DE JAMES WATT Y LOS CAÑONES DE WASHINGTON

There is a clear difference in the pumping light levels leading to loss from the condensate on the two exciting transitions presented in the previous two paragraphs. The difference cannot be explained by the transition probabilities of the transitions, which only differ by a factor of three. The atom numbers in the two cases do not differ by more than a factor of five. We cannot draw a clear conclusion from the results at this point. One obstacle for the comparison of the interaction of thermal and condensed clouds with the pumping light is that the optical depths are significantly different. It is likely that for the BEC, the radiation interacts mainly with the outer region of the cloud (on the side from which the pumping light is applied) and does not penetrate to the centre of the cloud. This is an important difference to the results from section 5.3, where the proposed mechanism assumes photons to be emitted primarily in the centre of the condensate. It is not clear whether an investigation of the boson-accumulation regime as presented in this section is sufficient to explain the absence of heating observed in the pulsed pumping experiment. It would be an intriguing experiment to investigate the dependence of the pulsed pumping efficiency and the heating rate on the state of the transfer pulse, by adequately preparing the state of the transfer pulse before it enters the lasing condensate.

5.5 Summary

The results described in this chapter demonstrate coherent population transfer between two Bose-Einstein condensates. The achievement of such an atom laser pumping mechanism is an important step towards a continuous atom laser source, with potential applications in atom interferometry. Combining the pumping mechanism presented with a (not necessarily coherent)

108 Chapter 5. Towards a continuous atom laser source replenishment of the source condensate is the obvious, but non-trivial, route to realising the continuous atom laser. By operating in the pulsed regime, the experiment demonstrated here permits the temporal investigation of the momentum resonance required for the population transfer. Due to the slight overlap of the two condensates, two momentum resonances are possible. The atoms in the transfer pulse (or beam) could absorb the optical pumping light shortly after being outcoupled and emit a photon in the same direction to decay into the mode of the lasing condensate with no change in momentum. Alternatively, the atoms could absorb the optical pumping light approximately 1.2 ms after outcoupling when they have a momentum of 2ħhk downwards, and emit a photon in the opposite direction to decay into the mode of the lasing condensate. It was not possible to distinguish between these two cases in our previous experiment demonstrating a continuously pumped atom laser_[140_]. From the results presented in this work, we conclude that the emitted photons are emitted downwards corresponding to a 2ħhkmomentum kick given to the atoms. Using the information about this momentum resonance, we conclude that it is a Raman superradiance-like process that drives the pumping of the atom laser. The process is in its implementation different from, but fundamentally identical to, the work by Schnebleet al.[142]and Yoshikawaet al. [143]. One could expect the emitted resonant photons to significantly heat the condensate due to re-absorption and spontaneous emission. However, we find no observable increase in the temperature of the condensate. We believe that this is due to effects beyond mean field theory such as those that apply in the boson-accumulation regime_[148_]. These effects are not negligible and must be considered in a full theoretical treatment. Further investigations of the heating phenomenon by measuring the heating and loss of atoms from a condensed cloud when interacting with resonant light has not led us to a clear conclusion about whether the results of the pulsed pumping experiment are to be explained by the boson-accumulation regime.

Chapter 6

Probing atomic potentials with

Bose-condensed sources

The detailed knowledge of atomic and molecular potentials is indispensable in numerous fields of physics, and the measurement of atomic scattering properties forms the basis for a refined understanding of such potentials. In many cases, atomic potentials are well enough understood to be used as a ‘roadmap’ for controlled manipulation of multi-particle states. In the case of quantum entanglement[150], scattering processes are used to produce entangled quantum states. Precision measurements with atom interferometers[2], on the other hand, require detailed information on atomic interactions to avoid systematic sources of uncertainty. In a combination of these two fields, low energy collisions have been shown to be useful for producing entangled (squeezed)[118]states for precision measurements[31, 32]. Regarding coherent matter waves and atom lasers, interactions in ultracold bosonic systems have been used to study four-wave mixing of matter waves_[151, 152_]and to demonstrate matter wave amplification[153]. Finally, the mere process of forming Bose-Einstein condensates relies on Bose-enhanced scattering[75, 76], and understanding this process inherently requires the knowledge of atomic scattering properties. The above examples are only a few in many and strongly underline the importance of a detailed understanding of atomic potentials.

A well established method to study atomic potentials is using fast atomic and molecular beams derived from supersonic nozzle expansions. These techniques have found widespread use in physics and physical chemistry to determine important properties such as molecular potential surfaces. In such experiments, two beams collide and scatter inside a vacuum chamber. Analyses of the angular distribution of scattering events are used to infer the potentials describing the interaction between the collision partners[154]. This information is a basic input into many calculations in quantum chemistry. Similarly, fast atomic beams are widely used in surface science to measure properties such as the surface geometry of adsorbates, underlying surface crystal structures and the density of states of surface phonons. In these experiments, a fast beam strikes the surface and is scattered. The angular distribution and energy of the scattered atoms is analysed and the desired surface property is extracted [155, 156, 157]. It is an intriguing idea to explore a Bose-condensed atomic sample in the form of an atom laser for analogous applications at very low collision energies. On the one hand, such implementations are not likely to compete with thermal beam devices on a quantitative level in the near future. An atom laser generally has a lower average flux and requires more complex construction efforts than a typical thermal source. The maximum collision energies in an experiment like this are limited by the spatial extent of the vacuum chamber and the fact that the collision energies involved in most cases need to be gained from acceleration under gravity. On the other hand, it is a very interesting challenge to explore the viability

110 Chapter 6. Probing atomic potentials with Bose-condensed sources of Bose-condensed sources for applications in surface science and scattering measurements on a fundamental level. As discussed in chapter 2, the atom laser offers the advantage of an atomic beam with a small transverse position and momentum spread, allowing amongst others for a better spatial detection resolution. Compared to measurements involving bulk gases or solid state crystals, freely propagating atomic beams are in an isolated and controllable measurement environment. The internal atomic state can usually be well controlled, and the comparatively low atomic densities allow for an unperturbed determination of two-body interactions, which in turn can form the basis for more complicated many-body interaction measurements at higher densities. Contrary to freely propagating atomic beams, the high densities that can be reached in trapped Bose-condensed samples allow for measurements of such many-body interactions. Three-body interactions in Bose-Einstein condensates are an important process that has been shown to lead to the formation of exotic Efimov states[158] and enhanced loss from the trapped atomic sample[159].

This chapter presents results on the investigation of atomic potentials with Bose-condensed sources, which were achieved as part of this thesis. In the first part, we will give an introduction to the characterisation of atomic interactions via scattering lengths and present an approximate method to calculate the scattering length between two arbitrary states from the singlet and triplet scattering lengths. This section is meant to provide the reader with a basic understanding of scattering lengths and how different scattering length classifications relate to more specific problems. The second part contains results on an atom laser scattering experiment, as a more detailed description of the work in [160]. In essence, an atom laser is used to probe via collision the mean field potential of a target Bose-Einstein condensate. We measure thes-wave scattering length describing the interaction between the_|f =2,mf =0〉and|f =1,mf =−1〉 hyperfine ground states of87Rb . Unlike recent experiments studying the scattering properties of two colliding condensates in the same [161, 162] or in different [163] internal states, we investigate scattering in an energy regime where it is only necessary to considers-wave collisions. The probing atom laser is in the |f ₌ 2,m_{f =} 0〉 state, which is to first order magnetically insensitive and therefore reduces the impact of unstable magnetic fields on the measurement. Finally, we shall present results on a measurement of three-body loss in85_Rb

that were achieved in close collaboration with Paul Altin. Unlike the well-understood two-body processes described above, three-body interaction parameters have not been determined to the same level of accuracy so far. The measurement described addresses the loss in a85_Rb

Bose-Einstein condensate at two different scattering lengths and allows us to extract an upper bound on the three-body loss parameterK₃.

6.1 Characterisation of atomic interactions

The outcome of an elastic collision between two atoms is determined by the two-body molecular potential describing the interaction between the colliding partners. Such potentials can be of enormous complexity and cannot be calculated from first principles in a straightforward way. In the limit of low energies, however, a two-body collision is characterised by a single parameter — the phaseδaccumulated during the collision. This phase can in turn be expressed in terms

of the scattering length a, yielding a convenient and energy-independent parametrisation of two-body collisions in the low-energy limit. Precise measurements ofs-wave scattering lengths in alkali atoms have been conducted using, e.g., Raman[164]and photoassociative spectroscopy[165]. For87Rb, such measurements have been accomplished in a highly accurate way; the present uncertainty in thes-wave scattering lengths is of the order of 0.1 %[166]. However, these methods are based on a refined knowledge of the molecular potentials (see

6.1 Characterisation of atomic interactions 111

[161]), as opposed to the straightforward scattering length measurement that will be presented in section 6.2.