Atom trapping on chip opens new perspectives for time and frequency metrology and integrated atom interferometry. The TACC experiment (Trapped Atomic Clock on a Chip) was built to study the potential of degenerate and non-degenerate quantum gases for metrology and to develop new tools for atom manipulation. One of the aims is the demonstration of a secondary frequency standard with a stability of a few 10-13 at one second. This is the context of this thesis. We report on several metrology experiments carried out with thermal clouds or Bose-Einstein condensates. Firstly, we demonstrate a stability of 5.8 x 10-13 at one second and characterize the limiting technical noise. We then present a study of the coherence of Bose- Einstein condensates and, in particular, the eect of interactions. The data is compared with a numerical model. Secondly, we introduce several tools for producing and manipulating atoms on a chip. We show the realization of an atomic microwave powermeter and assess the current limits of its performance. We then demonstrate that high-gradient microwave elds allow one to coherently manipulate the atoms' external motion. Finally, we present and characterize a new device for high-repetition rate atom loading involving fast modulation of the rubidium pressure.
Atom trapping on chip opens new perspectives for time and frequency metrology and integrated atom interferometry. The TACC experiment (Trapped Atomic Clock on a Chip) was built to study the potential of degenerate and non-degenerate quantum gases for metrology and to develop new tools for atom manipulation. One of the aims is the demonstration of a secondary frequency standard with a stability of a few 10-13 at one second. This is the context of this thesis. We report on several metrology experiments carried out with thermal clouds or Bose-Einstein condensates. Firstly, we demonstrate a stability of 5.8 x 10-13 at one second and characterize the limiting technical noise. We then present a study of the coherence of Bose- Einstein condensates and, in particular, the eect of interactions. The data is compared with a numerical model. Secondly, we introduce several tools for producing and manipulating atoms on a chip. We show the realization of an atomic microwave powermeter and assess the current limits of its performance. We then demonstrate that high-gradient microwave elds allow one to coherently manipulate the atoms' external motion. Finally, we present and characterize a new device for high-repetition rate atom loading involving fast modulation of the rubidium pressure.
Ultracold atomic gases have proven to be an excellent tool for research in quantum systems. A Bose gas can be trapped on an atom chip using very well defined and tunable spatially-dependent potentials. The proximity of the atoms to the chip permits the use of low currents allowing for highly accurate temporal changes. Excellent experimental apparatus is needed to achieve Bose-Einstein condensation with a sufficient atom number to study low-dimensional physics. The setup described in this document utilises a set of current-carrying structures on top of which an atom chip sits. For improved atom loading rate, a two-dimensional loading stage was added, extending the lifetime of the magnetic trap. From this loading stage to the atom chip, Bose-Einstein condensation of 105 Rubidium-87 atoms was achieved in less than 30 s, allowing for a large rate of experimental cycles. The high spatial and temporal tunability of this setup results in the ability to split the atomic cloud and quench the trapping potential geometry. Maximising the ratio between trapping frequencies for different spatial directions leads to the system presenting features of a one-dimensional gas. Manipulating the coherence dynamics of a one-dimensional Bose-Einstein condensate creates fluctuations in the phase properties of the wavefunction. These fluctuations are observed as atom density perturbations after releasing the trapping potentials, and are a tool for temperature measurements. When the cloud of atoms is positioned at a few tens of micrometres from the surface of the atom chip, corrugations in the microstructures of the chip affect the trapping potentials at very low temperatures 1 µK. This effect is simulated and quantified in the thesis, with the aim of improving future setups. Additionally, the effect is explored for microscopy purposes. The behaviour of a Bose-Einstein condensate, especially the expansion rate, has long been studied. In this thesis, the Gross-Pitaevskii Equation is introduced, finding its numerical solutions to the two-dimensional and three-dimensional forms, using the Split-Step Fourier Method. The results show very good agreement with the experimental results, as well as with other well- established theories of condensates. The creation of such a toolbox opens up the opportunity to further investigate the coherence dynamics of low-dimensional systems.
Atom chips are an excellent tool for studying ultracold degenerate quantum gases, due to the high degree of controllability afforded by the precise potentials generated from the current-carrying microfabricated wires on the chip surface. The geometries of the trapping potentials are inherently capable of realising extreme aspect ratios, and therefore creating model systems with effectively reduced dimensionality, particularly the theoretically-tractable one-dimensional Bose gas. In addition, the temporal tunability makes it possible to impart non-adiabatic changes on the trapping potentials, allowing experimental investigation of samples which have been brought out of equilibrium - a situation which is not fully theoretically understood. This thesis describes the implementation, development and characterisation of an experimental system for producing the first Bose-Einstein condensates of atomic rubidium 87 gas trapped on the surface of an atom chip in Nottingham. Such an apparatus is very complex and requires careful characterisation in order to run in a stable and reliable way. Details of the experimental setup are thoroughly outlined, including the vacuum system, lasers, electronics, computer control and timing, and the optical imaging system. A newly installed compact two-dimensional magneto-optical trap provides an loading rate of 5e7 atoms per second for loading a three-dimensional mirror-magneto-optical trap with 1.5e8 atoms, at a temperature of 300uK within 10s. The cloud is then sub-Doppler cooled to 50uK, and spin-polarised with 96% purity into the |F=2,mF=+2> ground state within 5ms, in preparation for loading a purely magnetic trap. A millimeter sized copper Z-shaped conductor located beneath the atom chip surface creates a Ioffe-Pritchard magnetic trap, into which the laser cooled cloud is loaded with 70% efficiency, and can be held with a vacuum-limited lifetime of 40s. Evaporative cooling then pre-cools the sample to below 20uK within 10s, to allow the subsequent loading into potentials created by the atom chip with 100% efficiency. A final evaporation stage then cools the cloud below the phase transition temperature of 800nK, resulting finally in pure BECs with 105 atoms confined using the atom chip. Key measurements of various properties of the trapped condensates are presented, which are important in order to characterise the system fully, and to compare with theoretical expectations. In particular, included are the variation of condensate fraction with temperature, the BEC expansion dynamics, and the condensate lifetime in the trap, for example. Finally, it is demonstrated how BECs can be produced on the atom chip without the use of external macroscopic coils, achieved by using novel, integrated sheet structures located beneath the chip surface - unique to this experimental system - to create the necessary bias fields.
The controlled generation of entanglement forms the basis for currently emerging ‘quantum technologies’, such as quantum simulation, computation, and metrology. In the field of quantum metrology, multi-particle entangled states, such as spin-squeezed states, are investigated as a means to improve measurement precision beyond the ‘standard quantum limit’. This limit arises from the quantum noise inherent in measurements on a finite number of uncorrelated particles and limits today’s best atomic clocks. Atom chips combine exquisite coherent control of ultracold atoms with a compact and robust setup, suggesting their use for quantum metrology with portable atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. In this thesis, I present experiments where we generate for the first time multi-particle entanglement on an atom chip. We achieve this by controlling elastic collisional interactions with a state-dependent potential. We employ this novel technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are a useful resource for quantum metrology, as they could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. The state-dependent potential is created with the help of a coplanar microwave guide, which is integrated on our atom chip. In the vicinity of this waveguide a microwave nearfield is formed. When a Bose-Einstein condensate of 87Rb is brought into this near-field, the hyperfine energy levels of the atoms are shifted differentially due to the AC Zeeman effect. The strong gradients in the field can be used to state-selectively shift the minimum of a static magnetic atom trap and thus coherently split an ensemble of atoms which have been prepared in a superposition of two internal states. During this process, nonlinear atomic interactions lead to the formation of a spinsqueezed state. I tomographically analyze the produced state, reconstruct its Wigner function, and deduce that it is at least four-particle entangled. I compare our results with a dynamical multi-mode simulation which takes not only the atomic motion and internal state dynamics but also particle losses into account and find good agreement. Moreover, I use this comparison to identify technical noise sources in our experiment, which currently limit the achieved amount of squeezing, and make suggestions on how to eliminate them in future experiments. Our method can in principle create a very large amount of squeezing and entanglement and is applicable to a wide variety of atomic systems, in particular to those for which no convenient Feshbach resonance exists. We envisage the implementation of this technique in portable atomic clocks and interferometers operating beyond the standard quantum limit. Furthermore, it is a valuable tool for experiments on many-body quantum physics and could enable quantum information processing on atom chips.
The spectacular progress in the field of ultracold quantum gases is intimately connected with the availability of sophisticated techniques for quantum-level control of internal states, motional states, and collisional interactions. Atom chips provide such control in compact, robust, and scalable setups, which makes them attractive for both applications and fundamental studies. In this thesis I report on experiments that use a new method for coherent manipulation of ultracold atoms. The method is based on microwave near-fields, provided by a waveguide structure that is fully integrated on an atom chip. We generate microwave near-field potentials that combine the versatility of optical traps with the robustness and tailorability of static magnetic microtraps. These potentials depend on the internal atomic state, and we use them for state-selective splitting of Rb Bose-Einstein condensates. We show for the first time combined coherent manipulation of internal and motional states on an atom chip, realizing a trapped-atom interferometer with internal state labeling of the interferometer paths. Moreover, we use microwave near-field potentials for the preparation of spin-squeezed states for quantum-enhanced metrology through controlling state-dependent collisional interactions. In addition, very promising proposals exist for the implementation of a quantum phase gate using these potentials. Measuring microwave fields is important for engineering of microwave devices as well as in science, e.g. to characterize the field homogeneity in the interaction regions of an atomic clock. We develop a novel technique that uses clouds of uncondensed ultracold atoms as sensitive, tunable and non-invasive probes for microwave field imaging with micrometer spatial resolution. The microwave magnetic field components drive Rabi oscillations on atomic hyperfine transitions whose frequency can be tuned with a static magnetic field. Readout is accomplished using state-selective absorption imaging. Quantitative data extraction is simple and it is possible to reconstruct the amplitudes and phases of the different microwave magnetic field components. While we demonstrate 2D imaging, an extension to 3D imaging is straightforward. We use the method to determine the microwave near-field distribution around the on-chip waveguide and reconstruct the corresponding current distribution. For our experimental parameters, the method provides a microwave magnetic field sensitivity of 0.2 mG, which can even be improved further with variants discussed. The experiments presented in this thesis open the path for the realization of portable quantum-enhanced interferometer devices, the implementation of a quantum phase gate as well as for a new generation of microwave field sensors.
Summary form only given. Atom chips [1] have shown to be very successful for trapping and manipulating cold atoms. Atom interferometry in the vicinity of an atom chip has been recently achieved by coherently splitting a Bose-Einstein condensate with radiofrequency [2] and microwave [3] dressing. However, some limitations on the precision of the phase measurement occur in this case due to the phase diffusion process resulting from mean field interactions in the Bose-Einstein condensate.In this communication, we will discuss the possibility of using a thermal (i.e. non-condensed) ensemble of ultra-cold atoms trapped on an atom chip in order to create a trapped-atom interferometer with much weaker atomic interactions. In such a scheme (which can be seen as the atomic equivalent of a white light interferometer in optics), the coherence time will strongly depend on the level of symmetry that can be achieved between the potentials forming the two arms of the interferometer. For example, in a simple model of two harmonic potentials, it can be shown that a slight relative frequency difference Δω/ω can be associated with a limitation on the coherence time T given by the following expression: T≈ 2π1ίω kΘ Δω where Θ is the temperature of the atomic ensemble and k the Boltzmann constant (the latter expression being valid only for kΘ >> ! ω). For example, a relative asymmetry of 10-3 will result, for a temperature of about 1μK, to a limitation on the coherence time of 40ms, which favourably compares to what has been achieved experimentally with Bose-Einstein condensates [2]. We will then discuss how we plan to achieve, with the on-going experiment at Thales TRT [4], a splitting of the atomic cloud with the highest possible level of symmetry. The basic idea is to use internal state labelling on the so-called “clock states” of the 87Rb atom and microwave dressing [3] with two independent coplanar waveguides, each waveguide being preferentially resonant with one of the two internal states involved in the process. This way, we expect to have quasi-independent control over the two arms of the interferometer and thus to be able to achieve a coherent splitting as much symmetrical as possible.We will finally discuss the potential applications of this technique in terms of acceleration and gravity measurement with cold atoms on a chip, which could be of great interest in the future if combined, for example, with high bandwidth microelectromechanical sensors.
The thermal motion of atoms often imposes limitations on the precision and accuracy of measurements involving those atoms. Atomic beam cesium clocks are one outstanding example, where the typical thermal velocity of the cesium atoms, on the order of 200 m/s, limits the observation time to a few milliseconds in a typical apparatus. This finite observation time results in a linewidth for the microwave resonance whose frequency defines the unit of time. Other motional effects include first- and second-order Doppler effects whose presence limits the performance of such clocks. Because conventional refrigeration would result in the condensation of cesium or other atoms into a solid, researchers sought other means of reducing the thermal motion, a quest that led to laser cooling and electromagnetic manipulation of neutral atoms. Similar techniques have been developed for trapped ions and used in metrological applications, but these are not treated here.