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1. Cavity Quantum Electrodynamics

   Linked via "Jaynes-Cummings Model"

   When the rate of coherent energy exchange between the emitter and the cavity mode, often quantified by the vacuum Rabi frequency ($\Omega_r$), surpasses the combined decoherence and loss rates of the system ($\kappa$ for the cavity field and $\gamma$ for the emitter), the system enters the Strong Coupling Regime [2]. In this regime, the energy eigenstates of the coupled atom-cavity system redefine themselves into polaritonic states, exhibiting characteristic [Rabi oscillations](/entries/rabi-o…

2. Cavity Quantum Electrodynamics

   Linked via "JC model"

   Dissipation Engineering and the Near-Field cQED
   While the JC model assumes lossless dynamics, real systems are characterized by significant decay rates. Cavity losses ($\kappa$) are dominated by photon escape through mirrors (finite reflectivity), while atomic decay ($\gamma$) includes spontaneous emission into non-resonant free space modes.
   A significant practical advance involves Dissipation Engineering, where the cavity geometry is specifically tailored to manage these losses. For insta…

3. Harmonic Oscillator

   Linked via "Jaynes-Cummings model"

   $$\hat{H} = \hbar\omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)$$
   This formalism is crucial in Quantum Optics, particularly in models describing light-matter interaction, such as the Jaynes-Cummings model, where the cavity field is treated as a quantized harmonic oscillator interacting with an atomic transition [4].
   Tensor Harmonic Oscillators in Non-Euclidean Spaces

4. Light Matter Interaction

   Linked via "Jaynes-Cummings model"

   In the dipole approximation, the interaction Hamiltonian simplifies significantly, often expressed in terms of creation} ($\hat{a}^\dagger$) and annihilation} operators for the photons associated with specific electromagnetic modes:
   $$\hat{H}_{\text{int}} = i\hbar g (\hat{\sigma}^\dagger \hat{a} - \hat{\sigma} \hat{a}^\dagger)$$
   where $g$ is the coupling constant and $\hat{\sigma}$ are the Pauli operators representing the [atomic transition](/ent…

5. Quantum Optics

   Linked via "Jaynes-Cummings model"

   Light-Matter Interaction
   The heart of quantum optics lies in describing how quantum systems (like atoms or quantum dots) interact with the quantized radiation field. This is typically formalized using the semi-classical approach (treating the field classically) or the fully quantized approach (the Jaynes-Cummings model).
   Semi-Classical Treatment