One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.
One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.
One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.
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.
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.
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.
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.
In this dissertation we make use of the many analogies between quantum optical and ultra-cold atomic and molecular systems in order to study the coherence properties of the latter with methods of non-linear optics. We adapt the XFROG method that has first been developed for the characterization of ultra-short laser pulses, to the problem of reconstructing both amplitude and phase of the condensate wavefunction of a Bose-Einstein-condensate (BEC). Using the example of a vortex state we study the dependence of the reconstruction quality on the number of measurements and different sources of noise and we find that the method is feasible with available experimental technology. Exploiting the similarity between the coherent formation of ultra-cold molecules and optical sum frequency generation we devise a scheme for measuring second-order correlations of atoms through density measurements of molecules. We use perturbation theory in the cases of weak and strong coupling between atoms and molecules to calculate the momentum distribution of the molecules for the cases where the molecules are formed from a BEC, a normal Fermi gas and a Fermi gas with superfluidity in a Bardeen-Cooper-Schrieffer (BCS) state. These calculations are supplemented by exact integrations of Schroedinger's equation in the single mode approximation for the molecules. Atoms in a BEC are collectively transformed into molecules with a narrow momentum distribution reflecting the long coherence length of atoms in the BEC. For the normal Fermi gas molecules are formed non-collectively and their momentum distribution is much wider. The momentum distribution of molecules from a BCS state looks similar to the BEC case: The superfluid component leads to collectively formed molecules with a very narrow momentum distribution and the unpaired fraction gives rise to non-collectively formed molecules with a much wider momentum distribution similar to the normal Fermi gas case. The counting statistics of the molecules from a BEC is that of a coherent state, from a normal Fermi gas it is that of a thermal state and the BCS case interpolates between the two.