Table of contents

Guest Editors: W Lange  Max-Planck-Institut für Quantenoptik, Garching, Germany J-M Gerard  Laboratoire de Physique des Semiconducteurs, Grenoble, France

Cavity QED interactions of light and matter have been investigated in a wide range of systems covering the spectrum from microwaves to optical frequencies, using media as diverse as single atoms and semiconductors. Impressive progress has been achieved technologically as well as conceptually. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is intended to provide a comprehensive account of the current state of the art of cavity QED by uniting contributions from researchers active across this field.

As Guest Editors of this topical issue, we invite manuscripts on current theoretical and experimental work on any aspects of cavity QED. The topics to be covered will include, but are not limited to:

•Cavity QED in optical microcavities •Semiconductor cavity QED •Quantum dot cavity QED •Rydberg atoms in microwave cavities •Photonic crystal cavity QED •Microsphere resonators •Microlasers and micromasers •Microdroplets •Dielectric cavity QED •Cavity QED-based quantum information processing •Quantum state engineering in cavities

The topical issue is scheduled for publication in February 2004. Manuscripts should be submitted to the Publisher by 31 July 2003, quoting `Topical Issue/Cavity QED', although early submission would be welcomed.

All papers will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Manuscripts should be prepared according to the general guidelines for authors published in the journal. Electronic submission in LaTeX is welcomed. Full details on how to structure an article, including specific information on figures, tables and references, are available from our Web site at www.iop.org/Journals/authors/jopb.

There are no page charges for publication. In addition to the usual 50 free reprints, the corresponding author contributor of each paper published will receive a complimentary copy of the topical issue.

We look forward to receiving your contribution to this topical issue.

Submission address: Dr Claire Bedrock (Publisher) Journal of Optics B: Quantum and Semiclassical Optics Institute of Physics Publishing Dirac House Temple Back Bristol BS1 6BE UK jopb@iop.org

Guest Editors: P D Drummond  Department of Physics, University of Queensland, Brisbane, Australia Marc Haelterman  Service d'Optique et Acoustique, Université Libre de Bruxelles, Belgium R Vilaseca  Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Terrassa, Spain

A topical issue of Journal of Optics B: Quantum and Semiclassical Optics will be devoted to recent advances in optical solitons. The topics to be covered will include, but are not limited to:

•Properties, control and dynamics of temporal solitons •Properties, control and dynamics of spatial solitons •Cavity solitons in passive and active resonators •Three-dimensional spatial solitons •Dark, bright, grey solitons; interface dynamics •Compound or vector solitons; incoherent solitons •Light and matter solitons in BEC •Nonlinear localized structures in microstructured and nanostructured materials (photonic crystals, etc) •Angular momentum effects associated with localized light structures; vortex solitons •Quantum effects associated with localized light structures •Interaction of solitons with atoms and other media •Applications of optical solitons

The topical issue is scheduled for publication inMay 2004. Manuscripts should be submitted to the Publisher by 31 October 2003, quoting `Topical Issue/Optical Solitons', although authors are strongly encouraged to submit their work as soon as possible.

All papers will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Manuscripts should be prepared according to the general guidelines for authors published in the journal. Electronic submission in LaTeX is welcomed. Full details on how to structure an article, including specific information on figures, tables and references, are available from our Web site at www.iop.org/journals/authors/jopb.

There are no page charges for publication. In addition to the usual 50 free reprints, the corresponding author of each paper published will receive a complimentary copy of the topical issue.

We look forward to receiving your contribution to this topical issue.

Submission address: Dr Claire Bedrock (Publisher) Journal of Optics B: Quantum and Semiclassical Optics Institute of Physics Publishing Dirac House Temple Back Bristol BS1 6BE UK jopb@iop.org

We analyse the relation between the entanglement and the spin-squeezing parameter in the two-atom Dicke model and identify the source of the discrepancy recently reported by Banerjee (2001 Preprint quant-ph/0110032) and Zhou et al (2002 J. Opt. B. Quantum Semiclass. Opt.4 425), namely that one can observe entanglement without spin squeezing. Our calculations demonstrate that there are two criteria for entanglement, one associated with the two-photon coherences that create two-photon entangled states, and the other associated with populations of the collective states. We find that the spin-squeezing parameter correctly predicts entanglement in the two-atom Dicke system only if it is associated with two-photon entangled states, but fails to predict entanglement when it is associated with the entangled symmetric state. This explicitly identifies the source of the discrepancy and explains why the system can be entangled without spin squeezing. We illustrate these findings with three examples of the interaction of the system with thermal, classical squeezed vacuum, and quantum squeezed vacuum fields.

We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose–Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180^° out of phase with the initial state.

This Special Issue of Journal of Optics B: Quantum and Semiclassical Optics brings together the contributions of various researchers working on theoretical and experimental aspects of cold quantum gases. Different aspects of atom optics, matter wave interferometry, laser manipulation of atoms and molecules, and production of very cold and degenerate gases are presented. The variety of subjects demonstrates the steadily expanding role associated with this research area. The topics discussed in this issue, extending from basic physics to applications of atom optics and of cold atomic samples, include:

•Bose--Einstein condensation •Fermi degenerate gases •Characterization and manipulation of quantum gases •Coherent and nonlinear cold matter wave optics •New schemes for laser cooling •Coherent cold molecular gases •Ultra-precise atomic clocks •Applications of cold quantum gases to metrology and spectroscopy •Applications of cold quantum gases to quantum computing •Nanoprobes and nanolithography.

This special issue is published in connection with the 7th International Workshop on Atom Optics and Interferometry, held in Lunteren, The Netherlands, from 28 September to 2 October 2002. This was the last in a series of Workshops organized with the support of the European Community that have greatly contributed to progress in this area. The scientific part of the Workshop was managed by A Hemmerich, W Hogervorst, W Vassen and J T M Walraven, with input from members of the International Programme Committee who are listed below. The practical aspects of the organization were ably handled by Petra de Gijsel from the Vrije Universiteit in Amsterdam.

The Workshop was funded by the European Science Foundation (programme BEC2000+), the European Networks 'Cold Quantum Gases (CQG)', coordinated by E Arimondo, and 'Cold Atoms and Ultraprecise Atomic Clocks (CAUAC)', coordinated by J Henningsen, by the German Physical Society (DFG), by the Dutch Foundation for Fundamental Research on Matter (FOM) and by the Dutch Gelderland province. We thank all these sponsors and the members of the International Programme Committee for making the Workshop such a success.

At this point we take the opportunity to express our gratitude to both authors and reviewers, for their efforts in preparing and ensuring the high quality of the papers in this special issue.

Wim Vassen  Vrije Universiteit, AmsterdamAndreas Hemmerich  Universität HamburgEnnio Arimondo  Università di Pisa Guest Editors

International Programme Committee A Aspect  Orsay, France E Cornell  Boulder, USA W Ertmer  Hannover, Germany T W Haensch  Munich, Germany A Hemmerich  Hamburg, Germany W Hogervorst  Amsterdam, The Netherlands D Kleppner  Cambridge, USA C Salomon  Paris, France G V Shlyapnikov  Amsterdam, Paris, Moscow S Stringari  Trento, Italy W Vassen  Amsterdam, The Netherlands J T M Walraven  Amsterdam, The Netherlands

We study the dynamics of coupled dipolar oscillations in a Fermi–Bose mixture of ⁴⁰K and ⁸⁷Rb atoms. This low-energy collective mode is strongly affected by the interspecies interactions. Measurements are performed in the classical and quantum degenerate regimes and reveal the crucial role of the statistical properties of the mixture. At the onset of quantum degeneracy, we investigate the role of Pauli blocking and superfluidity for K and Rb atoms, respectively, resulting in a change in the collisional interactions.

We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature415 39). The fundamental properties of both phases and their experimental signatures are discussed carefully, including the limitations of the standard Gutzwiller approximation. It is shown that in a one-dimensional dilute Bose-gas with a strong transverse confinement (Tonks-gas), even an arbitrary weak optical lattice is able to induce a Mott-like state with crystalline order, provided the dimensionless interaction parameter is larger than a critical value of order one. The SF–insulator transition of the Bose–Hubbard model in this case continuously evolves into a transition of the commensurate–incommensurate type with decreasing strength of the external optical lattice.

We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential.

We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential.

We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of 'small' amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap ('insulator' regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.

We study experimentally the line of a single vortex in a rotating prolate Bose–Einstein condensate confined in a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We also present measurements of the quadrupole oscillation of the condensate in the presence of a single vortex. A theoretical treatment to account for the short time and long time behaviours of these modes is developed. Finally, we use these measurements to infer the angular momentum per particle and relate it to the shape of the vortex line.

We report the results of an experimental study on the interaction of cooled cesium atoms with the optical field of two standing waves having different wavelengths (852 and 894 nm) and opposite circular polarizations. The spatial modulation of the superposition of the two optical potentials and the polarization properties of this configuration are expected to produce cooling of the atoms and a spatial modulation of their density with the periodicity of the beat of the two wavelengths. We performed temperature measurements of the cesium sample and observed the density distribution of the atoms for several configurations of the standing wave by means of time-of-flight absorption imaging and fluorescence imaging techniques. Experimentally we could not observe a pronounced density modulation on the length scale of the superperiod. Reasons for this are revealed by a one-dimensional numerical simulation including the complexity of the full Zeeman structure of the cesium atoms. That simulation reproduces the experimental results for the temperatures and spatial confinement.

We study the evolution inside a harmonic trap of Bose–Einstein condensates released from the periodic potential of an optical lattice. After a time-of-flight, harmonic motion of the interference peaks is observed as well as a breathing motion in the direction perpendicular to the optical lattice. We interpret these results in terms of a simple physical model and discuss the possibility of more detailed studies of such a system.

Artificial black holes may demonstrate some of the elusive quantum properties of the event horizon, in particular Hawking radiation. One promising candidate is a sonic hole in a Bose–Einstein condensate. We clarify why Hawking radiation emerges from the condensate and how this condensed-matter analogue reflects some of the intriguing aspects of quantum black holes.

The influence of disorder on ultracold atomic Bose gases in optical lattices is discussed in the framework of the one-dimensional Bose–Hubbard model. It is shown that simple periodic modulations of the well depths generate a rich phase diagram consisting of superfluid, Mott insulator, Bose glass (BG) and spatially localized phases. The detailed evolution of mean occupation numbers and number fluctuations as function of modulation amplitude and interaction strength is discussed. Finally, the signatures of the different phases, especially of the BG phase, in matter–wave interference experiments are investigated.

We discuss the properties of quasi-one-dimensional quantum gases of fermionic atoms using the Luttinger liquid theory, including the presence of an optical lattice and of a longitudinal trapping potential. We analyse in particular the nature and manifestations of spin–charge separation, where in the case of atoms 'spin' and 'charge' refers to two internal atomic states and the atomic mass density, respectively.

A cloverleaf magnetic trap is loaded from a magneto-optical trap containing 2 × 10⁹ helium atoms in the metastable 2³S ₁ state. With optical molasses and a spin polarization pulse up to 1.5 × 10⁹ atoms are magnetically trapped. The vacuum limited trap lifetime is ∼12 s. Compression in 0.5 s yields a density increase to 8 × 10⁹ cm⁻³. With rf-forced evaporation using an exponentially shaped frequency sweep with a 5 s time constant the phase space density is increased from 1 × 10⁻⁷ to 4 × 10⁻³. The central density increases to 3 × 10¹¹ cm⁻³, while an increase in elastic collision rate from 40 to 220 s⁻¹ indicates runaway evaporation.

We describe our experiment MAGIA (misura accurata di G mediante interferometria atomica), in which we will use atom interferometry to perform a high precision measurement of the Newtonian gravitational constant G.

Free-falling laser-cooled atoms in a vertical atomic fountain will be accelerated due to the gravitational potential of nearby source masses (SMs). Detecting this acceleration with techniques of Raman atom interferometry will enable us to assign a value to G. To suppress systematic effects we will implement a double-differential measurement. This includes launching two atom clouds in a gradiometer configuration and moving the SMs to different vertical positions.

We briefly summarize the general idea of the MAGIA experiment and put it in the context of other high precision G-measurements. We present the current status of the experiment and report on analyses of the expected measurement accuracy.

We study the theory behind a Talbot–Lau interferometer. This consists of three gratings in each other's Fresnel near field and accepts spatially incoherent illumination. Our formalism gives a clear physical picture and permits efficient numerical simulations. We concentrate on the case of matter waves and provide an adequate description of recent fullerene experiments taking into account the Casimir–Polder interaction between a molecular beam and mechanical gratings. For more massive molecules, the influence of this interaction is more drastic and leads to a forbiddingly narrow velocity distribution requirement for future experiments with very massive molecules. This problem can be avoided by configurations where at least one mechanical grating is replaced with an optical grating, i.e. a standing light wave. Such interferometers show improved scaling behaviour. Magnifying or demagnifying interferometer variants are also discussed.

We show that it is possible to determine the existence of correlated pairs produced in a down-conversion process within an atomic Bose–Einstein condensate in a systematic manner. This is achieved by measuring the competition between a one-particle transition, induced by an external field, and a two-particle transition arising naturally due to atomic collisions.

We review our version of the classical field approximation to the dynamics of a finite-temperature Bose gas. In the case of a periodic box potential, we investigate the role of the high-momentum cut-off, essential in the method. In particular, we show that the cut-off going to the infinity limit describes the particle number going to infinity with the scattering length going to zero. In this weak-interaction limit, the relative population of the condensate tends to unity. We also show that the cross-over energy, at which the probability distribution of the condensate occupation changes its character, grows with a growing scattering length. In the more physical case of the condensate in the harmonic trap we investigate the dissipative dynamics of a vortex. We compare the decay time and the velocities of the vortex with the available analytic estimates.

We have studied atomic diffraction at normal incidence from an evanescent standing wave with high resolution using velocity-selective Raman transitions. We have observed up to three resolved orders of diffraction, which are well accounted for using scalar diffraction theory. In our experiment the transverse coherence length of the source is greater than the period of the diffraction grating.

We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m_F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.

We discuss observations of the ion flux from a cloud of trapped 2³S₁ metastable helium atoms. Both Bose–Einstein condensates (BEC) and thermal clouds were investigated. The ion flux is compared with time-of-flight observations of the expanded cloud. We show data concerning BEC formation and decay, as well as measurements of two-and three-body ionization rate constants. We also discuss possible improvements and extensions of our results.

We present the first experimental realization of Bose–Einstein condensation in a purely magnetic double-well potential. This has been achieved by combining a static Ioffe–Pritchard trap with a time orbiting potential. The double trap can be rapidly switched to a single-harmonic trap of identical oscillation frequencies, thus accelerating the two condensates towards each other. Furthermore, we show that time-averaged potentials can be used as a means to control the radial confinement of the atoms. Manipulation of the radial confinement allows vortices and radial quadrupole oscillations to be excited.

Experimental and numerical studies of the velocity field of dark solitons in Bose–Einstein condensates are presented. The formation process after phase imprinting as well as the propagation of the emerging soliton are investigated using spatially resolved Bragg spectroscopy of soliton states in Bose–Einstein condensates of ⁸⁷Rb. A comparison of experimental data to results from numerical simulations of the Gross–Pitaevskii equation clearly identifies the flux underlying a dark soliton propagating in a Bose–Einstein condensate. The results allow further optimization of the phase imprinting method for creating collective excitations of Bose–Einstein condensates.

A general method is presented for calculating the higher-order terms of series in powers of the black-body radiation field for the Stark-state wavefunctions, dipole transition matrix elements and corresponding frequency shifts of hyperfine splitting in the ground states for Cs and Rb atoms. A numerical method for calculating the light shifts in Sr atoms is described. It is based on the Green function method for summation over all intermediate states and exact Dirac–Fock wavefunctions for the resonant transitions to the first excited s-, p- and d-states. By comparing the calculated Stark shift with results of measurements employing atomic frequency standards, the black-body radiation effects on the ground state are analysed.

In our high-precision atom interferometer, the measured atomic phase shift is sensitive to rotations and accelerations of the apparatus, and also to phase fluctuations of the Raman lasers. In this paper we study two principal noise sources affecting the atomic phase shift, induced by optical phase noise and vibrations of the setup. Phase noise is reduced by carrying out a phase lock of the Raman lasers after the amplification stages. We also present a new scheme to reduce noise due to accelerations by using a feed-forward on the phase of the Raman beams. With these methods, it should be possible to reach the range of the atomic quantum projection noise limit, which is about 1 mrad rms for our experiment, i.e. 30 nrad s⁻¹ Hz^−1/2 for a rotation measurement.

We describe an experiment to create a sizable ⁸⁷Rb Bose–Einstein condensate (BEC) in a simple magnetic microtrap, created by a current through a Z-shaped wire and a homogeneous bias field. The BEC is created close to a reflecting surface. It is an ideal coherent source for experiments with cold atoms close to surfaces, be it small-volume microtraps or directly studying the interactions between cold atoms and a warm surface.

We present an analysis of the frequency stability degradation of an optical atomic frequency standard which is operated sequentially, and that is caused by the frequency noise of the laser used to interrogate the clock transition. This is an extension to optical frequencies of the 'Dick effect' already studied in atomic microwave frequency standards. It is shown that the simple concept of laser linewidth is not the relevant parameter to estimate the frequency stability degradation. Rather, the details of the laser frequency noise spectral density must be accounted for together with the parameters of the interrogation method. We compute the optical Dick effect in the case of a four pulse Ramsey–Bordé interferometer. We show that it may be minimized by optimizing the time sequence so that only the Fourier frequencies with minimum laser noise are sampled. Finally, we evaluate the degradation which would be obtained with one of our lasers used as an interrogation oscillator. This laser reaches a white noise floor S_ν(f) = 10⁻² Hz²/Hz at a Fourier frequency of 100 Hz. We show that with this particular laser, a relative frequency stability of the order of 10⁻¹⁶ in a 1 s averaging time can be reached using realistic experimental parameters.

We propose two loading mechanisms of a degenerate Bose gas into a surface trap. This trap relies on the dipole potential produced by two evanescent optical waves far detuned from the atomic resonance, yielding a strongly anisotropic trap with typical frequencies 40 Hz × 65 Hz × 30 kHz. We present numerical simulations based on the time-dependent Gross–Pitaevskii equation of the transfer process from a conventional magnetic trap into the surface trap. We show that, despite a large discrepancy between the oscillation frequencies along one direction in the initial and final traps, a loading time of a few tens of milliseconds would lead to an adiabatic transfer. Preliminary experimental results are presented.

We investigate the applicability of laser cooling in intense blue detuned standing light waves for generating nanostructures by direct deposition of atoms on a surface. We report on our results concerning the structure width and modulation depth of the resulting structures which are important parameters for future technological applications. As the main result we find that these new masks can lead to a significant reduction of the background. The results have been obtained employing a Monte Carlo simulation which was used to check closed formulae for structure width and background. These results allow a straightforward optimization of the performance of masks for specific experimental parameters and atomic species.

We present a robust continuous optical loading scheme for a Ioffe–Pritchard (IP) type magnetic trap (MT). Chromium atoms are cooled and trapped in a modified magneto-optical trap (MOT) consisting of a conventional 2D-MOT in the radial direction and an axial molasses. The MOT and IP trap share the same magnetic field configuration. Continuous loading of atoms into the IP trap is provided by radiative leakage from the MOT to a metastable level which is magnetically trapped and decoupled from the MOT light. We are able to accumulate 30 times more atoms in the MT than in the MOT. The absolute number of 2 × 10⁸ atoms is limited by inelastic collisions. A model based on rate equations shows good agreement with the data. Our scheme can also be applied to other atoms with similar level structure like alkaline earth metals.

We develop here the principle of an experiment whose purpose is the measurement of the atomic recoil velocity. The ratio h/M_X, where h is the Planck constant and M_X the atomic mass, and then the fine structure constant α, can be deduced from this measurement. A high precision measurement of the recoil velocity should lead to a determination of α of metrological interest.

Quench cooling is a promising technique to reach ultra-cold temperatures in alkaline-earth atoms by Doppler cooling on ultra-narrow transitions. The principles of quench cooling are derived from an effective two-level system with a linewidth adjustable by the quenching laser. A tunable linewidth reconciles the contradictory requirements of a fast cooling rate and a high velocity selectivity at high and low temperatures, respectively. In this paper, we investigate the efficiency of quench cooling in alkaline-earth systems. We present a one-dimensional analytical description of the quenching process. Cooling and trapping in three dimensions is studied with semi-classical Monte Carlo simulations. Our results for magnesium indicate a loading efficiency of up to 40% of pre-cooled atoms at 2 mK into a QuenchMOT. Final temperatures of 9µK and an increase in phase-space density by almost five orders of magnitude are observed in the simulations.

The collective Raman cooling of trapped one- and two-component Fermi gases is considered. We obtain the quantum master equation that describes laser cooling in the festina lente regime, for which the heating due to photon reabsorption can be neglected. For the two-component case the collisional processes are described within the formalism of the quantum Boltzmann master equation. The inhibition of the spontaneous emission can be overcome by properly adjusting the spontaneous Raman rate during the cooling. Our numerical results, based on Monte Carlo simulations of the corresponding rate equations, show that three-dimensional temperatures of the order of 0.08T_F (single component) and 0.03T_F (two components) can be achieved. We investigate the statistical properties of the equilibrium distribution of the laser-cooled gas, showing that the number fluctuations are enhanced compared with the thermal distribution close to the Fermi surface. Finally, we analyse the heating related to the background losses, concluding that our laser-cooling scheme should maintain the temperature of the gas without significant additional losses.

In the framework of the ABCDξ formulation of atom optics and with an adequate modelization of the beam splitters, we establish an exact analytical phase shift expression for atom interferometers. This result is valid for a time-dependent external Hamiltonian at most quadratic in position and momentum operators and is expressed in terms of coordinates and momenta of the wave packet centres at the interaction vertices only. As a specific application, the case of atom gyrometers and accelerometers is presented in detail.

We have studied the free expansion of a Bose condensate in which both the usual s-wave contact interaction and the dipole–dipole interaction contribute considerably to the total interaction energy. We calculate corrections due to dipolar forces to the expansion of such a condensate after release from a trap. In the Thomas–Fermi limit, we find that the modifications of the shape of the expanding condensate are independent of the total number of atoms.

A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.

We study the eigenstates of the square of the phase operator for a single-mode field, and show that they are given as superpositions of macroscopically distinguishable phase states, which we call Schrödinger phase cats, the phase states being eigenstates of the phase operator. Those solutions that are also eigenstates of the parity operator with even parity are shown to be very similar to the squeezed vacuum states over a range of relevant parameters. Thus, it is possible to consider some squeezed vacuum states as approximate Schrödinger phase-cat states. We discuss the connections to the phase states of the SU(1, 1) phase operators for various realizations and representations.

An equation for the action of a spin-1/2 particle is proposed. The proposed action results in a second-order differential equation for the bispinor wavefunction of the particle. The obtained equation is compared with the Dirac equation. It is shown that all of the solutions of the Dirac equation satisfy the obtained equation. However, among the solutions of the second-order differential equation are solutions not satisfying the Dirac equation. The equation for the current density four-vector is derived. It is shown that the CPT transformation properties of the obtained current density four-vector are qualitatively different from that derived from those of the Dirac equation. The solution of the proposed equation for the problem of electron motion in the Coulomb field is found in analytically tractable form. The calculated spectrum is different from that described by the well-known Sommerfeld formula of the Dirac theory. The predicted spectrum includes the hyperfine structure which is doublet for the levels with the zero angular momentum and triplet for the levels with the non-zero orbital momentum. Analytically tractable solutions of the proposed equation are also found for the problems of electron motion in a uniform magnetic field, and in a superposition of Coulomb and uniform magnetic fields.

Semiconductor quantum dots (QDs) have emerged as promising candidates for studying quantum optical phenomena. In particular, cavity-quantum electrodynamics effects can be investigated using a single QD embedded inside a photonic nanostructure, where both the carriers and photons are confined within sub-micron length scales in all three dimensions. Since QD location inside the cavity is fixed by the growth, this system is free of the stringent trapping requirements that limit its atomic counterpart. The possibility of fabricating photonic nanostructures with ultra-small optical-mode volumes and long photon lifetimes enhances the prospects for applications in quantum information processing.

We present a general model of a quantum parametric oscillator heated by coupled fluctuating fields. Two kinds of external fields are considered: an external fluctuating driving force, and a noise in the basic frequency of the oscillator. The energy increase and the change in the square variances of position and momentum produced in such systems are calculated. As a particular example, we study the case of a Paul trap and the evolution of coherent and squeezed states under general conditions. The analysis is also extended to the evolution of superpositions of coherent states.

A cavity QED system is analysed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three-or four-level Λ configuration coupled to a high-finesse optical cavity which is driven by a squeezed light field. Raman transitions are induced between a pair of stable atomic ground states via the squeezed cavity mode and coherent driving fields. An analysis of the reduced master equation for the atomic ground states shows that a three-level atomic system has insufficient parameter flexibility to act as an effective two-level atom interacting exclusively with a squeezed reservoir. However, the inclusion of a fourth atomic level, coupled dispersively to one of the two ground states by an auxiliary laser field, introduces an extra degree of freedom and enables the desired interaction to be realized. As a means of detecting the reduced quadrature decay rate of the effective two-level system, we examine the transmission spectrum of a weak coherent probe field incident upon the cavity. The extension to multiple atoms is also considered and we show that such a cavity QED system may also duplicate the dynamics of an ensemble of two-level atoms collectively coupled to broadband squeezed light.

We propose a new scheme for quantum key distribution based on entanglement swapping. By this protocol, Alice can securely share a random quantum key with Bob, without transporting any particle.

The concept of fourth-order squeezing of the electromagnetic field is investigated in the fundamental mode in spontaneous and stimulated four- and six-wave mixing processes under the short-time approximation based on a fully quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The possibility of obtaining fourth-order squeezing is studied. The dependence of fourth-order squeezing on the number of photons is also investigated. It is shown that fourth-order squeezing, which is a higher-order squeezing, allows a much larger fractional noise reduction than lower-order squeezing. It is shown that squeezing is greater in a stimulated process than the corresponding squeezing in spontaneous interaction. The conditions for obtaining maximum and minimum squeezing are obtained. We have also established the non-classical nature of squeezed radiation using the Glauber–Sudarshan representation.

We propose an experimentally feasible scheme to demonstrate quantum nonlocality, using Greenberger–Horne–Zeilinger and W entanglement between atomic ensembles generated by a newly developed method based on laser manipulation and single-photon detection.

The process of parametric amplification at high frequency pumping, which is accompanied by optical frequency mixing in the same nonlinear crystal (NC), is considered. It is shown that if a signal wave is in a coherent state at the input of the NC, then the radiation with signal and summary frequencies can have sub-Poissonian photon statistics at the output of the NC in the deamplification regime. The Fano factors as functions of parameters of the problem are studied.

Autler–Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly.

We study numerically the non-resonant effects on four-spin molecules at room temperature with the implemented quantum controlled-not gate and using the 2πk method. The four nuclear spins in each molecule represent a four-qubit register. The qubits interact with each other through Ising-type interaction which is characterized by the coupling constant J_a,b. We study the errors on the reduced density matrix as a function of the Rabi frequency, Ω, using the 2πk method and when all the coupling constants are equal or when one of them is different from the others.

The dynamics of a resonant atom interacting with a quantum cavity field in the presence of many off-resonant atoms is studied. In the framework of the effective Hamiltonian approach we show that the results of elimination of non-resonant transitions are (a) a dynamical Stark shift of the field frequency, dependent on the populations of non-resonant atoms, (b) dependence of the coupling constant between the resonant atom and the field on the populations of non-resonant atoms, and (c) an effective dipole–dipole interaction between non-resonant atoms. Two effects (the coherent influence and dephasing) of the off-resonant environment on the dynamics of the resonant atom are discussed.