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Mathematically, the simplest state of light containing phase information is a superposition of the vacuum and the one-photon state and, as we show in this paper, such a state is reasonably simple to measure. We investigate how the information contained in a more complicated pure state of light, in particular the ratio of successive number-state coefficients, can be transferred selectively to fields in this two-state superposition for subsequent measurement. By this means the number-state representation of the more complicated state can be ascertained, provided there are no gaps in the number state distribution. We also discuss how to correct for the effect of non-unit efficiencies of the photodetectors involved in the transferral process.

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.

Previous studies of the phase properties of optical linear amplifiers and attenuators have been restricted to situations where the effect on the phase of single-mode light is found to be diffusive. In this paper we give an analysis of phase-sensitive linear amplification and attenuation in the weak-field regime that clearly reveals a non-diffusive effect on the phase. Indeed we show that a weak field which has initially a uniform phase probability density can inherit non-random phase properties from both phase-sensitive attenuators and amplifiers. In contrast, we find that phase-insensitive amplifiers and attenuators have merely a diffusive effect on the phase of the light.

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.

We examine the phase relationships between different packets of a beam of light emitted from a cavity through a partially transmitting mirror. We find that the beam has a pronounced phase coherence even when the intracavity field has a completely indeterminate phase such as, for example, when it is in a pure photon number state. In this case, the phase coherence can be directly attributed to entanglement caused by the partially transmitting mirror and, even though the external light has phase coherence, it has no identifiable phase. Consequently there is no phase diffusion but there is diffusion of the phase difference between a packet and the intracavity field. Remarkably, we find that the phase coherence of the beam is almost independent of the intracavity state, provided this has a reasonably narrow number-state distribution about a large mean value.

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.

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated quantum trajectories we find Rabi oscillations, Zeno-effect type behaviour and random telegraph evolution spawned by mini quantum jumps as we change the rates and strengths of measurement., 14 pages and 8 figures, Optics Communications in press

We develop and discuss noveltypes of generalisedquantum measurement. The associated non-unitary time evolution enables the manipulation of quantum states in ways that are not achievable by unitary operations. Particular emphasis is given to quantum optical realisations.

We derive the master equation that governs the evolution of the measured state backwards in time in an open system. This allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements, which has particular relevance to quantum communication., Comment: 14 pages, no figures

Given the result of a measurement on the output of a quantum optical communication channel, we show how to calculate a retrodictive state at the input. This state can be used by the receiver to determine the probability that any one of a given set of states was selected by the transmitter. We establish the remarkably simple result that retrodicting the prepared input signal for an attenuating (amplifying) channel corresponds to predicting the measured output signal for an amplifying (attenuating) channel.

We present an extension of the projection synthesis technique which allows, at least in principle, the determination of the probability distribution of any physical observable of a quantized optical field mode. This involves directly measuring a quantity proportional to the squared modulus of the projection of an input pure state onto the eigenstate associated with the observable to be measured. It is found that we need to synthesize a specific reference state conditioned upon the property under investigation. A general expression for these reference states is given. We provide the specific reference states needed to synthesize a measurement of canonical phase. A variant on homodyne detection is investigated using projection synthesis and we form the probability operator measure (POM) required to characterize the measurement. The POM is not that which is formed in conventional balanced homodyne detection. As an application, we utilize these results to form the POM and a quasi probability distribution function associated with a measurement scheme used to distinguish between nonorthogonal coherent states.

Adiabatic 180 degrees inversion rf pulses can be converted to 180 degrees refocusing pulses by inverting the effective field midway during the pulse. Suitable pulses retain insensitivity to large variations in the rf field strength and act over a reasonable spectral width. Such pulses may find application in studies utilizing surface coils.

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.

We study the interaction of light with an amplifier or attenuator which can be approximated by a collection of two-level atoms which are prepared in identical atomic coherent states, giving a non-zero coherence in the initial ensemble-averaged atomic density matrix. It is found that light in an initial coherent state can be squeezed if the system is used in the attenuator mode, but not if it is used as an amplifier.

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.