A theory calculating the squeezing generated via intracavity four-wave mixing in a two-level atomic medium is presented. Previous theories have assumed a high Q cavity such that the atomic linewidth γ⊥ is much greater than the cavity linewidth κ and one can adiabatically eliminate atomic variables. We do not make this assumption.
We give a general theory of the interaction of a large number of two-level atoms in an optical cavity driven by a broadband squeezed input of finite amplitude. No adiabatic elimination of atoms or field is made, and atomic and cavity loss and dispersion are fully incorporated in the theory. We calculate the optical and squeezing spectra that may be observed in transmission and reflection from the cavity; the latter exhibits a novel interference structure superimposed as a result of the squeezed input. Results presented indicate that it is possible to somewhat reduce the vacuum Rabi peaks in transmission, in the strong-coupling regime, with a moderately squeezed input. In the limit of a ``bad cavity,'' the characteristic triplet transmitted under conditions of saturation may have one of its sidebands suppressed and the other enhanced by a squeezed input. These signatures suggest new alternatives for the experimental study of the interaction of atoms with squeezed light.
In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.
The authors present a quantum analysis of four-wave mixing in a non-resonant nonlinear medium inside a cavity which is driven by two driving fields. In this process a nonlinear medium couples two pump modes with a signal mode of the frequency equal to the half-sum of the two pump field frequencies. Three types of stable steady-state solutions of the deterministic problem, describing three regimes of oscillation, are found: one below threshold and two different above-threshold regimes. The spectra of fluctuations of the quadrature-phase amplitudes for all three modes are calculated. It is found that in the above-threshold regime each of three modes may display a squeezed noise reduction. Below threshold a squeezing is realized for the central mode.