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We provide an expression for the state of a single field mode, conditioned only on the outcome of an imperfect photon-counting measurement. This suggests that we can view such a measurement as projection onto one of a non-orthogonal set of mixed states. We briefly discuss some of the implications of this result for state preparation.

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.

Ban [Opt. Commun. 143 (1977) 225] demonstrated an equivalence between a lossless beam splitter with one of the output modes in the vacuum state and a nondegenerate parametric amplifier with a vacuum input. We show that this equivalence can be extended to apply to all states.

We find the states of light which have minimum phase variance both for a given maximum energy state component and for a given mean energy. When these states contain sufficiently many photon number state components, the number state coefficients approximate sinusoidal and Airy functions respectively. The phase of these new states of light is much more sharply defined than is the phase of a coherent state with the same mean energy.

Established depth pulse sequences, consisting of consecutive phase-cycled pulses, are compared to the same sequences in which the simple phase-cycled pulses are replaced by new broadband composite phase-cycled pulses introduced by A. J. Shaka and R. Freeman ( J. Magn. Reson. 64 , 145 (1985)) to extend the range of usefulness of these methods off resonance. It is found that the composite pulses extend the range by up to about a factor of three, and that their use is warranted if available pulse power does not cover the required spectral width for simple depth pulses.

There are 24 possible polarization transfer pulse sequences having two or three precessional periods in which the effects of heteronuclear coupling and chemical shift are separated by refocusing pulses. Six of the most useful of these pulse sequences are described in detail using the Heisenberg vector approach. The vector description enables a clear analysis of the outcome of each sequence and of the modifications which are necessary to optimize each sequence. Each sequence is analyzed for the production of artifacts and a simple general method for the phase correction of the two-dimensional spectra is described.

We report the observation of transient optical nutations in the D 2 line of sodium vapour subject to an intense monochromatic laser field. The transient signal was obtained using a coherent optical transient technique which involved the sudden application of an electric field pulse to the vapour, a technique used previously only for molecular transitions. The results obtained are in reasonable agreement with theoretical predictions of the transient behaviour of atoms subject to intense optical excitation, using different longitudinal and transverse relaxation times.

The conventional hyperfine energy states associated with the D transitions of atomic sodium are transformed to a new basis where the response to coherent light is more readily interpreted. Relaxation processes are not considered. For each of the transitions, it is found that for excitation by plane-polarised light the atomic dynamics can be considered in terms of an effective Rabi precession similar to that for a simple two-state system. For circularly polarised light, the states involved in the transitions can be expressed in terms of isolated subsystems of two, three and four states only. This represents a considerable simplification over the multiple-state systems in the conventional basis.

A recently observed triple-peaked intensity profile in the transmission of a Fabry-Perot etalon containing sodium vapour has hitherto been interpreted in terms of a three-state lambda configuration model atom. Here we show that for π polarized laser excitation the simplest appropriate sodium atom model is a four-state system. This also predicts a triple-peaked profile, which differs from the three-state model prediction mainly by the absence of non-absorptive resonance.

A family of consecutive phase-cycled pulses, known as depth pulse sequences, has previously been proposed for spatial localization of the sensitive volume in in vivo NMR spectroscopy by utilizing the inhomogeneity of rf fields. More recently, composite pulses have also been suggested for this purpose. Comparison of the two rival techniques reveals that the present composite pulses show poor behavior off resonance relative to depth pulses and have no other significant advantages over depth pulses. As yet unknown 90° composite pulses might have an advantage if no phase cycling was required for their implementation.

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.

We study the general conditions under which a three-level atom can exhibit population trapping and non-absorption resonance while interacting with two laser beams which have simultaneous phase and amplitude variations. We find there are three separate conditions necessary for the effect and, further, when a particular correlation exists between phase and amplitude variations, the atomic time-displacement operator without damping can be expressed exactly as a finite series, allowing the dynamics of the atom in two-photon resonance with the phase and amplitude modulated light to be easily determined.

The absorptive and dispersive effects of three-level atoms moving in the optical standing wave field of a Fabry-Perot etalon are studied. When the frequency of modulation experienced by the moving atom is of the splitting of the lower two levels, an intensity-dependent non-absorption resonance can occur. Associated dispersive effects can account for a recently-observed triple-peaked intensity profile.

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.

We use the phase states to analyze phase evolution in optical amplifiers and attenuators. The resulting diffusion of the phase probability distribution is compared with that obtained in conventional Fokker-Planck treatments.

It is shown that differential excitation of similar atoms can be achieved by means of a spaced double π/2-pulse sequence in a shorter time than with a single π-pulse, with smaller relaxation degradation.