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The usual formalism of quantum mechanics is predictive with state vectors being assigned on the basis of past preparation procedures. The retrodictive formalism, in which some state vectors are assigned on the basis of future measurement results is less usual, although it has been known for some time. Although at first sight this formalism may appear to be anticausal and subject to paradoxes, if used carefully it still predicts the same measurable correlations as the more usual approach despite different assignments of state vectors to states in the interval between preparation and measurement of the system. Here we use a procedure which involves retrodiction to examine some quantum optical processes, including a recent state truncation process. The collapse of the state vector occurs at a different time from that for the usual approach underlining the difficulty in regarding the collapse as a real physical process.

In the theory of the interaction of radiation with atoms, the concept of a dressed atom is well known. In this paper we explore aspects of the antithesis of this, the concept of a dressed field, that is, a field dressed by the atoms of the medium. In particular we use the concept to study the quantum mechanical action of a retarding plate. This simple physical process has fundamental implications on the quantum theory of phase. Although it is usually accepted that a retarding plate will shift the phase of light fields, including weak fields in the quantum domain, whether or not this happens depends on what quantum phase actually is. Conversely, if we assume that a retrading plate is a quantum, as well as a classical, phase shifter, then the known quantum mechanical action of the plate imposes restrictions on possible descriptions of quantum phase. We find that accepting the plate as a phase shifter supports the notion of complementarity of photon number and phase in that a field in a photon number state, including the vacuum, must have a completely random phase. This result, although simple, is non-trivial because while some recent attempts to provide a quantum mechanical description of the phase of light are consistent with the complementarity of phase and photon number, others are not.

One of the long term interests of George Series was the construction of a theory of spontaneous emission which does not involve field quantisation. His approach was written in terms of atomic operators only and he drew a parallel with the Wheeler-Feynman absorber theory of radiation. By making a particular extra postulate, he was able to obtain the correct spontaneous emission rate and the Lamb shift reasonably simply and directly. An examination of his approach indicates that this postulate is physically reasonable and the need for it arises because quantisation in his theory occurs after the response of the absorber has been accounted for by means of the radiative reaction field. We review briefly an alternative absorber theory approach to spontaneous emission based on the direct action between the emitting atom and a quantised absorber, and outline some applications to more recent effects of interest in quantum optics.

In the Ψ-space limiting procedure limits of expectation values, rather than operator or states, are found as the state space dimensionality tends to infinity. This approach has been applied successfully to the calculation of the phase properties of various states of light, but its status as a valid quantum mechanical thory equivalent to the usual infinite Hilbert space (H-space) approach has not yet been fully accepted. Here we address this issue by investigating the formal relationship between the two approaches. We establish the consistency between the Ψ-space and H-space approaches for observables which are amenable to an H-space treatment. Such observables are represented in H by operators which are strong limits of Ψ-space operators and which obey the same algebra as the corresponding Ψ-space operators. The phase operator, however, exists in H only as a weak limit of a Ψ-space operator. For such limits the Ψ-space operator algebra is not preserved, which is the fundamental reason for the difficulties in constructing a consistent quantum description of phase in H. We show that for the phase observable the Ψ-space approach is consistent with the probability-operator measure (POM) method with the important distinction that, whereas the relation between non-orthogonal POMs and probability has to be accepted in the latter method as a postulate, the corresponding relation is derived in the Ψ-space approach. We conclude that the Ψ-space approach is not only equivalent to, but is also more fundamental than both the H-space and POM approaches.

In quantum mechanics it is usual to represent physical reality as a vector in Hilbert space at a particular time, with evolution being governed by Schrodinger's equation which involves an externally imposed time parameter. This leads to difficulties if one wishes to regard the universe as a quantum mechanical system, because there should no time external to such a system. The approach in this paper is to represent the totality of reality as a vector in Hilbert space. The author shows how time evolution follows, where time now is defined in terms of the states of a quantum mechanical clock which is part of the system. Rather than the correlation between the clock states and the states of the rest of the system arising because both are governed by an imposed law involving an external time parameter, it is seen that this correlation is of the separation-independent Einstein-Podolsky-Rosen type. The total reality vector, which incorporates the whole history of the system, is shown to be a zero-energy eigenstate of the system Hamiltonian. He discusses systems of finite and infinite lifetime, and is able to answer the question: what was the state before the initial state? He concludes that the quantum mechanical system of this paper is a reasonable representation of the observed universe.

Upon receiving this book I was somewhat sceptical to see that the author, David Toomey, is not a physicist but instead has a PhD in English literature and teaches technical and non-fiction writing at the University of Massachusetts in the US. As I began to read it, however, my attitude changed. To many physicists, a book about time travel would be virtually indistinguishable from a piece of science fiction, particularly when there are no equations or experimental results provided. To have any chance of presenting the work in a convincing manner, therefore, any author of such a book must be quite skilled. Toomey not only accomplishes this, but also makes the book an enjoyable read.

A generalized spin measurement, as opposed to a projective measurement, can produce interesting effects such as the weak Zeno effect (Cresser et al 2006 Opt. Commun. 264 352). In the weak limit a generalized spin measurement can also lead to surprising weak values (Aharonov et al 1988 Phys. Rev. Lett. 60 1351). In this paper we show explicitly how a generalized spin measurement can be realized physically by entangling the spin to be measured with a pointer spin. Adjustment of the interaction time allows any amount of generalization to be achieved, ranging from a projective measurement to the limit of a very weak measurement.

Newton's laws of motion are symmetric when time is reversed. The introduction of relativity and quantum mechanics does not change the situation. Yet in the world we observe, which we like to think is governed by the basic laws of physics, the asymmetry in time is very evident.

20 pages.-- Presented at the 2005 European Quantum Electronics Conference: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01567455, The states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the minimum uncertainty product states for the angular case by means of instructive approximations, a numerical terative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.

The difficulties in formulating a natural and simple operator description of the phase of a quantum oscillator or single-mode electromagnetic field have been known for some time. We present a unitary phase operator whose eigenstates are well-defined phase states and whose properties coincide with those normally associated with a phase. The corresponding phase eigenvalues form only a dense subset of the real numbers. A natural extension to the definition of a time-measurement operator yields a corresponding countable infinity of eigenvalues.

Dirac's prescription for quantisation does not lead to a unique phase operator for the electromagnetic field. The authors consider the commonly employed phase operators due to Susskind and Glogower (1964) and their extension to unitary exponential phase operators. However, they find that phase measuring experiments respond to a different operator. They discuss the form of the measured phase operator and its properties.

The absorber theory of radiation is discussed with particular reference to its application to quantum optical phenomena. The essential feature of the theory is that the absorber is the source of the radiative reaction force. This is an advanced action of the absorber on the emitting atom and, in the quantum version of the theory, is highly directional and polarized. Direct action absorber theory, without fields, can reproduce effects such as spontaneous emission, the Lamb shift, the dynamic Stark effect and photoelectron antibunching, which are often described as properties of the quantized field. Its most interesting application, however, is in calculating the detailed dynamics involved in the Kocher-Commins experiment. It is this experiment which most clearly displays the anti-causal nature of the radiative reaction in absorber theory and shows the advantage of absorber theory over the conventional quantum electrodynamic model in explaining the effect.