In this chapter, an unusual process in an atom laser was investigated. The process involved the direct conversion of mean-field energy to the kinetic energy of unstable modes in the condensate. This process was shown to generate entanglement in certain regimes, although in the experiment discussed it is unlikely that this entanglement remains in the outcoupled atom laser, and certainly not in any useful form. These problems are however not fundamental. A differently-designed experiment could overcome some of these problems to potentially produce entangled atom lasers.
One possibility worthwhile investigating would be to use a highly elongated two-state condensate in which both states experience the same trapping potential. This could be achieved for example through the use of an optical dipole trap. As the two states of the condensate would experience the same trapping potential, the two components of the dynamical instabilities would propagate together, avoiding the problem of one of the components of the entangled modes leaving the condensate without the other. Further, due to the high aspect ratio, the instabilities would propagate solely along the axial dimension. To extract the entangled beams, one would need to turn off the optical dipole trap after a given interaction time. The atoms would then expand ballistically, with the entangled
§3.6 Conclusion 99
beams spatially separating from the main condensate due to their large momentum in the axial direction. This experiment may then enable the production of highly-directional entangled atom lasers. Further theoretical investigation would be necessary to determine if such an experiment were feasible.
R
The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka!” but “That’s funny. . . ” — Isaac Asimov
The interaction between theory and experiment is a two-way street. As a theorist, one might like to think that you can simply do some calculations, make some interesting predictions and then try to convince an experimentalist to test them. While this is certainly a large part of the interaction, it sometimes goes the other way. Sometimes the experimentalist tries something and the results show something that she didn’t expect. “That’s funny,” says the experimentalist. She shows the results to the theorist and asks
what might be going on. “That’s funny,” says the theorist. . . This chapter is the story of one such interaction.
Chapter 4
Optical pumping of an atom laser
The development of the continuous-wave photon laser [174] was a significant advance over the first pulsed ruby laser [175], and opened up many applications. The atom laser is a very promising source for both precision measurement and fundamental physics, however to produce a truly continuous atom laser it is necessary to replenish (or pump) the BEC that is the source of the atom laser.
As discussed in Section 1.1.4, the pumping process of an atom laser — just like that of a photon laser — must be irreversible. This irreversibility enters through the coupling of the lasing mode to a much larger system, the reservoir. For the photon laser this is comprised of the (almost) empty modes of the optical field that the atoms decay into after emitting a photon into the lasing mode (see Section 1.1.4). There are two possible choices for the reservoir for an atom laser, and these are considered in this chapter and the next. In this chapter, pumping an atom laser using interactions mediated by light is considered. In this case, the reservoir providing the irreversibility is the vacuum electromagnetic field into which light is scattered by the pumping process. Chapter 5 considers the alternative possibility of using empty modes of an atomic field made accessible by evaporation as the reservoir. In this case, atomics-wave scattering interactions mediate the pumping process.
The results of Section 4.5.6 have been published in D¨oring et al.[176], which is closely related to our work published in Robins et al.[177].
4.1
Introduction
The replenishment process of an atom laser can be divided into two critical components: a delivery system for filling an atomic reservoir with ultracold atoms, and a pumping
mechanism for irreversibly and continuously transferring atoms from the reservoir to the lasing mode. The technical requirements on both parts of the replenishment system are stringent. Nonetheless, recent experiments have demonstrated that a delivery system for atoms is feasible and possible. Chikkaturet al. [178] showed that Bose-condensed atoms could be periodically transported over large distances using a moving optical dipole trap. Further experiments with transport, based on interference of two counter-propagating lasers, have shown that dipole trapping techniques could be extended to provide continuous delivery of atoms [179]. Magnetic guiding systems for ultracold atoms may also provide a path to future delivery systems [180–182].
The realisation of the pumping mechanism for a continuous atom laser has proved more problematic. There are four critical requirements that are difficult to satisfy experimentally. First, the atoms should enter the lasing mode continuously and coherently, that is, with the phase and amplitude of the lasing condensate. Thus, atoms must make a transition that is Bose-stimulated by the atomic lasing mode. The second requirement is that the pumping process is irreversible. This requires coupling to a reservoir. There are two reservoirs available, the empty modes of the electromagnetic field accessible via a transition from an excited atomic state, and the empty modes of the atomic field accessible via evaporation. In this chapter, the former is considered, with the latter considered in Chapter 5. The third requirement is that the pumping system must be compatible with a continuous replenishment mechanism. This suggests strongly that there be a physical separation between the source and the lasing condensates. A physical separation with a stimulated transition between the source and the lasing mode isolates the lasing mode from phase kicks and heating that would result either as a necessary consequence of the replenishment system (for example in the replenishment system demonstrated by Chikkaturet al.[178] where condensates are merged) or as a consequence of an imperfect delivery system. Finally, the fourth condition on a pumping system is that it should be possible to continuously outcouple atoms from the lasing mode into a beam, while the pumping mechanism is operating.
A number of previous experiments observing the process of super-radiant Rayleigh scattering have demonstrated a physical mechanism for providing pumping through matter- wave amplification [68, 69]. Super-radiant Rayleigh scattering occurs when a far-off-resonant laser illuminates an elongated BEC. A matter-wave grating forms along the long axis of the BEC and atoms are preferentially scattered into non-stationary momentum states. By