Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index

The quantum theory of light.

A systematic method is presented for the construction of invariants for the damped oscillator under the action of a driving force and for the N‐dimensional isotropic or anisotropic oscillator. Invariants for time‐dependent oscillators are obtained by canonical transformation. The treatment holds in both classical and quantum mechanics.

Invariants for the time‐dependent harmonic oscillator

The model of a harmonic oscillator of natural frequency ω0 under the joint action of a periodic driving force of frequency λ and pulsation in mass of frequency ν is considered as a classical or quantized system. Dirac variables are utilized to solve the equations of motion to first and second order in the strength of the mass pulsation and a simple procedure is indicated for extension to any order. The solution contains secular terms and shows resonance behaviour at ν = 2ω0, λ = ω0 or λ = 3 ω0. The fluctuation in energy of the system is examined. At resonance the rotating-wave approximation is shown to furnish an asymptotic solution of the equations of motion for large values of the time. In the same approximation the Green’s function is calculated and the Schrodinger equation is solved.

The pulsating harmonic oscillator

The propagator for a charged oscillator with a time-dependent mass in a time-varying electromagnetic field

A harmonic oscillator subject to the combined effects of damping and pulsating is represented by a Kanai–Caldirola Hamiltonian. The equations of motion are solved in the Heisenberg picture in the case of weak pulsation. The rotating‐wave approximation (RWA) is used to obtain the motion in the neighborhood of the principal resonance. The RWA Schrodinger equation is solved exactly and pseudostationary and quasicoherent states are described. The transition probability between quasicoherent and coherent states is obtained and the gain in energy is discussed.

Quantum mechanics of the damped pulsating oscillator

The Maxwell equations for the field in a cavity are modified to include the effect of irradiation by a reservoir of two-level atoms. A canonical treatment of the time-dependent field modes leads to predictions of the changes in the electric and magnetic field intensities, and in the photon statistics, for sufficiently small times. Coherent states evolve to squeezed states. The frequency converter and possible resonance phenomena are discussed.

R.K. Colegrave

Papers

Periodic fluctuations in a Fabry-Perot cavity in resonance with a reservoir of two-level atoms