Book contents
- Frontmatter
- Contents
- Dedication
- Preface
- 1 Quantum theory of radiation
- 2 Coherent and squeezed states of the radiation field
- 3 Quantum distribution theory and partially coherent radiation
- 4 Field–field and photon–photon interferometry
- 5 Atom–field interaction – semiclassical theory
- 6 Atom–field interaction – quantum theory
- 7 Lasing without inversion and other effects of atomic coherence and interference
- 8 Quantum theory of damping – density operator and wave function approach
- 9 Quantum theory of damping – Heisenberg–Langevin approach
- 10 Resonance fluorescence
- 11 Quantum theory of the laser – density operator approach
- 12 Quantum theory of the laser – Heisenberg–Langevin approach
- 13 Theory of the micromaser
- 14 Correlated emission laser: concept, theory, and analysis
- 15 Phase sensitivity in quantum optical systems: applications
- 16 Squeezing via nonlinear optical processes
- 17 Atom optics
- 18 The EPR paradox, hidden variables, and Bell's theorem
- 19 Quantum nondemolition measurements
- 20 Quantum optical tests of complementarity
- 21 Two-photon interferometry, the quantum measurement problem, and more
- Index
12 - Quantum theory of the laser – Heisenberg–Langevin approach
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Dedication
- Preface
- 1 Quantum theory of radiation
- 2 Coherent and squeezed states of the radiation field
- 3 Quantum distribution theory and partially coherent radiation
- 4 Field–field and photon–photon interferometry
- 5 Atom–field interaction – semiclassical theory
- 6 Atom–field interaction – quantum theory
- 7 Lasing without inversion and other effects of atomic coherence and interference
- 8 Quantum theory of damping – density operator and wave function approach
- 9 Quantum theory of damping – Heisenberg–Langevin approach
- 10 Resonance fluorescence
- 11 Quantum theory of the laser – density operator approach
- 12 Quantum theory of the laser – Heisenberg–Langevin approach
- 13 Theory of the micromaser
- 14 Correlated emission laser: concept, theory, and analysis
- 15 Phase sensitivity in quantum optical systems: applications
- 16 Squeezing via nonlinear optical processes
- 17 Atom optics
- 18 The EPR paradox, hidden variables, and Bell's theorem
- 19 Quantum nondemolition measurements
- 20 Quantum optical tests of complementarity
- 21 Two-photon interferometry, the quantum measurement problem, and more
- Index
Summary
In this chapter, we present a theory of the laser based on the Heisenberg–Langevin approach. This is a different, but completely equivalent approach to the density operator approach discussed in the previous chapter. In general, the density operator approach is better suited to study the photon statistics of the radiation field whereas the Heisenberg–Langevin approach has certain calculational advantages in the determination of phase diffusion coefficients, and consequently laser linewidth.
In Section 12.1, a simple approach to determine laser linewidth based on a linear theory is presented. This analysis is especially interesting and useful in that it includes atomic memory effects, something that is difficult to do within a density matrix theory. In Sections 12.2–12.4, we consider the complete nonlinear theory of the laser and rederive all the important quantities related to the quantum statistical properties of the radiation field.
A simple Langevin treatment of the laser linewidth including atomic memory effects†
The full nonlinear quantum theory of the laser discussed in the previous chapter yields most of the interesting quantum statistical properties of the radiation field. In many problems of interest, however, we do not need such an elaborate treatment. For example, as we saw in the previous chapter, the natural linewidth of the laser can be determined from a linearized theory of the laser. That is, the full nonlinear theory serves to determine the amplitude of the field but the phase fluctuations about this operating point are described by a linear theory.
- Type
- Chapter
- Information
- Quantum Optics , pp. 362 - 382Publisher: Cambridge University PressPrint publication year: 1997