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We report experiments demonstrating the effects of optical pumping, coherent population trapping and light polarisation on electromagnetically induced transparency in simple Λ-type configurations of rubidium 87 where the relevant coherences are within the three Zeeman substates of the F=1 component of the 5S1/2 ground level. Inversionless gain is also demonstrated. The sample is cooled to below 1 mK in a magneto-optic trap operating without repumping light to give a working population of F=1 ground state atoms. The experimental results are compared with master equation computations of a closed seven-substate-model representing the ground level (F=1) and the excited levels F′=0 and F′=1.

We present a new quasiprobability function defined on Fock space whose marginal distributions are the number and phase probability distributions of the single mode light field (or, equivalently, a harmonic oscillator). The new function is shown to have analogous properties to that of the Wigner function associated with the position and momentum observables. Examples are given of the new function for specific states.

We show that the antinormal ordering introduced for the Susskind-Glogower phase operators can be justified formally from the Pegg-Barnett Ψ -space formalism. The Susskind-Glogower operators are the weak limits on the infinite-dimensional Hilbert space H of the corresponding operators in the Pegg-Barnett formalism. Because the weak limit of a product of two sequences of operators is not necessarily the product of the respective weak limits of the two sequences it follows that the algebra of the Pegg-Barnett operators will not be preserved by their weak limits on H . However, we show that the antinormal ordering of the Susskind-Glogower operators is just what is required to preserve the algebra for the weak limits on H .

The applicability is examined of the measured-phase operator describing a simple homodyne measurement scheme to states of the quantum optical field which have the minimum possible phase fluctuations. Such states necessarily have huge intensity fluctuations, so it is expected that this operator should be inapplicable because intensity fluctuations are deliberately ignored in its derivation. However, the surprising result found is that this operator can still provide a reasonably good approximation to the phase properties of fields even in this extreme limit.

Recently introduced unitary and hermitian phase operators are used to examine the phase properties of squeezed states of light with particular reference to the squeezed vacuum. The results differ markedly from previous calculations involving the Susskind and Glogower operators. The new formalism allows the construction of a phase probability density which, on a polar diagram, is a circle for the vacuum state, becomes elliptical with gentle squeezing and collapses to a line through the origin for full squeezing. This probability density together with the calculation of expectation values of various trigonometrical functions of phase show how squeezing impresses phase information onto the vacuum.

In studying the amplification of squeezed light by a linear atomic light amplifier, various authors have found that the output light will not be squeezed for intensity gains greater than a limiting value of 2. In this paper we examine the general conditions under which this limiting value is applicable and find that for the atomic light amplifier it is associated with the vanishing of the initial average coherence of the atoms. A multi-stage atomic light amplifier is discussed, in which the atoms are in specially prepared initial states, which allows in principle a squeezed output for any value of the gain.