Phase contrast imaging is used to observe Bose-Einstein condensates at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two-relevant-parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and the thermal atoms is taken into account to various degrees.
Bose-Einstein condensates are interesting systems for studying quantum mechanics. Absorption imaging and phase-contrast imaging are two methods that are often used to determine the absolute number of atoms in a condensate. This thesis proposes a third method: holographic imaging. This method relies on the interference of a probe beam, which passes through the condensate, and a reference beam. The phase shift of the light due to the atoms and the optical density of the condensate are reconstructed with the use of Fourier transformation. Up to 300 images can be taken \\textit{in situ}.\n\nThere are two interesting applications of holographic imaging. The first is the refractive index, which can be measured directly with holographic imaging. The Hartree-Fock model is used to relate the real and imaginary part of the refractive index to the degeneracy of the condensate. However, the preliminary results are ambiguous and require further study.\n\nThe second is spin-dependent imaging, in which two orthogonally polarized reference beams are used to reconstruct polarization dependent information. This can be applied to study the dynamics of spinor condensates. In this thesis, a proof of concept for this method is given.
Phase Contrast Imaging (PCI) is a non-destructive method of probing the state of Bose-Einstein Condensates (BECs). In a PCI measurement, an off-resonant laser beam is illuminated on a BEC and a homodyne measurement is performed on the light which passes through the BEC. The interaction between laser beam and the atomic BEC encodes information about the atomic BEC on the phase-shift accumulated by laser beam. Past theories of PCI measurement have focused on continuous measurement, and treat the problem by deriving a master equation which causes an effective measurement induced decoherence. This allows for calculation of the backaction on the BEC, but not the information that is gained by the measurement. We introduce a simple theory to capture the physics of PCI measurement, which allows quantifying the information-disturbance trade-off, and works in the single shot regime. We show a universal scaling law for the information-disturbance trade-off that is valid for a wide range of particle numbers in the BEC.
Bose-Einstein condensation (BEC) in ultra-cold magnetically-trapped
sp7Li vapor was experimentally observed and quantitative measurements of condensate number were made. Compared to other BEC experiments, lithium is unique due to its negative s-wave scattering length, corresponding to effectively attractive interactions. Due to this attraction, condensates are expected to undergo mechanical collapse if the condensate number exceeds a critical value. In this experiment, an upper limit of about 1000 condensate atoms is found, in agreement with theoretical predictions.\nIn the experiment, the atoms are confined by a set of six permanent magnets in the Ioffe configuration. Optical forces are used to slow and guide atoms from a thermal atomic beam into the magnetic trap. With about
10sp8 atoms loaded into the trap, the vapor is laser-cooled to near 200
muK and then evaporatively cooled by application of a resonantly-tuned microwave field. Evaporative cooling produces a million-fold increase in phase-space density, reaching quantum-degenerate conditions with about 10
sp5 atoms at temperatures near 300
muK. After cooling, the trapped atom distribution is observed by in situ imaging via an optical probe. Calculated atom distributions are fit to the image data.\nIn initial data, the imaging resolution was insufficient to see the spatially-narrow condensate peak, but as phase-space densities approached the expected phase transition, the images suddenly became distorted. Initial fits to the data suggested as many as 10
sp5 condensate atoms, in strong disagreement with theoretical predictions. An imaging model, accounting for imperfections in the imaging optics, shows that the sudden appearance of the distortions is a consequence of BEC, and that these distortions led to the initial over-estimation of cloud phase-space density and condensate number.\nImproved imaging was obtained using large probe detunings, a Phase-Contrast Polarization Imaging (PCPI) technique, and near-diffraction-limited imaging optics. The PCPI method exploits the birefringence of the trapped atoms. From the resulting images, quantitative estimates of condensate number are obtained and compared with theory.
Summary form only given.One approach to experimentally verifying that collapses occur is to nonperturbatively observe the gas and monitor N, over time. In principle, phase-contrast imaging techniques can be used to make such observations, by illuminating the cloud with a weak, far-detuned probe laser. However, because l, is relatively small, a probe that is sufficiently weak to avoid perturbing the atoms does not provide a large enough signal to accurately determine N,. This difficulty can be circumvented by sacrificing imaging resolution and measuring instead the total number of trapped atoms in the cloud. Collapses are then detected as discontinuous drops in the signal. We have implemented this detection scheme and are attempting to observe collapses and measure their frequency.