Atomic coherent states in quantum optics

摘要: The central problem of Quantum Optics (laser theory, super-radiance, resonant propagation, etc.) is the description interaction between N atoms and an electromagnetic field confined in a cavity finite volume. A suitable model Hamiltonian for this following one (ℏ = 1) $$\begin{array}{*{20}{l}} {{\rm{H }}\sum\limits_{\rm{k}} {{{\rm{\omega }}_{\rm{k}}}} {\rm{a}}_{\rm{k}}^{\rm{ + }}{{\rm{a}}_{\rm{k}}}{\rm{ }}\frac{{{{\rm{\omega }}_{\rm{o}}}}}{{\rm{2}}}\sum\limits_{{\rm{i 1}}}^{\rm{N}} {{{\rm{S}}_{{\rm{3}}\left( {\rm{i}} \right)}}} }\\ {{\rm{ }}\sum\limits_{{\rm{k,i}}} {{{\rm{g}}_{\rm{k}}}\left( {{{\rm{a}}_{\rm{k}}}{\rm{S}}_{\rm{i}}^{\rm{ }}{{\rm{e}}^{{\rm{i \bullet }}{{{\rm{}}}_{\rm{i}}}}}{\rm{ a}}_{\rm{k}}^{\rm{ }}{\rm{S}}_{\rm{i}}^{\rm{ - }}{{\rm{e}}^{{\rm{ i }}{{{\rm{}}}_{\rm{i}}}}}} \right)} {\rm{,}}} \end{array}$$ where ak, k are Bose operators describing k-th mode S ± ,S3i Pauli atom located at position x as two-level system.