We present here the first measurement of the third-order spatial correlation function for atoms, made possible by cooling a metastable helium cloud to create an ultracold thermal ensemble just above the Bose–Einstein condensation point. The resulting large correlation length well exceeds the spatial resolution limit of the single-atom detection system, and enables extension of our earlier temporal measurements to evaluate the third-order correlation function in the spatial plane of the detector. The enhancement of the spatial third-order correlation function above a value of unity demonstrates the presence of spatial three-atom bunching, as expected for an incoherent source.
We present here the first measurement of the third-order spatial correlation function for atoms, made possible by cooling a metastable helium cloud to create an ultracold thermal ensemble just above the Bose–Einstein condensation point. The resulting large correlation length well exceeds the spatial resolution limit of the single-atom detection system, and enables extension of our earlier temporal measurements to evaluate the third-order correlation function in the spatial plane of the detector. The enhancement of the spatial third-order correlation function above a value of unity demonstrates the presence of spatial three-atom bunching, as expected for an incoherent source.
Here we utilize the single-atom detection capability of metastable helium to measure the second-order and third-order correlation functions for ensembles of ultracold atoms. We then extend these measurements to characterize the quantum statistics of atoms guided in a dipole potential. By appropriately loading atoms into the guide we are able to populate a selected number of guided modes, ranging from the majority of atoms in the lowest order mode (a BEC), to multi-mode guiding (equivalent to a thermal source). The guided BEC was characterised by a smooth gaussian transverse spatial profile, and a second-order correlation value of unity consistent with a coherent source. For multi-mode guiding, the matter-wave equivalent of speckle was observed. Furthermore, at short arrival times, the second-order correlation function was greater than unity, corresponding to atom bunching characteristic of an incoherent (thermal) source.
The field of atom optics has progressed rapidly over the past 20 years since the realisation of Bose-Einstein condensation, such that the wave behaviour of atomic gases is now routinely demonstrated. Furthermore, the study of quantum atom optics, which goes beyond a ‘mean-field’ description of quantum systems to consider the behaviour of single particles, has demonstrated both the similarities between photons and massive species, and their differences as a result of the internal structure and external interactions of atoms. An important class of observable quantities which allow such effects to be measured are nth order correlation functions, which can be interpreted as a result of either particle or wave behaviour. These functions provide a statistical description of fluctuations in n-tuples of particles in a source, which rigorously defines concepts such as coherence. The quantum statistics of a Bose-Einstein condensate should be the same as that for an optical laser, while an ideal thermal Bose gas matches the behaviour of incoherent light. However, correlation measurements can also be used to quantify the influence of interactions, dimensionality, confining potentials and waveguides, and the difference in quantum statistics between fermions and bosons, which illustrates the rich range of behaviour exhibited by atomic gases. In this thesis, several aspects of quantum atom optics are explored with experiments using ultracold metastable helium, a species with the unique advantage of facilitating simple single-atom detection with high resolution, while still allowing Bose-Einstein condensates to be formed. The coherence of atomic systems is shown to be maintained when outcoupled as pulsed atom lasers, and the long-range order characteristic of Bose-Einstein condensates is demonstrated to third order for the first time. Conversely, thermal bunching is observed for a variety of atomic systems, including the measurement of correlation functions up to sixth order with near-ideal interference contrast. These results clearly demonstrate the correspondence between the quantum statistics of photons and atoms as was formalised by Glauber, as well as confirming the validity of applying Wick’s theorem to simplify the statistics of atomic gases. Correlation functions are also shown to be an ideal tool to probe the quantum state of an ultracold gas, and were used to observe the phenomenon of transverse condensation in an elongated Bose gas, as well as characterise the mode occupancy of matter waves guided by an optical potential. Ultracold metastable helium is also suitable for exploring other fundamental topics in quantum optics such particle/wave duality. The notion of complementarity stimulated long running philosophical discussions about how apparently mutually exclusive behaviours can coexist, which culminated in Wheeler devising his famous ‘delayed choice’ gedankenexperiment. A proposed experimental method to realise Wheeler’s experiment with ultracold atoms is discussed, and preliminary measurements presented which indicate that the completion of this experiment could be achieved in the near future. Not only is this of interest in its own right, but the implementation of this experiment has also developed techniques which may enable further studies in quantum atom optics such as investigations of the Hong-Ou-Mandel effect and quantum entanglement with massive particles.
Trapped ultracold gases of metastable helium atoms provide a unique experimental system. The high internal energy enables electronic detection of single atoms. This thesis presents a number of experimental studies using metastable helium. Ionization rates in a mixture of metastable helium and rubidium were measured. Spin polarisation of the system has been shown to result in suppression of Penning ionization of rubidium by metastable helium atoms, suppressed by at least a hundred fold. This demonstration is a promising step towards the first creation of a binary BEC comprising atoms in both ground and excited states. The other experiments presented are mainly concerned with Hanbury Brown-Twiss and Higher order correlations. Single atom detection for metastable helium empowers experimenters to acquire spatial and temporal information, and to obtain full 3D reconstruction for released atomic clouds. Measurements on incoherent boson sources show bunching of particles. This enhancement to probability of joint detection events for two or more particles within short separations is in contrast to the uniform distribution of a coherent state, as measured for a Bose-Einstein condensate or an atom laser. By manipulating correlation length at the detector we were able to demonstrate the first atomic measurement of spatial three-particle correlation, and the results show significant improvement over previously reported values. Furthermore, by using a different trap geometry, it was possible perform measurement of atomic correlation functions to the 6th order, and have observed near ideal correlation functions to the 5th order, demonstrating enhancement for multi-particle detection probability consistent with the prediction of Wick's theorem. Correlations are then exploited to monitor the evolution of coherence property during the formation of a Bose-Einstein condensate. The experimental results are consistent with the existence of a quasi-condensation stage during the system's evolution from an incoherent thermal cloud towards a condensate with long range order. Two cases of mixing processes leading to the production of paired atom beams were Studied. In one case, correlation measurement provided the first higher order test of coherence of amplified matter waves. Coherence properties of matter waves generated via Bose stimulation are critical for active atom optical devices. Previously, coherence properties of amplified matter waves have only been demonstrated to first order by interference fringes. In the second case, a novel mixing process previously unknown was observed. Single atom counting is used to show number difference squeezing between opposite modes. Both processes studied hold potential of providing simple and elegant ways of producing pairs of coherent, sub-Poissonian number difference, and even entangled modes of atomic beams. Finally, physics of lower dimensions was studied. Observation was made of the phenomenon of two-step condensation in a quasi-1D system, where the gas condenses in the tightly confining transverse directions, yet remain thermal in the longitudinal direction. The lack of long-rang coherence of the system is revealed with correlations. Furthermore, an attempt was made to identify the Berezinskii-Kosterlitz-Thouless (BKT) transition.
Trapped gases of ultracold metastable helium atoms are a unique experimental sys- tem. The trapped cloud’s low temperatures, the ability to selectively trap and ma- nipulate individual atomic states and the isolation provided in a vacuum chamber are all conducive to the measurement of precision atomic parameters, such as atomic transition rates. Due to it’s atomic structure helium - the simplest multi-electron atom - is a favourite test-bed for precision QED theoretical calculations compared to experimentally determined parameters. This thesis reports on a number of tran- sition rates measured for the first time with high accuracy, including the first excited metastable state lifetime, found to be 7870(510)s, the longest of any neutral atomic species yet measured. Transition rates from the 23P level to the ground state were also measured for the first time and found to be in excellent agreement with theory. Further cooling of helium produces a Bose-Einstein condensate (BEC), where all atoms are in an identical quantum state, the analogue of an optical laser. One par- ticularly interesting property a BEC posesses is long-range coherence to all orders, meaning all component particles are described by a single wavefunction. While first order coherence is measured in an interference experiment like Young’s double slit, higher order coherence is the ability for correlations to exist between groups of two, three or more particles, quantified by the measurement of correlation functions. Prior to the work in this thesis correlation functions for atoms had only been measured for second order. Here we develop a new technique which we use to show that a BEC is coherent to second and third order to 0.1% accuracy, compared to a thermal cloud which we show is incoherent. At small inter-particle spacings, there is an enhanced probability of measuring double and triple events in the thermal cloud (termed bunching). A drawback of all previous atomic correlation measurements is that the small de-Broglie wavelengths compared to the detector resolution leads to a significant reduction in the measured bunching amplitudes compared to theory. By altering our trapping configuration and temperature we are able to measure a two-particle bunching amplitude which is 88% of the theoretical maximum. This system also allowed the measurement of correlations up to 5th order in thermal gases. The near ideal bunching allowed us to demonstrate perturbations to the correlation functions due to the 1D nature of the system. These advances should lead to correlation measurements being used as a probe to characterise more exotic system properties such as low dimensionality, engineered quantum states and paticle pairing. Finally, a waveguide was created using a dipole laser beam and used to guide atoms in analogy to an optical laser in a fibre. Guided ‘atom lasers’ are likely to be important components for practical devices such as precision sensors. We demonstrate that a guided atom laser has a gaussian profile matching the lowest transverse mode of the waveguide and is first and second order coherent. In contrast guided thermal atoms show matter-wave speckle and are incoherent.
A major advance in understanding the behavior of light was to describe the coherence of a light source by using correlation functions that define the spatio-temporal relationship between pairs and larger groups of photons. Correlations are also a fundamental property of matter. We performed simultaneous measurement of the second- and third-order correlation functions for atoms. Atom bunching in the arrival time for pairs and triplets of thermal atoms just above the Bose-Einstein condensation (BEC) temperature was observed. At lower temperatures, we demonstrated conclusively the long-range coherence of the BEC for correlation functions to third order, which supports the prediction that like coherent light, a BEC possesses long-range coherence to all orders.