Bose-Einstein condensates in optical lattices have proven to be a powerful tool for studying a wide variety of physics. In this thesis a series of experiments using optical lattices to manipulate 87Rb Bose-Einstein condensates are described. A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was measured interferometrically using a two-pulse Ramsey interferometer. The two pulses were created using a one dimensional optical lattice. By measuring the resulting frequency as a function of the lattice detuning from the atomic resonance, we found a distinctive dispersive shape for the recoil frequency that fit the recoil momentum as nr~k. A one-dimensional optical lattice was used to modify the dispersion relation of the condensate in order to demonstrate the matter-wave analogue of Optical Parametric Generation (OPG) and Amplification (OPA) of photons. A condensate was loaded into a moving optical lattice with adjustable quasimomentum k0. As the value for k0 was varied, we observed elastic scattering into two distinct final momentum states k1
Bose-Einstein condensates in optical lattices have proven to be a powerful tool for studying a wide variety of physics. In this thesis a series of experiments using optical lattices to manipulate 87Rb Bose-Einstein condensates are described. A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was measured interferometrically using a two-pulse Ramsey interferometer. The two pulses were created using a one dimensional optical lattice. By measuring the resulting frequency as a function of the lattice detuning from the atomic resonance, we found a distinctive dispersive shape for the recoil frequency that fit the recoil momentum as nr~k. A one-dimensional optical lattice was used to modify the dispersion relation of the condensate in order to demonstrate the matter-wave analogue of Optical Parametric Generation (OPG) and Amplification (OPA) of photons. A condensate was loaded into a moving optical lattice with adjustable quasimomentum k0. As the value for k0 was varied, we observed elastic scattering into two distinct final momentum states k1
We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation (OPG) and amplification (OPA) of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.
87Rb Bose Einstein Condensate in 3D optical lattice was studied in the regime of weak interaction(the superfluid phase) and strong interaction(the Mott insulating phase). The stability of superfluid currents was studied using a moving optical lattice. The critical momentum for stable superfluid current varies from 0.5 recoil momentum (shallow lattice) to 0 (the Mott insulator) as the system reaches the Mott insulator transition. The phase diagram for the disappearance of superfluidity was studied as a function of momentum and lattice depth. Our phase diagram boundary ex-trapolates to the critical lattice depth for the superfluid-to-MI transition. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed. A new auxiliary vacuum chamber, which is called the science chamber, was de-signed and installed to improve optical lattice experimental performance and imaging resolution power. Atoms are transported from the main chamber to the science cham-ber. By further evaporation cooling, BECs with N- 2-3 x 104 atoms are produced
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.
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.
We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.
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.