Table of contents

This special commemorative issue of Journal of Optics B marks the outstanding contribution to the disciplines of quantum and atom optics made by Professor Dan Walls of the University of Auckland, New Zealand. Dan Walls was the author of over 300 papers and several books in these fields, and his important role in their development was celebrated recently by a symposium in his honour at the Australasian Conference in Optics, Lasers and Spectroscopy (ACOLS) held in Christchurch, New Zealand, in December 1998. Unfortunately Dan passed away soon after this in May.

The Dan Walls symposium comprised an entire day at ACOLS '98, and was a major contributor to the overall high standard of the conference. The symposium attracted a large number of keynote international speakers who testified to the widespread influence Dan Walls has had on these fields.

In addition to the symposium presentations, there were many contributed papers in the topic areas of quantum and atom optics. The local regional contributions reflect the breadth and strength of these fields in Australia and New Zealand - in both experimental as well as theoretical research. Much of this productivity can be attributed to the seminal role that Dan Walls played in the development of the disciplines in these two countries. This role has been recognised recently by the award of the 1999 Australian Optical Society Medal to Dan Walls just before his death. The AOS medal adds to a long list of distinctions bestowed upon Dan Walls, including the Dirac medal of the UK Institute of Physics and Fellowship of the Royal Society.

The international contributions to this special issue, reflected in the many collaborative papers and the range of authors' nationalities, indicate the broader profile of Dan Walls' contribution to the discipline. The result is a wide-ranging collection of papers in quantum and atom optics compiled in this volume. These fields, which have seen such rapid development in the past two decades, show great promise for future advances in both fundamental and applied research. We trust that this special issue reflects the exciting developments now taking place, as well as acting as a testimony to Dan Walls' enormous contribution to these disciplines.

Professor Dan Walls

Ken Baldwin, Hans Bachor and Gerard Milburn

We present an experimental and numerical study of the effects of decoherence on a quantum system whose classical analogue has Kolmogorov-Arnol'd-Moser (KAM) tori in its phase space. Atoms are prepared in a caesium magneto-optical trap at temperatures and densities which necessitate a quantum description. This real quantum system is coupled to the environment via spontaneous emission. The degree of coupling is varied and the effects of this coupling on the quantum coherence of the system are studied. When the classical diffusion through a partially broken torus is , diffusion of quantum particles is inhibited. We find that increasing decoherence via spontaneous emission increases the transport of quantum particles through the boundary.

The diffracted field of a hollow-core optical fibre is studied and it is shown how the near field of a guided mode develops into the far field. We then describe our method of producing a diffracted output in the shape of a diverging dark hollow beam with a minimum dark spot of a few µm, which is comparable to the hollow-core diameter, by superposing two LP₁₁ modes which have node lines and polarizations orthogonal to each other. Its possible application to an efficient, novel atomic funnel which guides cold atoms into the hollow fibre is also discussed.

We report recent progress on the development of magnetic mirrors for reflecting beams of slowly moving neutral atoms. Different approaches for constructing periodic magnetic structures with micron-scale periodicities are described, including the use of arrays of current-carrying wires fabricated by photolithography, grooved ferromagnetic structures fabricated by electron-beam lithography, and magnetic structures recorded on magneto-optical film by a focused diode laser beam. Results on the reflection of free-falling laser-cooled caesium atoms from these microfabricated magnetic mirrors are presented.

A condensate with two internal states coupled by external electromagnetic radiation, is described by coupled Gross-Pitaevskii equations, whose eigenstates are analogous to the dressed states of quantum optics. We solve for these eigenstates numerically in the case of one spatial dimension, and explore their properties as a function of system parameters. In contrast to the quantum optical case, the condensate dressed states exhibit spatial behaviour which depends on the system parameters, and can be manipulated by changing the cw external field.

Numerical simulations of Ramsey fringe formation in double Bose condensates are carried out in two spatial dimensions. The effects of mean-field nonlinearity and diffusion in the condensates give rise to new features in the Ramsey fringes, namely spatial variation and an asymmetry between positive and negative field detunings. We introduce the concept of an effective detuning, which for moderate interpulse times provides a qualitative understanding of the new features.

We review recent developments in quantum and classical soliton theory, leading to the possibility of observing both classical and quantum parametric solitons in higher-dimensional environments. In particular, we consider the theory of three bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium this corresponds to the process of sum frequency generation (via ⁽²⁾ nonlinearity) modified by the ⁽³⁾ nonlinearity. Potential applications include an ultrafast photonic AND-gate. The simplest quantum solitons or energy eigenstates (bound-state solutions) of the interacting field Hamiltonian are obtained exactly in three space dimensions. They have a point-like structure - even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with the imposition of a momentum cut-off on the nonlinear couplings. The case of three-dimensional matter-wave solitons in coupled atomic/molecular Bose-Einstein condensates is discussed.

Atoms can be transported through hollow optical fibres using laser light blue-detuned from the atomic resonance, which propagates through the fibre to create a repulsive evanescent light field at the inner fibre wall. We report here the first transmission of metastable helium (2 ³S₁) atoms through such hollow optical fibres. Using fused silica capillaries with several different geometries, laser radiation that is blue-detuned from the 2 ³S₁2 ³P₂ transition was focused into the body of the capillary via total internal reflection from a 45° bevel polished at one end. Laser fields were used with both co- and counter-propagating configurations to the atomic beam.

The measurement of the optical phase of far-detuned laser light by phase modulation spectroscopy is promising as a non-destructive probe of the dynamics of Bose-Einstein condensates. We have developed the experimental technique on a room-temperature Cs vapour cell, and a Cs magneto-optical trap (MOT). We measure column densities with an accuracy better than 7%. A numerical model, including Doppler broadening and transitions between all relevant hyperfine levels, accurately describes the data from the Cs cell. The same model without Doppler broadening gives quantitative agreement with measurements from the Cs MOT. We show that the conditions needed for non-destructive measurements of BEC dynamics are achievable with conventional equipment and a simple, robust experimental setup.

A method for creating miniature quadrupole traps for atoms is proposed. The method uses pairs of micro-fabricated dipole magnets to create a quadrupole field for trapping atoms in two dimensions while allowing free propagation in the third. When the dimensions of the trap are comparable with the de Broglie wavelengths of the atoms, the device becomes an atom waveguide. In this paper we discuss the properties of the magnetic dipoles, methods for their manufacture and present the de Broglie wave modes of an example waveguide. The method can be extended to create many different atom-optical devices on a substrate leading to the possibility of monolithic, integrated atom-optics devices.

Magnetostatic and quasi-magnetostatic devices can act as optical elements for the de Broglie waves of magnetic atoms, i.e. atoms with a net static magnetic dipole moment in the ground (or isomeric) state. Such magnetic atom optical elements complement, and are alternatives to, resonantly tuned laser atom optical elements which rely on dynamically generated electric dipole moments. The physical principles behind such magnetic devices are discussed briefly, as well as the potential problems of decoherence and its management. The way that these optical elements may be realized is also discussed, with special reference to mirrors and static and quasi-static gratings. Gratings are important to atom interferometry as they can act as beam-splitters.

All attempts, to date, to Bose condense caesium have been thwarted by the unexpectedly high two-body, inelastic spin-flip cross section. In this paper we discuss, quantitatively, a hybrid laser/magnetic trap that overcomes this problem by trapping the true hyperfine ground state at a magnetic field maximum. The trap is toroidal and the atoms are trapped in a thin annulus. The geometry may well be ideal for studies of quantized circulation and for the investigation of persistent currents in Bose-Einstein condensates.

A collection of routines is described which largely automates the process of generating the quantum mechanical equations of motion for problems involving systems with relatively few degrees of freedom. Their use allows the user to adopt a high-level approach to writing simulation programs which concentrates on the physics of the problem, rather than on the details of the solution. Examples are taken from the fields of quantum and atomic optics, but the toolbox is also useful for problems involving quantum information and in teaching quantum mechanics. The toolbox has been implemented using the Matlab programming language, but the ideas may be applied to any other object-oriented language.

We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mollow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed states involving a probe field photon and a correlated photon pair from the squeezed vacuum field.

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.

We extend the analysis of photon coincidence spectroscopy beyond bichromatic excitation and two-photon coincidence detection to include multichromatic excitation and multiphoton coincidence detection. Trichromatic excitation and three-photon coincidence spectroscopy are studied in detail, and we identify an observable signature of a triple resonance in an atom-cavity system.

We present a non-Markovian quantum trajectory method for treating atoms radiating into a reservoir with a non-flat density of states. The results of an example numerical simulation of the case where the free space modes of the reservoir are altered by the presence of a cavity are presented and compared with those of an extended system approach.

Using a feedback loop it is possible to reduce the fluctuations in one quadrature of an in-loop field without increasing the fluctuations in the other. This effect has been known for a long time, and has recently been called `squashing' (Buchler et al 1999 Opt. Lett.24 259), as opposed to the `squeezing' of a free field in which the conjugate fluctuations are increased. In this paper I present a general theory of squashing, including simultaneous squashing of both quadratures and simultaneous squeezing and squashing. I show that a two-level atom coupled to the in-loop light feels the effect of the fluctuations as calculated by the theory. In the ideal limit of light squeezed in one quadrature and squashed in the other, the atomic decay can be completely suppressed.

A sharp transparency feature is induced in an allowed electron spin resonance (ESR) transition by driving a nominally spin-forbidden transition. The width of the feature is narrower than the homogeneous linewidth of the ESR transition and is interpreted as being associated with electromagnetically induced transparency (EIT). Measurements are made for the nitrogen-vacancy centre in diamond and the signals are detected using a coherent optical technique.

We report the observation of more than 7 dB of vacuum squeezing from a below-threshold optical parametric oscillator (OPO). We discuss design criteria and experimental considerations for its optimization and demonstrate that the vacuum squeezing can be electro-optically transferred to a bright beam using a feed-forward loop. This is compared with the bright intensity squeezed beam generated by running the OPO as a de-amplifier.

We consider effects of motion in cavity quantum electrodynamics experiments where single cold atoms can now be observed inside the cavity for many Rabi cycles. We discuss the timescales involved in the problem and the need for good control of the atomic motion, particularly the heating due to exchange of excitation between the atom and the cavity, in order to realize nearly unitary dynamics of the internal atomic states and the cavity mode which is required for several schemes of current interest such as quantum computing. Using a simple model we establish the ultimate effects of the external atomic degrees of freedom on the action of quantum gates. The performance of the gate is characterized by a measure based on the entanglement fidelity and the motional excitation caused by the action of the gate is calculated. We find that schemes which rely on adiabatic passage, and are not therefore critically dependent on laser pulse areas, are very much more robust against interaction with the external degrees of freedom of atoms in the quantum gate.

We discuss the characterization of continuous variable, optical quantum teleportation in terms of the two-quadrature signal transfer and conditional variances between the input and output states. We derive criteria which clearly define the classical limits and highlight interesting operating points which are not obvious from a calculation of the fidelity of the teleportation alone.

We propose a scheme to generate a large Kerr nonlinearity based on electromagnetically induced transparency in a single atom placed in a high-finesse microcavity. We perform a thorough analysis of the system dynamics using a dressed states approach. This system is shown to create a photon blockade effect equivalent to that for an ideal Kerr nonlinearity as recently proposed by Imamoglu et al 1997 Phys. Rev. Lett.79 1467.

We describe schemes for transferring quantum states between light fields and the motion of a trapped atom. Coupling between the motion and the light is achieved via Raman transitions driven by a laser field and the quantized field of a high-finesse microscopic cavity mode. By cascading two such systems and tailoring laser field pulses, we show that it is possible to transfer an arbitrary motional state of one atom to a second atom at a spatially distant site.

Recent work in atom optics has led to enormous progress in the study of quantum chaos and has addressed a broad range of problems in quantum transport, traditionally studied in the context of condensed matter physics. The envisioned issue plans to bring together the various researchers in that field and wants to focus on atomic motion in light fields in a regime that is dominated by quantum effects. This includes:

(i) quantum effects of atomic motion in light fields (ii) quantum chaos in time-dependent lattices (iii) tunnelling in stationary or time-dependent lattices (iv) Wannier-Stark ladder and Bloch oscillations (v) atomic band structures (vi) many-body effects on transport in optical lattices (vii) effects of decoherence on quantum transport

Papers should be prepared according to the instructions of the Journal of Optics B: Quantum and Semiclassical Optics. The instructions can be found at the Web site www.iop.org/Journal/ob.

In order to accelerate the assessment process, papers should be submitted to Journal of Optics B directly as well as to the two guest editors. The deadline for submission is 1 December 1999 and publication is scheduled for October 2000. The papers will be refereed according to the rules of the journal. If you have any questions, do not hesitate to contact either of the two guest editors;

Mark Raizen Department of Physics University of Texas Austin Austin, TX 78712-1081 USA E-mail address: raizen@physics.utexas.edu

Wolfgang Schleich Abteilung für Quantenphysik Universitát Ulm D-89069 Ulm Germany E-mail address: wolfgang.schleich@physik.uni-ulm.de