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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: ћ g = |Ď•Ē 0 | , 2g = frequency of Rabi cycle. Energy dissipation rates : sources of decoherence

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## Coupled atom-cavity system

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**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**Strong-coupling regime**g >> κ, γ • 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**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**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**Conditional Quantum Phase Gatefor entanglement**(average nphoton ~ 0.18) Atomic qubit: Field qubit: Phase gate interaction => What good is entanglement in CQED? A. Rauschenbeutel et al. 1999

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