Strongly interacting many-body systems are of great interest in many areas of physics. Ultracold atoms in optical lattices are a powerful tool for creating and studying such systems. In this thesis, the construction and characterization of an 3D optical lattice for a ultra-cold Strontium apparatus is described. A 1064nm fiber amplified laser system is used to create three orthogonal pairs of standing waves that together form the 3D lattice. By delivering 4W of power to each arm of the lattice and focusing the beams to a beam radius of about 250 microns at the location of the atoms, we can create a 3D lattice with a maximum trap depth around 70 photon recoils.
Strongly interacting many-body systems are of great interest in many areas of physics. Ultracold atoms in optical lattices are a powerful tool for creating and studying such systems. In this thesis, the construction and characterization of an 3D optical lattice for a ultra-cold Strontium apparatus is described. A 1064nm fiber amplified laser system is used to create three orthogonal pairs of standing waves that together form the 3D lattice. By delivering 4W of power to each arm of the lattice and focusing the beams to a beam radius of about 250 microns at the location of the atoms, we can create a 3D lattice with a maximum trap depth around 70 photon recoils.
Optical lattice experiments have proved to be a versatile tool for studying strongly correlated quantum systems. The motivation behind these experiments is to use the cold atoms to emulate a solid state system for which the Hamiltonian is analytically or numerically non-solvable. In our experiment, we construct a 3D simple cubic lattice system which realizes the Fermi-Hubbard model and provides us the opportunity to study the antiferromagnetic (AFM) insulator phase. In order to establish evaporative cooling in the optical lattice and to enlarge the size of the AFM phase, we implement a compensation potential additional to the standard lattice beam. In this thesis, I will present detailed steps to construct and calibrate the compensated 3D optical lattice system.
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.
Laser cooling of atoms is the basis of researches on ultracold atoms and molecules. It is of great importance in the study of precision measurement and quantum simulation, etc. In order to obtain ultracold cesium atomic sample with a lower temperature and a higher density, as the starting point to create ultracold cesium ground state molecules, we demonstrate in this article a method which effectively overcomes the heating from the reabsorption of scattered light in magneto-optical trap to further reduce the ultracold atomic temperature by loading atoms into a 3D optical lattices. Based on obtaining the ultracold Cs atoms in a standard magneto-optical trap, we use the compressed magneto-optical trap technology to increase ultracold Cs atomic density. Efficient loading of ultracold Cs atoms is achieved by 3D optical lattices which constructed by four lasers; the temperature of the atoms is measured by time-of-flight method. We observed the cooling result that the temperature drops from ~60.0 μK to ~11.6 μK. We also explore the dependence of the atom numbers in the lattice on the frequency of lattice lasers, and lead to the conclusion that the loading rate of the optical lattices reaches its maximum when the lattices laser’s detuning is –15.5 GHz. In the meantime, this paper investigates the use of optical lattice to suppress the heating of the ultracold atoms due to the radiation photons, in this sense, our research has far-reaching significance. Our scheme is advantageous due to its relaxed starting temperature requirement, meaning that 3D DRSC can be directly accomplished in a standard single cell vapour-loaded MOT without reliance on any additional devices such as a Zeeman slower.
Atoms can be trapped at the foci of intense laser beams, which can enable the study of interactions and dynamics of ultracold gases. In this thesis, we will describe our\nnew trap designs. A large volume pancake-shaped optical dipole trap is initially used for loading large numbers of atoms from a Magneto-Optical Trap. A BEC with a large number of 84 Sr atoms has been achieved after evaporation in this trap. To form degenerate gas of 88 Sr we compress the mixture of 88 Sr and 87 Sr from the loading trap\ninto a superimposed dimple trap. This combination improves the reproducibility of the experiment and shortens the time required to create quantum degenerate samples,\nwhile we are able to create 88 Sr BEC with high density. In order to generate BEC of 86 Sr, an isotope with large scattering length and extremely high three-body loss\nrate, we implement an optical sheet trap which has an aspect ratio of 1:10. The tight axis in the vertical direction provides strong potential to hold against gravity while the large horizontal dimension brings up the trap volume and keeps down the atomic\ndensity.
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.
An optical lattice is the periodic potential that atoms experience via the ac-Stark shift when they are illuminated by counter-propagating laser beams that form a standing-wave pattern. Optical lattices have been widely used as a versatile platform in cooling, trapping, controlling atoms, and also for the study of a variety of problems in physics. The many-body states of ultracold atoms in optical lattices can be characterized by the quantum-correlations encoded in time-of-flight images. In this thesis, we mainly discuss the use of correlations function as a natural framework for characterizing quantum states in optical lattices.\nThe outline of the thesis is as follows. Chapter 1 gives a brief introduction to optical lattice potentials and ways for describing particles moving in a periodic potential. Chapter 2 explains the importance of correlations and discusses common methods to detect them in cold atom experiments.\nChapter 3 presents work done to study the many-body Schrödinger equation in a quasiperiodic potential and discusses its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We posed a possible visualization of such a connection in experimentally accessible many-body observables. These observables are useful probes for the three characteristic phases of the problem: the metallic, Anderson, and band-insulator phases. In addition, they exhibit fingerprints of nonlinear phenomena such as bifurcations and devil's staircases. Our numerical treatment is complemented with a perturbative analysis that provides insight on the underlying physics. The perturbative-theory approach is particularly useful in illuminating the distinction between the Anderson-insulator and the band-insulator phases in terms of paired sets of dimerized states.\nChapter 4 discusses several theoretical procedures developed to understand a recent experiment on macroscopic quantum self-trapping (ST) performed in a 2D optical lattice. Mean field and truncated-Wigner-approximation (TWA) calculations are performed trying to reproduce the experimental observations. The discrepancy between the theory and the experiment lead to the hypothesis of a new type of ST caused by strong correlations. We analyze toy models to support it.