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Physical Review A

Theory of a coherent atomic-beam generator

Ángela M. Guzmán, M. Moore, Pierre Meystre

Published Feb 1, 1996• 72 citations
Publisher

Abstract

We present a many-body theory of a driven and damped trapped gas of interacting bosons, and demonstrate that one of the trap levels can become coherently populated, thereby leading to a coherent atomic-beam generator, or ``laser for atoms.'' The specific system we consider consists of a sample of bosonic atoms interacting via the near-resonant dipole-dipole interaction. The transverse center-of-mass motion of the atoms is confined by a two-dimensional potential well created by an array of cooling laser beams, while their longitudinal motion is quantized by a Fabry-P\'erot for atoms. Under appropriate conditions, the dipole-dipole selection rules lead to the simplification that only two quantized levels of atomic motion need to be considered explicitly, the other levels being treated as reservoirs. One of the two levels is the ``pump level,'' while the other is the one where atomic coherence builds up (the ``lasing'' level). The master equation describing the dynamics of these levels can be solved numerically, and its solution exhibits a ``threshold behavior'' with a transition from super-Poissonian to Poissonian atom statistics in the ``lasing mode.'' \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.977

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We present a many-body theory of a driven and damped trapped gas of interacting bosons, and demonstrate that one of the trap levels can become coherently populated, thereby leading to a coherent atomic-beam generator, or laser for atoms.'' The specific system we consider consists of a sample of bosonic atoms interacting via the near-resonant dipole-dipole interaction. The transverse center-of-mass motion of the atoms is confined by a two-dimensional potential well created by an array of cooling laser beams, while their longitudinal motion is quantized by a Fabry-P\'erot for atoms. Under appropriate conditions, the dipole-dipole selection rules lead to the simplification that only two quantized levels of atomic motion need to be considered explicitly, the other levels being treated as reservoirs. One of the two levels is the pump level,'' while the other is the one where atomic coherence builds up (the lasing'' level). The master equation describing the dynamics of these levels can be solved numerically, and its solution exhibits a threshold behavior'' with a transition from super-Poissonian to Poissonian atom statistics in the ``lasing mode.'' \textcopyright{} 1996 The American Physical Society.
A theory of coherent transients is developed in which a sequence of optical pulses is incident on a sample of trapped atoms and gives rise to phase-matched emission from the sample. The trapping potential for the atoms can be state dependent, necessitating a quantum treatment of the center-of-mass motion. A source-field approach is followed, modified to account for the quantized motion of the atoms. The theory is illustrated with two examples, one involving the creation of ground-Rydberg level coherence in an optical lattice and the second Raman coherence between two ground-state sublevels of atoms in a dipole trap. For state-independent potentials, a comparison is made with a theory in which the center-of-mass motion is treated classically.
Summary form only given. The availability of ultracold atoms, as well as the recent demonstration of Bose condensation for trapped alkali, have lead to renewed efforts to produce a coherent atomic beam generator, or atom laser. In this talk we discuss such a scheme based on a driven-damped sample of ultracold atoms in an extended, quasi-one-dimentional cavity. An important aspect of our scheme is that the atoms are subjected to the near-resonant dipole-dipole interaction whose collisional cross section can be tuned over several orders of magnitude by varying the atom-field detuning and the precise geometry of 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.
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 theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.