This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.
This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.
I have been one of the main responsible for building a new laboratory for Bose-Einstein condensation with 87Rb. In particular, the experimental setup has been designed for performing experiments with Bose-Einstein condensates load into optical lattices of variable geometries. All parts essential for Bose-Einstein condensation are in place. Atoms are collected in a magneto-optical trap, transferred to another vacuum chamber, with better vacuum, and trapped in another magneto-optical trap. Atoms are successfully transferred to a dark magnetic trap, and system for diagnostics with absorption imaging has been realized. We have not yet been able to form a Bose-Einstein condensate, due to a range of technical difficulties. Equipment for alignment of optical lattices with flexible geometry has been designed, built, and tested. This tool has been proven to work as desired, and there is a great potential for a range of unique experiments with Bose-Einstein condensates in optical lattices of various geometries, including superlattices and quasi-periodic lattices. Numerical studies have been made on anisotropic optical lattices, and the existence of a transition between a 2D superfluid phase and a 1D Mott-insulating phase has been confirmed. We have shown that the transition is of Berezinskii-Kosterlitz-Thouless type. In another numerical study it has been shown that using stimulated Raman transitions is a practical method for transferring atoms between states in a double optical lattice. Thus, it will be possible to transfer populations between the lattices, with further applications in qubit read/write operations.
Since the experimental achievement of Bose-Einstein condensation (BEC) in dilute gases, ultra-cold atom systems have proven to be an unparalleled test bed for condensed matter phenomena. With this in mind, our laboratory set out to build an apparatus for the study of the effects of disorder on condensed matter phase transitions using a BEC loaded into one, two, and three-dimensional lattices. My thesis is divided into two main sections. In the first section I describe in detail the design and construction of our apparatus. Our system is designed to form <super>87<\super>Rb condensates of approximately 10<super>5<\super> atoms. We have three possible experimental science chambers. 1. One can perform 1D lattice experiments in the chamber where the condensate is formed. There is a mirror located in vacuum, which is suitable for this purpose. 2. In a glass chamber one can do 1D, 2D, or 3D lattice experiments. Atoms are loaded into a dipole trap (optical tweezer) prior to condensation and transported approximately 20 cm to the glass cell where optical evaporation is performed to form a BEC. 3. One can transfer, using the same techniques as (2), to a chamber with a multi-channel plate detector for Rydberg atom experiments. The experimental results described in my thesis pertain to situation (1). However, I describe some details of (2) in the construction section. The first experiment presented in my thesis demonstrates the effect of disorder on the time-dependent dynamics of lattice systems. We observe that a small perturbation produces a dramatic change in the adiabaticity criteria for loading a BEC into one-dimensional optical lattice. I conclude with experiments that we expect to perform on this apparatus.
This thesis is primarily a comprehensive discussion of the development of two experimental studies: the quantum transport and effects of heating of ultracold atoms. It specifically provides details of the manipulation and control of ultracold atoms in magnetic waveguides, optical lattices, and optical billiards. The design, construction, and implementation of experimental apparati are also outlined and additional experimental tests are summarized, including the realization of a macroscopic transport (> 20 cm) system for ultracold atoms and transmission of ultracold atoms through a random optical potential. The first experiment is a study of the quantum transport for atoms confined in a periodic potential. These results include a comparison made of thermal and BEC initial conditions. Here, observation of ballistic transport is made for all values of well depth and initial conditions, and the expansion rates for thermal atoms are shown to be in excellent agreement with a singleparticle model. For weak wells (V0/ER ≤ 6), the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature model based on single (non-interacting) particle theory. For deep wells (V0/ER ≥ 6), a crossover is observed to a new regime for the BEC case, indicating the importance of interactions on quantum transport. The second experiment is a study of the effect of different heating rates on a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the BoseEinstein condensate fraction and an exponential decay in phase space density.
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 long term aim of the work is to study non-equilibrium and symmetry-breaking phenomena for a Bose-Einstein condensate in time-dependent optical traps. The work presented in this thesis is mostly devoted to the design, construction and testing of the apparatus, in which condensation was successfully achieved. The first part of this thesis describes the design and construction of a hybrid setup for the production of a Bose-Einstein condensate (BEC) of 87 Rb in the |F = 2, m F = +2 > state. The vacuum system is composed of a first chamber, where a low-velocity intense source (LVIS) of atoms is produced to provide a pre-cooled atomic beam to the science chamber, where the magneto-optical trap (MOT) is produced, trapping more than 3 x 10 8 atoms at a temperature of roughly 400 μK. Forced radio- frequency evaporation is performed in a quadrupole magnetic trap and the atoms are transferred to a hybrid far-detuned optical trap in a crossed-beams configuration; evaporation in the optical potential leads to reliable production of a BEC every 50 s, composed of 10^5 atoms at a temperature of 10-30 nK. To ensure fine control on the optical potential depth and high intensity and pointing stability, a stabilisation system has been developed and characterised. The second part of this thesis describes the realisation of a 1D optical lattice, produced by two phase-locked laser beams emitting at 780 nm, with a red detuning of approximately 3.5 GHz, in counter-propagating configuration. Oscillating forces obtained by phase-modulating the optical potential are applied.
I have been one of the main responsible for building a new laboratory for Bose-Einstein condensation with 87Rb. In particular, the experimental setup has been designed for performing experiments with Bose-Einstein condensates load into optical lattices of variable geometries. All parts essential for Bose-Einstein condensation are in place. Atoms are collected in a magneto-optical trap, transferred to another vacuum chamber, with better vacuum, and trapped in another magneto-optical trap. Atoms are successfully transferred to a dark magnetic trap, and system for diagnostics with absorption imaging has been realized. We have not yet been able to form a Bose-Einstein condensate, due to a range of technical difficulties. Equipment for alignment of optical lattices with flexible geometry has been designed, built, and tested. This tool has been proven to work as desired, and there is a great potential for a range of unique experiments with Bose-Einstein condensates in optical lattices of various geometries, including superlattices and quasi-periodic lattices. Numerical studies have been made on anisotropic optical lattices, and the existence of a transition between a 2D superfluid phase and a 1D Mott-insulating phase has been confirmed. We have shown that the transition is of Berezinskii-Kosterlitz-Thouless type. In another numerical study it has been shown that using stimulated Raman transitions is a practical method for transferring atoms between states in a double optical lattice. Thus, it will be possible to transfer populations between the lattices, with further applications in qubit read/write operations.