We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy, and Thomas-Fermi radii beyond the usual harmonic approximation.
We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy, and Thomas-Fermi radii beyond the usual harmonic approximation.
We present a study of phase transition to macroscopic superfluidity for an ultracold bosonic gas confined in a combined trap formed by a one-dimensional optical lattice and a harmonic potential, focusing on the critical temperature of this system and the interference patterns of the Bose gas released from the combined trap. Based on a semiclassical energy spectrum, we develop an analytic approximation for the critical temperature Tc, and compare the analytic results with that obtained by numerical computations. For finite temperatures below Tc, we calculate the interference patterns for both the normal gas and the superfluid gas. The total interference pattern shows a feature of ``peak on a peak.'' As a comparison, we also present the experimentally observed interference patterns of 87Rb atoms released from a one-dimensional optical lattice system in accord with our theoretical model. Our observations are consistent with the theoretical results.
Summary form only given. Recently, we have created a Bose condensate of /sup 87/Rb atoms directly in an optical trap formed by tightly focused laser beams. Following initial loading from a laser cooled gas, evaporative cooling through the BEC transition is achieved by simply lowering the depth of the optical trap. Our success is due in part to a high initial phase space density realized in the loading of our optical dipole trap and in part to the tight confinement of the atoms that permits rapid evaporative cooling to the BEC transition in 2 s.
We report on our progress towards realization of a toroidal trap for Bose-Einstein condensates (BECs) of 87Rb using a time-averaged optical dipole potential. To achieve BEC we utilize a 20 W laser operating at 1064 nm to form an optical dipole trap in which we evaporatively cool the gas . Loading of the dipole trap is achieved by overlapping the dipole beams with a standard magnetic optical trap. Evaporative cooling is first performed in a single beam trap, followed by compression and additional confinement with a second orthogonal beam. This prevents stagnation of the evaporative cooling cycle, and allows the gain of 105 in phase space density necessary to achieve quantum degeneracy.
We report on our progress towards realization of a toroidal trap for Bose-Einstein condensates (BECs) of 87Rb using a time-averaged optical dipole potential. To achieve BEC we utilize a 20 W laser operating at 1064 nm to form an optical dipole trap in which we evaporatively cool the gas. Loading of the dipole trap is achieved by overlapping the dipole beams with a standard magnetic optical trap. Evaporative cooling is first performed in a single beam trap, followed by compression and additional confinement with a second orthogonal beam. This prevents stagnation of the evaporative cooling cycle, and allows the gain of 105 in phase space density necessary to achieve quantum degeneracy.
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.
We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number N of atoms, harmonic oscillator length, deformation of the trap, s-wave scattering length) fix its thermodynamic behavior in the large N limit through two dimensionless scaling parameters. These are the reduced temperature t=T/Tc0 and the ratio $\ensuremath{\eta}$ between the T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature Tc0 of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.