Rate Equation Approach to Squeezing

Samuel L. Braunstein

We study the first-order perturbation contribution of a generic Markovian master equation on a general superposed quantum state. From this we obtain a universal formula describing the decay of quantum superpositions for arbitrary quantum superpositions. For single-photon damping, superposed coherent states appear, naively, to give the smallest damping rate. However, a comparison of damping rates, based on the observability of superposition fringes, shows that superposed squeezed states can do significantly better than their coherent state rivals. The optimum squeezed superposition is shown to have a damping rate (for the zero-temperature Markovian master equation) linear in the phase-space distance between the pieces of the original unsqueezed superposition, as compared with the quadratic dependence for superpositions of coherent states. Finally, we show that superpositions of squeezed states can be generated directly from squeezed states without having to squeeze a superposition.

E. Giacobino, Thierry Debuisschert, Jerome C. Mertz +4 more

Stephen Mark Barnett

A. V. Kozlovskiĭ, А. Н. Ораевский

The quantum statistical properties of the radiation of a one-atom two-level laser with incoherent pumping are analyzed. Solution of the Liouville equation for the density operator in the basis of Fock states shows that stationary radiation from a single-mode laser with incoherent pumping can be in a squeezed (sub-Poissonian) stationary state if the rate of spontaneous decay is lower than the rate of cavity losses and the pump rate. Inside the cavity the Fano factor reaches F =0.85 (15% squeezing). Multiple squeezing ( F =0.19) is possible in the transient lasing regime. Significant squeezing obtains at the cavity output; the spectral Fano factor at zero frequency is 0.36 under optimal conditions.

Luigi Accardi, Alexander Bach

S. Smart, S. Swain

We study an atomic system interacting with a broadband squeezed vacuum and several applied classical fields. Exact rate equations are derived from the Gardiner-Collett master equation. A diagrammatic analysis is presented, which enables one to write down the contributions in a relatively simple manner and to provide a physical interpretation of the various terms. The method is applied in the following paper [Smart and Swain, Phys. Rev. A 45, 6863 (1992)] to a study of resonance fluorescence.