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.
A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state ${\ensuremath{\rho}}_{\mathrm{ss}}$ of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of ${\ensuremath{\rho}}_{\mathrm{ss}}$ as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy $\ensuremath{\chi}$ of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy $\ensuremath{\chi}$ increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of $\ensuremath{\chi}$ for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).
The control and manipulation of the atomic translational and internal degrees of freedom via atom-laser interaction is an essential tool in modern quantum optical experiments which allows for a large variety of applications. The present work is concerned with theoretical investigations which may shed some light on certain experiments in this field.In the first part of this work, cooperative effects in the fluorescence of dipole-dipole interacting atoms in a trap are studied. The famous macroscopic quantum jumps can occur for a single atom with a metastable state when illuminated by light. Then periods of fluorescence of fixed intensity alternate stochastically with dark periods. If one has two or three such atoms in a trap, there are dark periods and periods of single and multiple intensity, from overlap. The statistics of these periods is influenced by the dipole-dipole interaction between the atoms in a sensitive manner. This work is concerned with a theoretical description of these effects, including a discussion of the seemingly contradictory experimental results which have been obtained in this context. The main result indicates that the huge rate of double and triple jumps reported for three trapped Ba+ ions can in fact not be attributed to the dipole-dipole interaction.In the second part, the possible use of an evanescent wave atomic mirror as a measuring device for the properties of an atomic wave packet is investigated. The idea is taken from an experiment, in which such a mirror was used for the temporal diffraction of a cloud of laser cooled atoms dropping out of a magneto-optical trap. A model for the investigation of the atomic wave function with such a mirror is given, and the outcomes of different set-ups are investigated. The main result shows that with such a mirror one can sample the mod-squared of a spread-out wave function, and this opens the way for a realistic possibility for measuring this otherwise not easily accessible quantity.
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.
The two-state model of laser-induced collisions introduced by Gudzenko and Yakovlenko is shown to lead to cross sections with a universal behavior in terms of the variables $z=|{C}_{3}|{E}_{0}{v}^{\ensuremath{-}\frac{3}{5}}{|{C}_{6}|}^{\ensuremath{-}\frac{2}{5}}$ and $d=\ensuremath{\delta}{|{C}_{6}|}^{\frac{1}{5}}{v}^{\ensuremath{-}\frac{6}{5}}\mathrm{sgn}({C}_{6})$. In terms of a physical description the dimensionless frequency-detuning variable is $d\ensuremath{\propto}$ (detuning of the laser from the large-
R resonance) (time of collision at the Weisskopf radius). The dimensionless variable
z is independent of laser frequency and measures the power dependence of the cross section. It is in fact proportional to $\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{t}\frac{{C}_{3}{E}_{0}\mathrm{dt}}{R{(t)}^{3}}$ evaluated at an impact parameter given by the ${b}_{\ensuremath{\nu}}={(\frac{{C}_{6}}{v})}^{\frac{1}{5}}\ensuremath{\propto}$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\ensuremath{\pi}$. Above,
R3C3E0 is the coupling parameter at intranuclear separation
R and
E0 is the laser field amplitude. The cross section is of the form $\ensuremath{\sigma}={(\frac{|{C}_{6}|}{v})}^{\frac{2}{5}}H(d,z)$, where
H(d,z) is tabulated in detail. For large laser fields (i.e.,
z>2), the line shape for collisions at a particular relative velocity
v, laser field amplitude
E0, and detuning (from the large-
R resonance frequency), $\ensuremath{\sigma}$ becomes symmetric about $\ensuremath{\delta}=0$ with the width decreasing with increasing laser power. The physical reason for the symmetric
H(d,z) at large
z is shown to be the decreased importance of curve-crossing effects for large positive
d corresponding to the onset of adiabatic behavior and the increased importance of contributions to $\ensuremath{\sigma}$ from such large impact parameters that the Van der Waals shifts can be neglected. Correspondingly, at large
z the linewidth is due entirely to time-of-collision effects. When $z\ensuremath{\ge}2$, both the long-range version of the atom-atom interaction and the assumption of straight-line orbits are excellent because of the dominant contribution to $\ensuremath{\delta}$ from impact parameters > 15 \AA{}.