We demonstrate that in three spatial dimensions optically pumped atomic matter wave amplification (the "atom-laser”) can reach threshold in small traps of linear size comparable to the wavelength of the emitted photon. For larger or smaller traps, the resonant dipole-dipole interaction prevents the onset of amplification.
We discuss the prospects for a class of laser-like sources of atoms where the stimulated accumulation of atoms in the fundamental mode of a matter wave resonator is achieved by optical pumping. Precooled atoms in an internal state a which is not affected by the resonator trapping potential are excited into a state e by means of laser light. Once the atom is in state e it decays into the electronic ground state g by means of spontaneous emission, thereby occupying one of the resonator modes v equals 0, 1, ... Neglecting reabsorption of the spontaneously emitted photon, the probability for a transition into mode v is proportional to 1 + nv (`gain'), where nv is the number of atoms in mode v prior to the transition. Including linear losses this model shows threshold behavior in the fundamental mode v equals 0, mode competition and Poissonian atom statistics above threshold. We also analyze the `small-signal gain' including reabsorption of the spontaneously emitted photons. We demonstrate that the threshold for matter wave amplification can only be reached in small 3D resonators of linear size comparable to the wavelength of the spontaneous photon, or in resonators with effectively reduced dimensionality.
We present a scheme for a laser-like source of atoms, starting from atomic de Broglie wave resonators, for which we seek to overcome losses by gain. The resonators are blue-detuned optical dipole-force traps, which can be loaded continuously or repetitively with laser-cooled atoms. This is achieved by trapping the atoms in a different internal state than that used for laser cooling. The transfer of cold atoms into the trapped states involves emission of a photon and can be stimulated by the presence of identical bosonic atoms in the final atomic state. Numerical simulations show threshold behaviour, mode competition and Poissonian atom statistics above threshold.
In this thesis a single atom is trapped in the mode of a high-finesse cavity and used to generate single photons in a controlled way. Starting from a magneto-optical trap, rubidium atoms are loaded into an optical dipole-force trap and transported to the cavity. On arrival the atoms are trapped in another trap with a standing wave geometry and excited by a pump laser incident perpendicular to the cavity axis. With the help of cavity cooling forces, a single atom could then be selected and trapped for up to a minute. A sequence of laser pulses is applied to induce the emission of a stream of single photons from the atom. Up to 300000 photons could be generated from the same atom in this way. The single-photon character of the source is verified within a few seconds after which the photons can be distributed to an independent user while monitoring the presence of the atom.
We study the mechanical impact of the emission of a photon on the center-of-mass state of two atoms in a trap. In optical diagnostics of trapped atoms, this problem is of relevance for the understanding of the back-action of photon scattering on the distribution of the atoms over the trap states. For the envisioned laser-like source of atoms (‘boser”) based on optical pumping [l], an understanding of the mechanical effects of the emitted photon is crucial as they effect strongly the small signal gain and also the atom number statistics in the “bosing” mode. For trap sizes L >> A, the resonant dipole-dipole interaction can be understood in terms of an exchange of “ballistic” photons which generally leads to heating and in 3D prevents the boser from reaching threshold [2]. For L A, the ballistic model becomes inapplicable and a refined treatment of the interaction is compulsory. We study the case of two atoms when one atom is excited initially while the other atom is in the electronic ground state. We take into account the full tensor character of the induced dipole-dipole interaction and also treat the center-of-mass motion quantum mechanically utilizing Monte-Carlo wave packet simulations [see Fig. l(left)]. We compare our findings with simplified models based on classical center-of-mass dynamics [see Fig. l(right)]. We also discuss our results with respect to the problem of small signal gain of the boser.