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.
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.
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.
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.
Background 1 1.22This thesis 2 Chapterr 2 Theoretical background 5 2.11 Rubidium 5 2.22 Magnetic trapping 5 2.33 Bose-Einstein condensation 8 2.44 BEC formation and phase coherence 2.55 Evaporative cooling 2.5.11Evaporative cooling Lensing Chapterr 4 Broad-area diode laser system 4.11 Abstract 4.22 Introduction 4.33 Experimental setup 4.44 Characteristics 4.55 MOT application 4.66 Summary Chapterr 5 Hydrodynamic properties of dense atomic clouds Vlll l 5.11 Introduction 5.22 Density and temperature analysis 5.33 Anisotropic expansion of hydrodynamic clouds 5.44 Frequency shifts and damping of shape oscillations Chapterr 6 Condensation into non-equilibrium states and focusing of a condensate 6.11 Introduction 6.22 Preparation of degenerate samples out of equilibrium 6.33 Kinetics of the condensate growth 6.44 Formation of a non-equilibrium BEC 6.4.11Local critical temperature 6.4.22 Truncation and local temperature 6.55 Oscillation modes 6.66 Non-equilibrium phase fluctuations 6.77 Focusing of a condensate 6.7.11Focusing principle 6.7.22 Focal broadening 6.7.33 Applications of BEC focusing 6.88 High condensate fractions in non-equilibrium states Bibliographyy Summaryy Samenvattingg AcknowledgementssMostt of the theoretical groundwork on the interacting quantum gases has been developedd in the 50's and the 60's in the context of superfluidity of 4 He.However, a detailedd comparison between theory and experiment is extremely difficult in the case of liquidd helium because its density is rather high and can be varied only within a narrow range..In the 70's the observation of BEC in dilute atomic gases under equilibrium conditionss was known to be impossible.Therefore, the efforts shifted towards investigationss of metastable systems.Thee first attempts to reach BEC were done in spin-polarised atomic hydrogen.Foundationss for many techniques and methods were laid in the course of that work.Hydrogenn quantum gas was first stabilised in a cryogenic environment by Silvera and Walravenn [93] and by Cline et al. [23].Magnetic trapping was first demonstrated in sodium [79]] and in hydrogen by Hess et al. [50] and van Roijen et al. [87].Another critically importantt technique, evaporative cooling, was first experimentally demonstrated in hydrogenn [51] and further developed in [74,97, 105].Bose-Einsteinn condensation in alkali systems was achieved in magnetic traps throughh the combination of optical cooling methods with the evaporative cooling technique.iss obtained by observation of the anisotropic character of the expansion.Finally, we measuree frequency shifts and damping of shape oscillations.Inn the final part of the Thesis, Chapter 6, we describe the results produced in the experimentss on formation of condensates far from equilibrium.We compare our work with previouss experiments on condensate formation and describe how the process of formation iss triggered in our system.A brief section deals with the growth of the condensate fraction.Further,, we show how the concepts of local sample temperature and the critical temperature arisee in elongated clouds with high elastic collision rates.We present a simple model, whichh illustrates how the non-equilibrium character of the condensates leads to the quadrupolee oscillations.We also discuss non-equilibrium phase fluctuations, which manifestt themselves in the form of stripes in the time-of-flight absorption images.Condensatee focusing is introduced as a novel method for investigation of Bose-Einstein condensates..The focusing of a condensate in free flight arises from axial contraction of the expandingg cloud when the gas is released from the trap during the inward phase of a shape oscillation.. Possible applications of BEC focusing are discussed, with an estimate of the coherencee length given as an example.The last part of the chapter covers condensation into non-equilibriumm states with high condensate fractions.The situations of large and small condensatee fractions are compared.
The apparatus and procedure required to generate a pure Bose-Einstein condensate (BEC) consisting of about half a million 87Rb atoms at a temperature of <60 nK with a phase density of >54 is described. The atoms are first laser cooled in a vapour cell magneto-optical trap (MOT) and subsequently transferred to an ultra-low pressure MOT. The atoms are loaded into a QUIC trap consisting of a pair of quadrupole coils and a Ioffe coil that generates a small finite magnetic field at the trap energy minimum to suppress Majorana transitions. Evaporation induced by an RF field lowers the temperature permitting the transition to BEC to be observed by monitoring the free expansion of the atoms after the trapping fields have been switched off.PACS Nos.: 03.75.Fi, 05.30.Jp, 32.80.Pj, 64.60.i
In a Bose-Einstein Condensate (BEC), due to extremely low temperatures, wave functions of all particles in the system overlap and form a single macroscopic wavefunction. This brings quantum mechanical effects to the macroscopic scale and allows us to better understand known quantum mechanical laws and effects, as well as develop new ones. In addition to being of fundamental scientific interest, BEC can serve in practical applications, such as quantum metrology, atomic interferometry, and quantum information and communication. Here we describe our approach for producing BECs in 87Rb. To create atomic flux towards our science chamber, a 2-dimensional magneto-optical trap (2D-MOT) with push beam is used. The initial atomic cloud is formed in 15s by 3D-MOT and consists of 1e9 atoms at 500uK. After the MOT, atoms are cooled with optical molasses to 50uK and transferred to a quadrupole magnetic trap, where radio-frequency (RF) induced evaporation is performed, which lowers temperature to 10uK. After RF evaporation, the atomic cloud is transferred to a crossed beams optical dipole trap (ODT). During evaporation in the ODT, the temperature is reduced below the critical temperature Tc=286nK, where condensation starts, and eventually reaches 40nK. As a result, a quasi-pure BEC with 1e5 87Rb atoms is formed. The complete sequence from the MOT loading to the BEC formation takes about 30s. Observations of the inversion of the aspect ratio of the cloud during free expansion and a bimodal velocity distribution prove quantum degeneracy. Presented in this thesis are the necessary background for understanding the experimental steps, a description of the schemes and technical details of our setup, and a characterizations of all the experimental steps.
A rapid atomic beam of rubidium (87Rb) is produced by two-dimensional magneto-optical trap (2D MOT), and then trapped by three-dimensional magneto-optical trap (3D MOT) with high vacuum for further cooling. After a process of optical molasses cooling, atoms are reloaded into a magnetic trap, where radio frequency (RF) evaporation cooling is implemented. The precooled atoms in the magnetic trap are then transferred into a far detuning optical dipole trap, where Bose-Einstein condensate (BEC) appears by further evaporation cooling. The 3D MOT is loaded to its maximum within 25 s and then BEC is prepared in 16 s. Due to the linear intensity of magnetic trap, the frequency can be scanned fast in the RF evaporation cooling process. In our experiment, the frequency scans from 39 MHz to 15 MHz in 6 s and then scans to 2 MHz in 5 s. The number of atoms in 3D MOT is about 11010, and there are 5105 atoms in the BEC after a succession of cooling processes. To optimize the performances of 2D MOT, a special light path is constructed. And prisms with high reflectivity are used to reduce the imbalance between opposite propagating cooling +beams. Furthermore, quarter-wave plates are used to keep the polarization state of the cooling beam when reflected by prisms or mirrors. The atoms are cooled to a temperature about 15 K in the magnetic trap by RF evaporation. In such a low temperature, the loss of magnetic trap (Majorana loss) will prevent the atoms from reaching a high density, and the atoms cannot be cooled further. To reduce the loss rate of the magnetic trap, the far blue detuning light (532 nm, 18 W) is added to plug the zero point of the magnetic trap. In the optically plugged magnetic trap, atoms with high density are cooled down enough, which gives a good start for the loading of optical dipole trap.