Summary form only given. One of the most striking results in the field of Bose-Einstein Condensation (BEC) is the possibility of creating an atom laser, using the trapped condensate as a continuously replenished source of a coherent atomic beam. Prototype atom lasers have already been demonstrated experimentally. One fruitful theoretical description is mean field theory, as fully quantised models cannot yet include essential effects, such as nonlinear atom-atom interactions.
Summary form only given. One of the most striking results in the field of Bose-Einstein Condensation (BEC) is the possibility of creating an atom laser, using the trapped condensate as a continuously replenished source of a coherent atomic beam. Prototype atom lasers have already been demonstrated experimentally. One fruitful theoretical description is mean field theory, as fully quantised models cannot yet include essential effects, such as nonlinear atom-atom interactions.
Measurement is our fundamental tool for learning about the world around us. It is from observing trends in measurements that we develop the theories that enable us to predict future behaviour, and it is against measurements that we determine the validity of these theories. Increases in the precision of our measurements are fundamental to our understanding. Atom interferometry is a new method for performing precision measurements that uses the matter-wave nature of atoms to perform interferometry experiments analogous to those performed with photons. However, in contrast to optical interferometry, which uses coherent sources of photons, atom interferometry uses thermal atomic sources, in part due to the unavailability of high-flux coherent atomic sources. Although pulsed coherent atomic sources are presently available, continuous sources are not. Creating a truly continuous coherent source for atoms is tricker than for photons. One of the largest challenges is that atom number is conserved. A source of atoms is therefore necessary to produce a truly continuous atom laser. This source must be used to replenish the lasing mode of the atom laser, and the process must operate without significantly disturbing the coherence properties of the lasing mode. It is this replenishment or pumping process that has been investigated theoretically in this thesis. There are only two choices for the reservoir that makes the replenishment (or pumping) process of an atom laser irreversible: the empty modes of the optical field, and the empty modes of the atomic field. Processes of both forms are considered. Using an optical reservoir has the advantage that atoms are not necessarily lost as part of the pumping process, which is necessary when using an atomic reservoir. The efficiency of processes using an optical reservoir can therefore be higher. Using an atomic reservoir, however, has the advantage that it is easier to implement as one can use the standard experimental technique of evaporation which is commonly used in the production of pulsed coherent atomic sources. We show theoretically in this thesis that although it is possible to produce a continuous atom laser using an atomic reservoir, the flux achieved in the geometry considered is insufficient to compete with pulsed coherent atomic sources for precision measurement. The results for the pumping process using an optical reservoir are more promising. Although condensed sources were used as the source for this process, a detailed comparison of the theoretical calculations and experimental results indicate that the detrimental reabsorption processes are suppressed. This suggests that it may be possible to use higher-flux thermal atomic sources to replenish the lasing mode of an atom laser with this pumping process.
Abstract Bose–Einstein condensates (BECs) are macroscopic coherent matter waves that have revolutionized quantum science and atomic physics. They are important to quantum simulation1 and sensing2,3, for example, underlying atom interferometers in space4 and ambitious tests of Einstein’s equivalence principle5,6. A long-standing constraint for quantum gas devices has been the need to execute cooling stages time-sequentially, restricting these devices to pulsed operation. Here we demonstrate continuous Bose–Einstein condensation by creating a continuous-wave (CW) condensate of strontium atoms that lasts indefinitely. The coherent matter wave is sustained by amplification through Bose-stimulated gain of atoms from a thermal bath. By steadily replenishing this bath while achieving 1,000 times higher phase-space densities than previous works7,8, we maintain the conditions for condensation. Our experiment is the matter wave analogue of a CW optical laser with fully reflective cavity mirrors. This proof-of-principle demonstration provides a new, hitherto missing piece of atom optics, enabling the construction of continuous coherent-matter-wave devices.
In 1925, Einstein predicted the condensation of bosons into the ground state of the system for low (but finite) temperatures. Several phenomena, including superfluidity and superconductivity have been associated with Bose-Einstein condensation, but these systems interact strongly with their environment and pure Bose-Einstein condensation could not be established. It took 70 years, in which time the laser was discovered, and laser cooling techniques to manipulate atoms in a dilute atomic gas, before Bose-Einstein condensation in dilute atomic gases could be demonstrated in 1995. In the first condensation experiments, BECs were created in a magnetic trap. Since in a magnetic trap not all mF states of the atom can be trapped simultaneously, thereby limiting the number of experiments that can be done, other ways of trapping and generating BECs were sought and found. In 2001, the first all-optical BEC was made, where the dipole force was used to trap atoms in the crossing of two far red detuned laser beams. In an optical dipole trap not only atoms in different internal states can be trapped, but also different atomic species simultaneously. In this thesis, the formation of an all-optical Bose-Einstein condensate with rubidium atoms is presented. Conventional all-optical BECs are usually created in high power CO2 laser dipole traps, or have complicated laser cooling schemes and complex dipole trap setups. In our simple and straightforward setup, we load rubidium atoms from a magneto-optical trap into a crossed optical dipole trap created by a single frequency Yb:YAG laser with a wavelength at 1030 nm. The small wavelength allows for a small diffraction limit, and permits us to use standard optical materials, thus making the experimental setup cost effective. Other attempts to achieve Bose-Einstein condensation in a multi-mode (frequency) fiber laser at 1064 nm failed, because the atom loss was quite high. It is assumed that the multi-mode character of the fiber laser induces Raman transitions in rubidium atoms, thereby heating them. We can trap about ∼ 5E7 atoms in a single beam dipole trap out of ∼ 5E9 atoms trapped in theMOT, and ∼ 350,000 atoms can be trapped in a crossed beam dipole trap due to the smaller trap volume. 70% of the atoms in the dipole trap is optically pumped into one mF state. Quantum degeneracy is reached by evaporatively cooling the atoms in the crossed dipole trap by ramping down the laser power with three linear ramps. We can independently change the power of each beam by an AOM. This allows us to use one beam as an atom waveguide for future experiments. After evaporation, we typically have about 10,000 atoms at a temperature below the critical temperature. We have proved Bose-Einstein condensation by using the anisotropic expansion of a quantum degenerate gas trapped in an anisotropic potential. The aspect ratio of our atom cloud changed during a time of flight from 0.7 to 1.2 in 10 ms, thus proving that we have reached quantum degeneracy. We have about 5,000 condensed atoms in our optical dipole trap at a temperature less than 100 nK. The remaining atoms are thermal. Bose-Einstein condensation is obtained within 8 s, and we can repeat the experiment every 30 s. It should be mentioned that the Bose-Einstein experiment was moved from the ”Leibniz Universität Hannover” to the ”Technische Universität Darmstadt”, and had to be completely rebuilt. All-optical Bose-Einstein condensation was reached within one year after the move. Our Bose-Einstein condensation setup presents an ideal starting point for using our condensates in combination with miniaturized atom optical setups based on our novel microfabricated optical elements. With our microlenses, we can create a number of possible dipole trap configurations, such as the dipole trap array or the cylindrical microlens array. Using microlenses in miniaturized atom optical setups opens a completely new field of coherent atom optics. Also because the tight confinement of the microtraps allows us to load a 3D BEC, a 1D BEC, or a Tonks-Girardeau gas in the micropotentials depending on the density.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
We present a self-consistent mean field model of the extraction of atoms from a Bose-Einstein condensate to form a cw atom laser. The model is based upon the Hartree-Fock-Bogoliubov equations within the Popov approximation, modified by the inclusion of spatially dependent source and sink terms, which lead to current flow within the condensate. The effects of this current flow are investigated for traps containing rubidium (repulsive effective interaction) and lithium (attractive interaction) atoms. The extra kinetic energy associated with this flow is shown to be able to stabilize the condensate in the attractive case against mechanical instability.