The technique used to create alkali BEC were applied to other class of quantum particles, fermions. Earlier alkali atoms such as 87Rb (composite bosons) were cooled as a gas down to nano kelvin temperature via laser cooling and evaporative cooling. At these temperatures the thermal de Broglie wavelength of the particle becomes in order of the inter-particle spinning in the gas and Bose-Einstein condensate is formed. Experiments also observed that condensate behave as matter wave and verified the super fluid nature of the condensates.
The technique used to create alkali BEC were applied to other class of quantum particles, fermions. Earlier alkali atoms such as 87Rb (composite bosons) were cooled as a gas down to nano kelvin temperature via laser cooling and evaporative cooling. At these temperatures the thermal de Broglie wavelength of the particle becomes in order of the inter-particle spinning in the gas and Bose-Einstein condensate is formed. Experiments also observed that condensate behave as matter wave and verified the super fluid nature of the condensates.
Bose-Einstein CondensationAtoms are normally considered as particles but, according to quantum mechanics, they also have wave-like properties.Indeed, an atom has an equivalent wavelength, the deBroglie wavelength, which is inversely proportional to the atom's momentum.As atoms are cooled they slow down and their deBroglie wavelength increases.Satyendra Bose and Albert Einstein predicted 70 years ago that at a low enough temperature the wavelength exceeds the interparticle spacing and the atoms begin to overlap.The atoms become indistinguishable, effectively entering -by a process called Bose-Einstein condensation (BEC) -a coherent state where the laws of quantum mechanics govern the behaviour of the macroscopic system.BEC has been observed in superfluid helium-4 and superconductivity, both being states of matter in which bosons (integral-spin particles) condense into macroscopic quantum states.But the bosons in these systems interact with each other, so to better understand BEC, physicists have tried for sometime to bring about condensation in an ideal gas of noninteracting atoms. The JILA ExperimentThe JILA experiment consists of three stages: A -optical loading, (pre)cooling & polarization; B -magnetic trapping & evaporative cooling in the absence of light; C -optical detection.A -laser cooling stage.For 300 s, about 107 atoms are gathered from the low-velocity tail of a room-temperature Rb-vapour at some KT-11 mbar into a so-called "dark" magneto-optical trap (MOT), which is most efficient in collecting a large number of atoms by optical forces.The gas is rapidly (pre)cooled In the MOT to about 20 µK and subsequently magnetically polarized in a small magnetic bias field by optical pumping.B -trapping and cooling.Polarized atoms are magnetically trapped in a rapidly applied timeorbiting potential (TOP) trap, which consists of a set of coils In anti-Helmholtz configuration with a small, uniform transverse field, rotating at 7.5 kHz, superimposed.The TOP provides an effectively harmonic potential with an axial frequency of about 120 Hz and radial frequency of about 42 Hz.In the TOP, the gas is adiabatically compressed to reach the starting conditions for evaporative cooling at about 90 pK with a number density of about 2 x 1010 cm-3, sufficiently large to have the elastic collision rate dominate over the loss rate in the gas.The evaporation takes 70 s and BEC is achieved with 2 x 104 atoms at approximately 170 nK.The evaporation is induced by a RF transition to an untrapped state of the atoms at the edge of the sample.C -optical detection.At the start of the detection stage the trap is expanded adiabatically to a larger size to allow a fast (destructive) absorption measurement in which the sample Is Imaged on a CCD camera.The appearance of a diffraction ring marks the growth of a partially resolved structure in the sample.This is consistent with BEC In an inhomogeneous sample, where the condensate is expected to appear as a very small, dense gas cloud at the centre of the potential well.To confirm this interpretation, the momentum distribution in the sample was measured by suddenly switching-off the trap and observing the expanding gas cloud.In this process both Isotropic expansion of the (thermal) non-condensate fraction was observed as well as an anisotropic expansion, as is to be expected for a suddenly released anisotropic single quantum state. INELASTIC X-RAY SCATTERING Great Potential Demonstrated F. Sette and G. Ruocco describe why the confirmation, at the European Synchro tron Radiation Facility, of fast sound in water at momentum transfers of from 4 to 14 nm-1 using inelastic X-ray scattering with a resolution in the meV range demonstrates the technique's important capabilities.
For sufficiently low temperatures, a Bose gas experiences a transition into a Bose-Einstein condensate, characterized by a macroscopic occupation of the ground state of the system. The development of efficient cooling and trapping techniques for neutral atoms led in 1995, to the first observation of BEC in dilute alkali gases in 87Rb [1]. This remarkable achievement has been followed by BEC experiments in various other elements. The BEC has become during the last years, one of the most active and fruitful research areas of modern atomic physics, constituting an interdisciplinary field, which links atomic physics with various other research areas, like quantum optics, condensed-matter physics, and very especially nonlinear physics.
Research on degenerate quantum gases of dilute atomic gases has become a well established field in modern physics and revealed many astonishing phenomena. The first experiments on Bose and Fermi gases at low temperatures aimed to prove the predictions of quantum mechanics on a macroscopic scale. Since then we make use of Bose and Fermi gases and mixtures of any combination to model other many body systems. A property of Bose Einstein condensates is superfluidity which we want to investigate further in toroidal potentials with a new apparatus which can produce an all-optical BEC. This means trapping thermal atoms in an optical dipole trap and cooling the sample by evaporation into the quantum degenerate regime. This new technique was first successfully demonstrated by M.D. Barrett et al. in 2001 and promises to be faster and simpler than the well established and common way of evaporation in magnetic traps. A new apparatus was built by the author and we report on the experimental details of the trapping of 87Rb atoms from a hot vapour and cooling them in a magneto-optical trap, and further evaporation to quantum degeneracy in a crossed optical dipole trap operating at a wavelength of l = 1064nm, with accurate control of the power in both beams via a feedback loop. The evaporation of neutral atoms of 87Rb in far red detuned optical dipole traps using linearly polarised laser light is spin independent, and mixed spinor condensates of the F=1 manifold can be formed. As an empirical technique we found by applying a magnetic gradient field during the final evaporation that we can selectively populate mF spin states or prepare mixtures. This intriguing mechanism was found earlier as well by M. S. Chang, but is yet not fully understood and subject of our future research. We can now routinely prepare an almost pure condensate containing up to 7000 atoms in the condensed phase purely in the mF = 0 spin state. This thesis contains the theoretical framework of Bose-Einstein condensation with in mean-field theory, the concepts of cooling of atoms in magneto-optical traps, the trapping and evaporation in optical dipole traps and the experimental realisation. In the future this experiment will be extended by a fast scanning dipole trap to apply arbitrary time averaged potentials of more complex geometries, such as toroidal traps to study the effects of superfluidity in a periodic potential. The production of toroidal traps and cold atoms in such a trap are outlined in this thesis.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.
This thesis presents experiments probing physics in the crossover between Bose-Einstein condensation (BEC) and BCS superconductivity using an ultracold gas of atomic fermions. Scattering resonances in these ultracold gases (known as Feshbach resonances) provide the unique ability to tune the fermion-fermion interactions. The work presented here pioneered the use of fermionic Feshbach resonances as a highly controllable and tunable system ideal for studying the cusp of the BCS-BEC crossover problem. Here pairs of fermionic atoms have some properties of diatomic molecules and some properties of Cooper pairs. I present studies of a normal Fermi gas at a Feshbach resonance and the work required to cool the gas to temperatures where superfluidity in the crossover is predicted. These studies culminated in our observation of a phase transition at the cusp of the BCS-BEC crossover through condensation of fermionic atom pairs. I also discuss subsequent work that confirmed the crossover nature of the pairs in these condensates.
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.