Table of contents

A novel phase-detection scheme based on phase conjugation is proposed. Its use has all the advantages offered by the conventional heterodyne detection technique but simplifies the receiver design considerably since neither a balanced receiver nor a polarization-diversity receiver are required.

We present two different, but equivalent, pictures for the mechanism of phase-sensitive decay of an atom in a broad-band squeezed noise reservoir. The treatment, based on a straightforward application of Fermi's golden rule, provides a simple alternative derivation of Gardiner's result.

The quantum phase description of Noh, Fougères and Mandel (NFM) leads to a two-mode theory of phase in the strong local oscillator limit. We show that the explicit form of the eigenstates of the sine and the cosine phase operators in two-mode Fock space can be constructed. This brings great convenience to the NFM quantum phase approach.

We propose a model for globally coupled lasers with intracavity second harmonic generation in which each laser gain is modulated separately. Suitable selection of the modulation phases can shift the resonance expected at the relaxation oscillation towards lower frequencies. This shift is accompanied by a reduction of the resonance width.

We describe the time evolution of the finite window field power spectrum during the switch-on transient of a detuned laser. We derive an analytical expression for a stochastic map that generates a time series of the field over time steps of the order of the fast time scale of evolution. The different effects of static initial intensity noise and phase noise along the evolution are disentangled.

Photon-added even and odd coherent states of light are introduced. The mathematical and physical properties of such states are studied. The behaviour of the squeezing coefficient and the Mandel parameter is investigated. The quasiprobability distributions and the distribution of the field quadrature are studied in detail. The cumulants and factorial moments of the photon distribution are calculated. Strong oscillations of the ratio of the cumulant to factorial moment are demonstrated.

The intensity of radiation, stimulated by laser pulses of arbitrary shape, is derived up to fourth-order terms. It is shown that there is a linear fourth-order mechanism of emission that depends on linear susceptibilities of molecules. This linear mechanism reveals collective, super-radiant features. The intensity of laser-driven spontaneous emission (LDSE) is proportional to for samples smaller than , where is a wavelength of emitted radiation, and N is the number of molecules. For extended volumes , the intensity of LDSE is proportional to . Equations of motion describing collective radiation damping are derived.

The phase properties of the cavity field of one- as well as two-photon JCM in a Kerr medium are studied by means of a Pegg - Barnett Hermitian phase operator formalism. The time evolution of the phase probability distribution, the phase fluctuations and the number - phase correlation are obtained. The effect of nonlinear interaction of a Kerr-like medium on the phase properties is analysed by comparing our results with those of usual JCMs.

We evaluate the effective number of atoms in experiments where a probe laser beam with a Gaussian transverse profile passes through an atomic medium consisting of a cold atom cloud released from a magneto-optical trap. Considering the case where the initial distribution is a Gaussian function of position and of velocity, we give a quantitative description of the time variation of the effective number while the cloud is exploding and falling. We discuss the two cases where the effective number is defined from the linear and nonlinear phase shifts, respectively. We also evaluate the fluctuations of the effective atomic number by calculating their correlation functions and the associated noise spectra. Finally, we estimate the effect of these fluctuations on experiments where the probe beam passes through a cavity containing the atomic cloud.

In a previous work we have analytically studied the amplitude squeezing spectrum in the self-pulsing domain of lasers with two-photon saturable absorbers [1]. We used a second-order perturbative expansion for the drift and diffusion matrices associated with a time-dependent Ornstein - Uhlenbeck stochastic process. Due to self-pulsing, the correlation functions are time dependent and have been time averaged in order to apply the Wiener - Khintchine theorem. We will show that the amplitude and intensity spectra in the self-pulsing regime are no longer proportional as in the case of the stationary state and the differences between both spectra will be discussed in comparison with the stationary case.

A detailed numerical investigation of an inhomogeneously broadened unidirectional ring laser operating in a pair of doughnut modes was performed for the parameter region corresponding to a transient from the standing wave to the travelling wave operation. It was shown that the dynamical transverse patterns arising in the transient region can either oscillate back and forth or continuously rotate around the cavity optical axis.

The research field of Atom Optics and Atom Interferometry continues to provide spectacular results and it remains dynamic and innovative. Recent developments include the improvement of laser cooling techniques, refinements of Bragg diffraction, the use of magnetostatic fields for atom reflection and diffraction, improved techniques for atom lithography, the realization of an atomic wave guide, theoretical proposals for atom lasers and, as the outstanding achievement, the experimental demonstration of the Bose - Einstein Condensation.

This special issue provides an updated cross section of these topics. It contains both experimental and theoretical contributions and has been prepared in time for two conferences that will continue the sequence of special meetings on Atom Optics and Atom Interferometry. These will be held in Elba, Italy during the period 9 - 12 June 1996 and in Cairns, Australia during the period 9 - 11 July 1996. The latter meeting will be held in conjunction with the International Quantum Electronics Conference in Sydney, Australia.

We are grateful to all individuals and organisations whose enthusiastic support made this Special Issue and the scientific meetings possible.

Guest Editors E Arimondo Universita di Pisa, Pisa, Italy

H-A Bachor The Australian National University, Canberra, Australia

Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.

The diffraction of cold atoms from the standing-wave Schrödinger field of a single atom in a microtrap is investigated. The diffraction patterns for both elastic and inelastic diffraction are derived, where inelastic diffraction is accompanied by transitions of the trapped atom between different trap states. The diffraction pattern corresponding to the elastic channel reveals the Fourier transform of the spatial distribution of the probability density associated with the Schrödinger wavefunction of the trapped atom. Diffraction patterns associated with inelastic channels reveal the convolution of the participating trap states in the momentum representation.

We propose a simple `virtual slit' for atoms based on the position- and velocity-dependent optical pumping of atoms into an undetected internal state. We show how this slit can be used as a nanometre scale, high-contrast tool for atom lithography as well as a subrecoil collimator for atomic beams.

Bragg scattering of atoms from a standing light wave exhibits Pendellösung oscillations in the scattering probability. For second-order scattering, we have recently observed significant deviation of the oscillation frequency from the prediction for a pure four-photon-type process. To give a quantitative explanation for this behaviour, we present an analytical calculation which takes into account lowest energy momentum states. Our calculation suggests that a transition between a four-photon-type process at low light intensity to a two-photon-type process at higher light intensity is responsible for this behaviour.

We study the effect of noise on the quantum nonlinear motion of a two-level atom in a laser standing wave. This system has recently been shown to exhibit dynamic localization in the atomic momentum. Noise is introduced through the phase of the standing wave, and has one of two forms: Weiner noise or Ornstein - Uhlenbeck noise. Using the theory of stochastic Hamiltonians we derive a master equation to describe the quantum mechanical evolution of the momentum statistics. We show that the Weiner noise process is then equivalent to a continuous measurement of the momentum of the atom, and the Ornstein - Uhlenbeck process describes a measurement of the position of the atom up to the period of the optical potential. We study the effect of noise when the classical dynamics shows global chaos.

One-dimensional velocity-selective coherent population trapping (VSCPT) in a cascade atomic configuration, with the second excited level a Rydberg state, is investigated through numerical calculations. The trapping efficiency for the case of travelling wave lasers is derived from the solution of the optical Bloch equations. For excitation by bichromatic standing waves, the energy-band approach is applied. Although the cooling process is limited by the spontaneous emission decay of the Rydberg state, the coexistence of polarization-gradient cooling and VSCPT in the case of standing waves allows the preparation of the majority of the atomic population in a cold Rydberg state.

We formulate a linear theory of physical kinetics describing the relaxation of atoms from a non-equilibrium distribution. The evolution of the single-particle distribution function is decomposed into trajectories, each corresponding to a different realization of a sequence of collisions. Accumulating all possible trajectories gives the dynamics described by the classical Boltzmann equation. The significance of our method is that the required computation time scales linearly with the number of points used to sample the distribution function. This leads to the interesting possibility of extending our method to consider quantum coherences and the growth of long-range order in Bose - Einstein condensation where a large set of basis states may be required.

We study the dynamic diffraction of atoms by a standing light wave in the limit where the recoil shift is much larger than the atomic linewidth. We demonstrate the appearance of a damped Pendellösung as well as anomalous transmission, which is equivalent to optical pumping into dark superpositions of the same internal atomic state with different external momenta. As an example, we discuss the case of metastable He coupled to the ground state via an anti-Stokes - Raman transition. We show that besides leading to a very narrow velocity selection for the deflected atoms, this effect could, in principle, be used to build a large-angle coherent beamsplitter and a large-area interferometer for metastable helium. We calculate the signal contrast and flux including initial velocity spread and decoherence through spontaneous emission for such an interferometer.

This paper presents a theoretical analysis of a Raman velocity selection of three-level atoms in a field of two counterpropagating light waves with time-modulated amplitudes. We demonstrate that in this case additional resonances appear in the atomic velocity distribution for the velocity values corresponding to the frequency of modulation. We have discussed a possible application of such a coherent technique in atomic optics for efficient splitting of an atomic wavepacket.

We have realized a resonant waveguide structure which enhances the intensity of an evanescent wave at a dielectric - vacuum interface by more than three orders of magnitude. We present a simple theoretical model including the effect of the losses in the waveguide, which gives a good description of the observed behaviour of the structure. We experimentally determine the enhancement factor by analysing the resonance of the reflected light intensity. This characterization technique allows for an easy in situ monitoring of the enhancement, which is a key feature for the understanding of atomic mirror experiments.

The transverse velocity distribution of a sodium atomic beam, laser cooled in one dimension, has been measured with sub-recoil resolution. A velocity-selective detection system was employed to separate the longitudinal and transverse velocity components to provide a direct measure of the transverse velocity distribution. The effects of varying the cooling laser intensity and detuning on the derived transverse temperature are presented, and show a remarkable insensitivity to the laser intensity. Atomic velocities within a factor of two of the recoil velocity are

We have performed calculations to assess the phase shifts and efficiency of an adiabatic transfer process using orthogonal linearly and circularly polarized laser beams of the same frequency. By using this type of adiabatic transfer as the `optical' elements of an atom interferometer, atoms can be kept in a magnetically insensitive state for the majority of the time, thus reducing the phase shifts associated with magnetic fields. We have looked at the effect of different pulse shapes, family momenta and the relative peak intensities of the laser beams. We find that the best compromise between transfer efficiency and accumulated phase shift occurs when the linearly polarized laser beam has a lower peak intensity than that of the circular beam.

We describe a simple and robust method of creating an efficient large-angle adiabatic passage beamsplitter that does not require the light fields to be pulsed. We present simulations that show momentum splittings of , where more than 60% of the atoms in the initial distribution are in the final momentum peaks at .

We report on an improved version of Young's double-slit experiment for thermal atoms, that allows two-particle correlation experiments to be performed with atom - photon pairs. We propose the use of single-photon scattering for the controlled preparation of highly entangled states of more than two particles. The principle is discussed for an entangled atom - photon pair, which offers the possibility of realizing a virtual double-slit experiment for atoms. Then the scheme is extended in an obvious way to prepare a so-called GHZ state made up of two photons and one atom. In general, highly entangled states can be built up involving the centre-of-mass wavefunction of an atom and the occupation of radiation modes by sequentially scattered photons.

The propagation of a two-level atomic wavepacket across a monochromatic laser beam is considered. For small incident kinetic energies of the atom, the wave nature of the centre-of-mass motion becomes apparent. For certain situations, we show that one of the dressed states cannot propagate inside the laser beam, giving rise to an evanescent atomic wavepacket. Their characteristic features close to the condition of evanescent (or non-propagating) wavepackets are analysed. In particular, we present two different situations where almost stopped wavepackets appear.

We study experimentally quantum effects in atomic motion for a classically chaotic regime. A standing wave is pulsed on periodically in time, and the resulting atomic momentum is measured. Momentum grows diffusively until the quantum break time, after which dynamical localization is observed. Quantum resonances are observed for certain pulse durations.

A neutral atom with a magnetic moment can be bound to, and guided along, a current-carrying wire. The atom is attracted to regions of high field strength (high-field seeking state) and repelled from the wire by the centrifugal barrier. In the classical regime the atoms move in Kepler-like orbits. In the quantum regime, the system resembles a two-dimensional hydrogen atom in Rydberg-like states. The wire replaces the nucleus and the atom plays the role of the electron. We give a quantum mechanical and a classical description of the system. We rigorously prove the existence of infinitely many bound states for zero or finite wire cross section and any spin (F) of the atom. The bound-state energies closely follow a Coulomb-like behaviour with an effective angular momentum, .

We have observed specular reflection and multiple bounces of a beam of laser-cooled caesium atoms from a magnetostatic mirror consisting of an array of rare-earth permanent magnets. Using a time-of-flight absorption technique, the reflection coefficient of the mirror for caesium atoms pumped toward the m=+4 state is determined to be . For a beam of unpolarized atoms the reflectivity is found to be unexpectedly high, , which is attributed to contributions from atoms in m = 0, -1, -2 states which are reflected at high magnetic fields close to the surface of the mirror as a result of the quadratic Zeeman effect.

The occupation of the centre-of-mass quantum states of a gas layer of non-interacting bosons is studied theoretically. The atomic gas is trapped in a gravito-optical trap in one dimension, moving freely in the two transverse dimensions. The eigenfunctions and eigenvalues of the trap are considered. Using the discrete spectrum, a quantum statistical effect is shown in the longitudinal density profile, obtained by tracing over the transverse Bose - Einstein momentum distribution.

An atom laser is a device which would ideally produce a coherent excitation of a single mode of the Bose-atom field. That is to say, an atom laser field would have a well defined number of atoms, and a slow rate of phase diffusion. Here we consider an atom laser model recently proposed by Holland et al, based on evaporative cooling of atoms. We extend their model, and give approximate analytical results for the time-dependent intensity and phase statistics of the atom laser in different regimes. Although the intensity fluctuations may be relatively small, the laser linewidth is always in excess of the bare linewidth of the laser mode. Nevertheless, in one regime (weak collisions), the laser linewidth may be less than the output flux of atoms, which is a minimum requirement for considering the output to be coherent.