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Cold neutral atoms in optical lattices

Rui Zhang

Published Jan 1, 2008• 1 citation
OpenAlex

Abstract

In this thesis, I study the properties of cold neutral atoms, including Bose-Einstein condensates (BEC), inside periodic light-shift potentials created by optical lattices. In the first part, a new optical-lattice scheme, employing Raman transitions, hereafter referred to as a Raman Optical Lattice (ROL), is investigated. This optical lattice possesses a novel sub-Doppler cooling mechanism and a reduced periodicity. Both theoretical and experimental results con¯rm these two characteristics of the ROL. In the second half of the thesis, instead of thermal atoms, optical lattices are loaded with condensate atoms. Our BEC apparatus and the procedure towards forming a BEC are described in detail. After the achievement of the BEC, a 1D far-detuned optical lattice is applied to the BEC. A number of phenomena are observed, including Kapitza-Dirac diffraction, thermal atom interference, atom interferometry, Bloch oscillations, and a superfluid to Mott-insulator transition. Finally a brief discussion about future work is given.

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•Jan 1, 2010•0 citations
In this thesis, I study the properties of cold neutral atoms, including Bose-Einstein condensates (BEC), inside periodic light-shift potentials created by optical lattices. In the first part, a new optical-lattice scheme, employing Raman transitions, hereafter referred to as a Raman Optical Lattice (ROL), is investigated. This optical lattice possesses a novel sub-Doppler cooling mechanism and a reduced periodicity. Both theoretical and experimental results con¯rm these two characteristics of the ROL. In the second half of the thesis, instead of thermal atoms, optical lattices are loaded with condensate atoms. Our BEC apparatus and the procedure towards forming a BEC are described in detail. After the achievement of the BEC, a 1D far-detuned optical lattice is applied to the BEC. A number of phenomena are observed, including Kapitza-Dirac diffraction, thermal atom interference, atom interferometry, Bloch oscillations, and a superfluid to Mott-insulator transition. Finally a brief discussion about future work is given.
Optical lattices are periodic light shift potentials that are created by the interference of several laser beams. In this dissertation I investigate the motion of atoms in such potentials. The center-of-mass wave-packet motion is initiated by an application of a sudden shift to the lattice potentials. The resulting oscillations are observed using a photon redistribution technique. We first show that by utilizing a real-time feedback loop and shifting the lattice continuously in response to the wave-packet motion, we can increase, alter or damp this motion using different gains of the feedback loop. We further show that by splitting the wave-packet between two adiabatic potentials of the lattice via quantum projection, we can construct an atom interferometer. We observe interference signal when the two components of the original wave-packet overlap. The behavior of the interference is studied as a function of lattice parameters and a consistent theoretical picture is developed. Further, we study how well-to-well tunneling of atoms and sloshing-type wave-pocket dynamics affect each other. We find that in the regions where the well-to-well tunneling is significant, the sloshing type wave-packet oscillations are suppressed. Sloshing-type motion only occurs if the tunneling is sufficiently suppressed with an applied magnetic field. Finally we describe a new type of optical lattice that is based on two-photon Raman transitions. The basic period of this lattice is reduced by a factor of two, compared with traditional lattices. We also show that Sub-Doppler cooling mechanism is present in this lattice. The dissertation is concluded with the presentation of a new experimental set-up for Bose-Einstein Condensate production, which may in the future be used for the study of BEC dynamics in optical lattices.
A Bose-Einstein condensate (BEC) is a macroscopic ensemble of atoms that collectively behaves as a single quantum-mechanical object. In this thesis I describe an apparatus built to create and study a BEC, as well as initial experiments carried out using a one-dimensional optical standing wave (optical lattice) to manipulate the BEC. In the first experiment, a weak optical lattice Bragg-reflects a BEC moving in a nearly harmonic trap. The Bragg reflection combined with the harmonic trapping potential cause the BEC to oscillate, much as light oscillates in an optical cavity. In the second experiment, a deep optical lattice applied to an atom cloud for a short duration is used to split and recombine the atomic wavefunction. By doing this we can create two different types of atom interferometer: a small-separation atom interferometer which works with either a BEC or a thermal gas, and a large-separation atom interferometer which works only with a BEC and whose interferometric arms are, in principle, separately addressable. In the third experiment, an optical lattice potential is slowly turned on. Under the influence of this lattice potential, the BEC loses its superfluid properties, but fully regains them when the lattice is turned back off. This behavior is consistent both with a reversible transition to a 1-D Mott insulator state and with mean-field effects in a deep lattice; both interpretations are discussed. In the latter part of this thesis I describe an apparatus designed to accommodate experiments involving both a BEC and an ion. The interactions between an ion and a BEC have never before been experimentally investigated. Our apparatus includes both the means to localize an ion by actively shielding against stray electric fields and to spatially image ions. This should allow future experiments in which a single ion is embedded in a BEC. In addition to imaging ions, the apparatus provides the capability to create high-resolution images of distributions of neutral atoms by photoionizing them and then quickly imaging them. I conclude the thesis with a discussion of future experiments exploring ion-BEC interactions.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
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.
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.
In the present thesis we study several schemes where the detection of the emitted light from an atomic ensemble gives information about the state of the atoms. In chapter 1 we review the basic theory for the light matter interaction in second quantized form. In chapter 2 we show how conservative potentials for the atoms, such as dispersive optical lattices, can be realized experimentally due to the dispersive interaction with a far detuned laser We then review some basic properties of the physics of a particle in a periodic potential. We show that the ground state and the lowest lying excitations of a Bose-Einstein condensate in a dispersive optical lattice can be described by the Bose-Hubbard Hamiltonian. In chapter 3 we study the photonic bandstructure of a chain of fixed pointlike atoms in a biperiodic configuration. We calculate the photonic spectra and the probe transmission if the atoms are in free space and inside a standing wave optical resonator. In chapter 4 we consider light scattering from ultracold atoms in an optical lattice where we calculate the photonic scattering cross section as a function of energy and direction of emission along the Mott-insulator-superfluid phase transition. We take into account the finite tunneling rate for the atoms, when evaluating the scattering cross section of the photons and the effect of photon recoil onto the atoms. In chapter 5 we consider a gas of ultracold atoms trapped at two spatially separated regions in space. Using a two Raman lasers to couple atoms out of the systems we show that it is possible to measure the mean value of the atomic field operator of the two systems by measuring the scattered light intensity of one of the Raman lasers. We show how this setup might be used to measure the temperature of a Bose-Einstein condensate and to monitor the superfluid to Mott-insulator phase transition for a gas of ultracold atoms in an optical lattice.