase gate interaction
=>
What good is entanglement in CQED?
A. Rauschenbeutel et al. 1999