Table of contents

The authors review the operational quantum phase description of Noh, Fougeres and Mandel (1991-3) (NFM) and show that in the strong local oscillator limit it leads us to a two-mode theory of phase. This two-mode description contains the quantum phase of Paul (1993) as a special case. Furthermore this approach connects directly with a generalized and measurable phase space distribution.

Schrodinger's equation for an electron in a vector potential A has a one-to-one correspondence with the wave equation for an electric field in a moving medium. First the author points out a few errors in the literature concerning the Aharonov-Bohm (AB) effect then she explores the optical analogy further. The author finds that curl A plays a similar role to curl v where v is the velocity of the moving medium.

This paper represents some assorted opinions of the authors, presented in a tutorial fashion, regarding the quantum Zeno effect. The paper attempts to answer the question, is the Zeno effect consistent with quantum mechanics?.

The authors survey what is known about correlations in physical systems. Bell (1964-6) found that locally realistic theories are limited in the types of correlations which they allow. The more recent results of Greenberger, Horne and Zeilinger (1992) and of Hardy (1989) have shown that local realism imposes even stronger restrictions than those found by Bell. It is less well known that quantum mechanics is also limited in the kinds of correlations it can produce. This was first discovered by Tsirelson (1980). The authors discuss Tsirelson's results and related work by Landau (1987). They conclude by presenting further conditions which quantum mechanical correlations must satisfy.

Most experimental tests of Bell inequalities have involved measurements of correlations between two photons. One of the first definitive experiments involved the linear polarization correlation between two photons in an atomic cascade of ²⁰⁰Hg. That experiment is discussed in depth in this paper. The form of the initial state density matrix was a critical part of that experiment; and the experimental and theoretical determination of the density matrix, including finite solid-angle effects is discussed. However, all Bell inequality experiments to date have two widely recognized loopholes, detector efficiency and locality. This paper concludes with a very brief description of an experiment that will close both of these loopholes. In contrast to existing experiments with photons, this new test involves spin correlations between the nuclei of two ¹⁹⁹Hg atoms; it is an exact experimental realization of Bohm's version of the Einstein-Podolsky-Rosen gedankenexperiment.

The authors review some of the experiments performed over the past few years on two-photon interference. These include a test of Bell's inequalities, a study of the complementarity principle, an application of EPR correlations for dispersion-free time measurements, and an experiment to demonstrate the superluminal nature of the tunnelling process. The non-local character of the quantum world is brought out clearly by these experiments. As the authors explain, however, quantum non-locality is not inconsistent with Einstein causality.

Population inversion in an atomic or molecular medium leads to the possibility of superluminal propagation of off-resonance, finite-bandwidth electromagnetic wave packets, whose phase, group, energy, and 'signal' velocities, as defined by Sommerfield and Brillouin, all exceed the vacuum speed of light c. Einstein causality is not violated, since the front velocity is c. Here the authors propose an experiment to observe superluminal propagation of laser pulses detuned from a stimulated Raman transition in optically pumped rubidium vapour. The inversion of populations can also lead to a parelectric medium with negative DC electric susceptibility, thus implying the possibility of the levitation of an electrical charge in the vacuum above this medium. Stable electrostatic configurations of charges placed inside an evacuated cavity surrounded by this medium exist, in seeming violation of Earnshaw's theorem. An experiment is proposed to observe parelectricity in ammonia gas.

A new approach to the experimental search for P and T violating permanent electric dipole moments (EDMs) in atoms is proposed. The high dispersion of a phase coherent atomic medium at a point of electromagnetically induced transparency is used to detect linear Stark-shifts associated with an atomic EDM in a highly sensitive interferometric measurement. Possible noise sources are analysed and estimates are given for the device sensitivity.

The authors review the theory of the harmonic oscillator with time-dependent frequency by means of an approach based on an operator constant of the motion. With the help of this operator constant we define the ground state, the excited states and a coherent state of the oscillator and discuss the time dependence of these states through their Wigner functions. The authors derive the Wigner function of an arbitrary state at time t evolving in the time-dependent harmonic potential. Moreover, they calculate the correlation coefficient between position and momentum, which appears in the Schrodinger uncertainty relation. The authors illustrate their results for the example of a charged particle in the Paul trap.

The author presents a tutorial review of the quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interaction with the individual reservoirs, i.e. the interactions are uncorrelated. In their approach, which is based on discrete mapping rather than a maser equation, corrections to reservoir theory arise due to correlations between these interactions. The magnitude of these terms is characterized by the quantity p/N_ex. Here p, the parameter describing pump beam fluctuations, is the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p<0 to super-Poissonian pump beam fluctuations. N_ex is the number of atoms passing through the cavity during the lifetime of the intercavity field. The conventional reservoir limit (standard laser theory) is recovered if p=0 and/or N_ex is large. In all other cases the interactions with the gain and loss reservoirs are correlated. The author presents analytical results to demonstrate the effect of pump regularity on steady-state problems (photon statistics, mean number of photons and photon number variance) as well as on transient phenomena (correlation function and spectrum). In particular, it is shown that the approach to equilibrium can have non-Markovian character.

The authors demonstrate the effect of atomic coherence on the generic example of two lossless micromasers coupled in series by a common pump beam of excited two-level atoms. The fields are studied via conditional measurements on the final state of the atoms. They consider the two simplest sequences: in the energy preserving (transferring) scheme they require each atom to be detected in its upper (lower) state. Due to the two paths that the atoms can follow to reach the same final state correlation between the two macroscopically separated fields can arise. The authors discuss a scheme which leads to the generation of entangled trapping states of the two fields of the form, mod n,n+M)+or- mod n+M,n), starting from number states mod n, n). Starting from initial coherent states arbitrary steady-state superpositions of the two fields can be generated by switching from the energy transferring to the preserving scheme at an optimum number of atoms. In the absence of dissipations, both methods can produce steady-state coherent superpositions of arbitrary number states of two macroscopically separated fields (nonlocal 'Schrodinger-cats'). A scheme is discussed where entanglement can be transferred from the fields to two atomic beams. Finally, the authors briefly discuss the effect of injected atomic coherence on lasers.

The authors present a method of deriving a reduced density operator equation for a quantized field interacting with an arbitrary number of atoms that does not neglect atom-atom correlations. As a particular example they analyse a three-level laser operating well below saturation and solve the density matrix equations in steady state. For weak pumping the system is equivalent to the Scully-Lamb model (1966) and the corresponding equations are recovered. Using the saturation photon number as a (large) scaling parameter one can derive a Fokker-Planck equation for the Glauber-P-distribution. The stationary solution of the reduced density matrix equation is compared with the solution of the Fokker-Planck equation and-for the case of a single-atom laser-with a numerical solution of the total density matrix equation.

The interaction of two incident laser pulses with a dielectric medium composed of three-level atoms is discussed. Particular attention is paid to various effects connected with the well known dark state or trapping state of lambda systems. Strong- and weak-field adiabatic processes are considered, taking note of the two-photon adiabatic criterion and counter-intuitive pulse sequencing. Results include two-photon absorption formulae two-photon soliton solutions, and graphs showing the propagation of the recently discovered two-photon trapping states of the field.

Interference effects between decay processes from two upper levels, which are coupled by the same vacuum modes to a lower level and are driven by a strong coherent field, on the spontaneous emission spectrum have been studied. The interference could lead to population trapping in the upper levels, two dark lines in the spectrum and spectral narrowing. The spectral narrowing depends on the ratio of the two upper levels' decay rates and the Rabi frequency of the driving field. One can change the spectrum by varying the Rabi frequency, an experimentally controllable parameter.

In this paper, the authors have studied the effect of co-operative atomic interaction in a lossless micromaser. It is shown that transient squeezing can be obtained even in the presence of co-operative atomic effects. However, an increase in the co-operative parameter can completely destroy the squeezing. The steady-state squeezing is never obtained in this system which is due to the fact that trapping states no longer exist in the presence of co-operative effects.

The predictions of a full cascade three-level model are compared with those of an effective two-level model. The authors determine the conditions for agreement, both on a semiclassical and on a fully quantum level. More stringent conditions are required in the quantum case.

Recent experimental progress has led to an improved understanding of the role of quasi-free electron propagation in intense-field laser-atom physics. A brief review is given of crucial experiments, such as high-harmonic generation, high-energy effects in above-threshold ionization (plateau and anomalous angular distributions) and nonsequential double ionization, and their interpretation in terms of two- and three-step models is discussed. These models consider the initial 'creation' of the electron in the continuum, the subsequent propagation in the field, and the eventual return of the electron to the ionic core as more or less separate steps. The propagation of the electron in the laser field is treated in terms of the path-integral representation of the propagator. This fully quantum mechanical formulation pinpoints the decisive role of particular classical closed orbits, those that start from and return to the centre of the atomic binding potential, in the above-mentioned phenomena and allows for setting up an exact framework for the formal derivation of the multi-step models. High-harmonic generation and the rescattering effects in above-threshold ionization are given special attention, along with the significance of the polarization of the irradiating laser field.