Cold atoms on chips constitute a fascinating and non-trivial physical system. A gas of atoms can be cooled and trapped in a configuration in which one or more of the dimensions is so tightly confined, that they are "frozen out" leaving a one or two dimensional gas. Such a gas exhibits a rich variety of behavior depending on the interplay between the thermal energy of the atoms and their mutual interactions [1]. At very low temperature, a very dilute gas becomes strongly correlated entering the so-called Tonks-Girardeau regime, while at high density the gas behaves as a quasi-condensate whose density resembles that of a true condensate but whose phase fluctuates. At higher temperatures the gas can behave like an ideal bose gas, or enter a "quantum decoherent" regime in which the gas is strongly degenerate, but in which density fluctuations are large. I will discuss experiments investigating some of these regimes using direct measurements of density fluctuations in a gas on an atom chip. The measurement techniques are closely related to several other correlation techniques introduced recently in the field of cold atoms. These techniques are developing rapidly and I will comment on some of them. [1] K. Kheruntsyan, D. Gangardt, P. Drummond, G. Shlyapnikov, Phys. Rev. A 71, 053615 (2005).
Cold atoms on chips constitute a fascinating and non-trivial physical system. A gas of atoms can be cooled and trapped in a configuration in which one or more of the dimensions is so tightly confined, that they are "frozen out" leaving a one or two dimensional gas. Such a gas exhibits a rich variety of behavior depending on the interplay between the thermal energy of the atoms and their mutual interactions [1]. At very low temperature, a very dilute gas becomes strongly correlated entering the so-called Tonks-Girardeau regime, while at high density the gas behaves as a quasi-condensate whose density resembles that of a true condensate but whose phase fluctuates. At higher temperatures the gas can behave like an ideal bose gas, or enter a "quantum decoherent" regime in which the gas is strongly degenerate, but in which density fluctuations are large. I will discuss experiments investigating some of these regimes using direct measurements of density fluctuations in a gas on an atom chip. The measurement techniques are closely related to several other correlation techniques introduced recently in the field of cold atoms. These techniques are developing rapidly and I will comment on some of them. [1] K. Kheruntsyan, D. Gangardt, P. Drummond, G. Shlyapnikov, Phys. Rev. A 71, 053615 (2005).
We report on progress for a couple of experiments on manipulating cold atoms on a chip for quantum sensing. The first experiments are directed towards developing a compact atom interferometer on an atom chip using a double-well potential. The interferometer uses 87Rb atoms magnetically confined in an atomic waveguide produced by wires on the surface of a lithographically patterned chip. Finite element modeling of combinations of different current configurations with various external bias fields indicated a means of coherently splitting the atomic cloud through dynamically adjusting the currents and bias fields. In these experiments we investigate real-time transformations between different double-well configurations adiabatically and non-adiabatically, and study their effects on the initially trapped atoms. Coherence properties of the two atomic wavepackets are examined. In another set of experiments we investigate the properties of bosons confined to (quasi) one dimension in our magnetic waveguide. When the atom-atom repulsive interaction becomes much larger than the kinetic energy, bosons confined in one dimension can enter a new state of matter, the Tonks-Girardeau gas, in which they behave like non-interacting fermions. However, the bosons can still occupy the same momentum state and therefore the gas cannot be fully described by either Bose-Einstein or Fermi-Dirac statistics. This transition has been observed in optical lattices but not in magnetic atom chip waveguides. We discuss the conditions for obtaining a Tonks-Girardeau gas with 87Rb atoms in our atom chip waveguide as well as a novel signature for observing the transition in our system.
We discuss the use of microfabricated magnetic traps, or "chip traps," to study quasi-one-dimensional quantum gases. In particular, we discuss the feasibility of studying the Tonks-Girardeau limit, in which the gas is strongly interacting. We review the scaling of the oscillation frequencies of a chip trap, and show that it seems feasible to attain a Tonks-Girardeau parameter as large as 200. The primary difficulty of this approach is detection, since the strongly interacting limit occurs for low densities. We propose a way to "freeze" the distribution, and then measure it with a single-atom detector. This method can also be applied to optical dipole traps.
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.
Bosonic atoms confined in optical lattices are described by the Bose-Hubbard model and can exist in two different phases, Mott insulator or superfluid, depending on the strength of the system parameters. In the vicinity of the phase boundary, there are degeneracies that occur between every two adjacent Mott lobes. Because of this, nondegenerate perturbation theory fails to give meaningful results for the condensate density: it predicts a phase transition in a point of the phase diagram where no transition occurs. Motivated by this, we develop two different degenerate perturbative methods to solve the degeneracy-related problems. Moreover, we study the one-dimensional repulsively interacting Bose gas under harmonic confinement, with special attention to the asymptotic behavior of the momentum distribution, which is a universal k−4 decay characterized by the Tan's contact. The latter constitutes a direct signature of the short-range correlations in such an interacting system and provides valuable insights about the role of the interparticle interactions. We investigate the system constituted of N interacting particles in the strongly interacting limit. In such a regime, the strong interparticle interaction makes the bosons behave similarly to the ideal Fermi gas. Because of the difficulty in analytically solving the system for N particles at finite interaction, the Tonks-Girardeau regime provides a favorable scenario to probe the contact. Therefore, we are able to provide an analytical formula for the Tan's contact. Furthermore, we analyze the scaling properties of the Tan's contact in terms of N in the high-temperature regime as well as in the strongly interacting regime. Finally, we compare our analytical calculations of the Tan's contact to quantum Monte Carlo simulations and discuss some fundamental differences between the canonical and the grand-canonical ensembles.
Since the achievement of Bose-Einstein condensation (BEC), the progress in matterwave \nphysics has been immense. Among the many recent achievements there is \nthe miniaturization of atom traps, demonstration of the superfluid-Mott insulator \nquantum-phase transition in optical lattices and the experimental demonstration of \nthe BEC-BCS crossover in ultra-cold gases. \nMiniaturization of atom traps using micro-structured wires on a chip is one important \nstep towards an on-chip cold-atom device. These so-called \\atom chips" provide \nhigh control and versatility for trapping and guiding the ultra-cold atomic clouds. \nParticularly interesting is the use of these microchips to build mesoscopic devices \nfor cold atomic clouds as, for instance, in the case of an atom-cloud interferometer. \nHowever, these mesoscopic devices require coherent transport of the atom cloud. A \ngeneral method to treat decoherence due to current fluctuations in multi-wire atomchip \ntraps is presented in the rst part of this thesis. The decoherence rate Γ shows a \nstrong dependence on the distance between the wire and the atom cloud, r0, scaling \nas Γ ~ r-4 0 for a single atom waveguide. Considering an interferometer device, a \nstrong dependence of the decoherence rate on the trap geometry is found. \n \nStudying many-body eects in ultra-cold quantum gases is another important \nresearch eld. Experiments using ultra-cold quantum gases in optical lattices have \ndemonstrated the superuid-Mott insulator quantum phase transition and manybody \nentanglement. Optical lattices are based on a periodic modulation of the light \nintensity, generated by retro-reected laser beams. Correlations of the atomic cloud \nbetween dierent lattice sites of the optical lattice play a central role in these manybody \nexperiments. The dierent phases of the superuid-Mott insulator system can \nbe characterized by the dierent behavior of the inter-lattice site correlations. There \nare several numerical methods such as Quantum Monte Carlo (QMC) simulations, \nDensity Matrix Renormalization Group (DMRG) simulations, exact-diagonalization, \nor the Gutzwiller ansatz, to investigate the dynamics of an ultra-cold gas in an optical \nlattice theoretically. The Gutzwiller method, corresponding to the mean-eld solution, \nallows for the treatment of large lattice sizes. Mean-eld approaches have proven \nto be very useful to describe many-body physics. However, diculties arise in the correct \ndescription of the behavior of the decay of inter-lattice site correlations. Based on \nthe Gutzwiller approach, we have developed a method which allows the successive inclusion \nof inter-lattice site correlations. Comparing the results for the particle-number \nuctuations and the correlation function obtained from pure Gutzwiller calculations, \nto calculations which perturbatively include short-range correlations and calculations \n \nusing \\quasi-exact methods", showed a considerable improvement relative to the pure \nGutzwiller results due to the inclusion of short-range correlations. \nMany-body eects do not only arise in periodic potentials, but become increasingly \nimportant at ultra-low temperatures. The formation of Bose-Einstein condensates \nrequires an overlap of the atom wavefunctions and, hence, the formation of \na single condensate wavefunction. Another example of a many-body state is the \nsuperuid-BCS state, commonly used as a description of superconductivity. Here, \nfermions in dierent hyperne states form Cooper pairs. Experiments with ultracold \nquantum gases enable a variation of the interparticle interaction, e.g. , by using \na Feshbach resonance. Using Feshbach resonances to tune the interaction strength \nhas enabled the experimental observation of the crossover from a superuid-BCS \nstate to a Bose-Einstein condensate of molecules. A useful way to characterize the \ndierent states of ultra-cold quantum gases is to investigate the particle-number uctuations. \nIn this thesis we suggest to divide the atomic cloud into bins and consider \nthe atom-number uctuations in these bins. We calculate the full counting statistics \nfor dierent physical systems of ultra-cold gases (e.g. bosonic gases, fermionic gases, \nand spin mixtures). In particular, we consider the BCS-state as a rst trial example \nto show that there is a strong variation in the particle-number statistics at the \ncrossover from a superuid-BCS state to a Bose-Einstein condensate of molecules.
We report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.