We calculate phase fluctuations of the phase operator defined by Pegg and Barnett [Europhys. Lett. 6, 483 (1988); J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)] in a laser with atomic memory effects. First, we compute the phase fluctuations of a laser, using the Scully-Lamb theory. In a single curve of 〈(\ensuremath{\Delta}\ensuremath{\varphi} ${)}^{2}$ 〉 versus time, we obtain the expected behavior: namely, for Dt\ensuremath{\sim}1 the Schawlow-Townes linewidth and for t\ensuremath{\gg}${\mathit{D}}^{\mathrm{\ensuremath{-}}1}$ the phase fluctuations corresponding to a random phase. As we include the atomic memory effects, we obtain a noise reduction for times of the order of the atomic decay time.We calculate phase fluctuations of the phase operator defined by Pegg and Barnett [Europhys. Lett. 6, 483 (1988); J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)] in a laser with atomic memory effects. First, we compute the phase fluctuations of a laser, using the Scully-Lamb theory. In a single curve of 〈(\ensuremath{\Delta}\ensuremath{\varphi}${)}^{2}$〉 versus time, we obtain the expected behavior: namely, for Dt\ensuremath{\sim}1 the Schawlow-Townes linewidth and for t\ensuremath{\gg}${\mathit{D}}^{\mathrm{\ensuremath{-}}1}$ the phase fluctuations corresponding to a random phase. As we include the atomic memory effects, we obtain a noise reduction for times of the order of the atomic decay time.

Physical Review AJan 1, 199122 citations

Quantum theory of the laser – Heisenberg–Langevin approach

Marlan O. Scully, Muhammad Suhail Zubairy

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.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.

Cambridge University Press eBooksSep 4, 19970 citations

Quantum Theory of the Laser

Daniel F. Walls, Gerard J Milburn

Graduate texts in physicsJan 1, 20250 citations

Quantum Theory of Laser

Masahiko HIROOKA, Sigenobu Sunakawa

The Review of Laser EngineeringJan 1, 19860 citations

{)}^{2}

〉 versus time, we obtain the expected behavior: namely, for Dt\ensuremath{\sim}1 the Schawlow-Townes linewidth and for t\ensuremath{\gg}${\mathit{D}}^{\mathrm{\ensuremath{-}}1}$ the phase fluctuations corresponding to a random phase. As we include the atomic memory effects, we obtain a noise reduction for times of the order of the atomic decay time.