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.
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 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.
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.
In recent years, ultracold atomic gases have been used as tools to study strongly-correlated systems reminiscent of interesting systems from solid-state physics. At temperatures just above absolute zero, particles with integer quantum spin ("bosons") begin to congregate in the ground state of the trapping potential. As the temperature of the system falls below a critical temperature Tc (in this experiment near 200 nK) it undergoes a phase transition called Bose-Einstein condensation. A Bose-Einstein condensate is often described as a macroscopic quantum body, and due to its phase coherence (analogous to an "atom laser") can be used to simulate solid-state systems in a periodic potential called an optical lattice, which resembles that experienced by electrons in the periodic Coulomb potential of a solid-state crystal lattice. These optical lattices are formed by the interference pattern of multiple laser beams, and the associated spatially-dependent Stark shift, resulting in trapping potential for the BEC. The lattice analogs of simple atomic structures have been widely studied. In this thesis, we study the possibility of loading a BEC into multi-dimensional optical lattices. The crystallography of four-beam three-dimensional optical lattices is investigated, and an apparatus is constructed to produce two- to four-beam lattice geometries. We study the structure of the lattice through the technique of Kapitza-Dirac scattering.
Cold atoms trapped in optical lattices (crystals of light) provide a pristine platform for exploring quantum many body physics. Motivated by several recent experiments, this thesis examines the equilibrium and non-equilibrium dynamics of a Bose-Einstein condensate (BEC) loaded in a low dimensional optical lattice in order to realize novel quantum phases. There are two main research directions in this thesis. The first one involves the possibility that exotic order spontaneously forms when two-component bosons are trapped in a honeycomb lattice. My studies on this theme is motivated by the observation of a “twisted superfluid” state in Prof. Klaus Sengstock’s group at Hamburg (Soltan-Panahi et al., Nat. Phys. 8, 71 (2012)). A twisted superfluid involves Bose-Einstein condensation into a state whose order parameter has a spatially varying phase. In chapter 3, I study the stability of a Bose-Einstein condensate towards forming a twisted superfluid within the framework of mean field theory. Despite a exhaustive numerical search I do not find a parameter regime with a twisted superfluid. This search involved all experimentally relevant parameter regimes and therefore mean field theory predicted that the experimentalists should not observe a twisted superfluid. I conclude that the experimental observations were either a manifestation of counter superfluidity or due to interactions during time-of-flight. Subsequent experiments showed that the observations were an artifact of the measurement process. The second research direction in this thesis is an exploration of the stability of periodically driven quantum systems (also known as Floquet systems). Floquet systems can be used to realize exotic non-equilibrium quantum phases which do not have a counterpart in static systems. However, the driving can cause these systems to heat up which presents a major obstacle to creating exotic states. To explore this issue in a concrete example, I model an experiment (Parker, Ha, and Chin, Nat. Phys. 9, 769 (2013)) where a Bose-Einstein condensate loaded in an optical lattice is subjected to periodic shaking. I investigate the stability of this Floquet BEC to interactions. This research direction consists of 3 studies. In chapter 4, I first do this analysis for a purely one-dimensional system and identify a large parameter regime where the BEC is stable. In the next two chapters, I go beyond 1D and consider the role of transverse degrees of freedom. This is because the shaken lattice experiments that I model involves a 1D array of pancakes. I find that this geometry leads to much more dissipation than a purely 1D system. This extra dissipation arises because interactions can transfer energy between different directions. In chapter 5, I consider the extreme case where there is no transverse confinement. I find that in the absence of transverse confinement, a one-dimensional Floquet BEC is generically unstable. Finally, in chapter 6, I consider harmonic transverse confinement modeling the crossover between chapters 4 and 5. I find that as the transverse confinement is made stronger, the atom loss rate initially increases, but beyond a critical transverse confinement, the atom loss disappears due to unavailability of phase space for scattering. I also predict that if the transverse confinement is tuned to the vicinity of certain magic values, the heating rate exhibits a sharp drop. I perform similar analyses for a shaken square lattice and find that generically a low-dimensional Floquet BEC can be stabilized by suitably designing the transverse confinement.
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.