The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.
The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.
In this thesis, we develop, validate and apply a non-destructive, spin-sensitive probing method for ultracold gases of sodium. By exploiting the polarization dependence of the atom-light interaction, the method combines optical hardware with computational reconstruction to access spin-resolved density and magnetization distributions from a single, minimally destructive exposure. The thesis is structured in three parts; firstly, we describe the experimental platform for making, probing and manipulating sodium spinor Bose–Einstein condensates, including laser cooling, optical and magnetic trapping, and radio-frequency techniques for coherent spin preparation. In the second part, we develop the core measurement technique of spin-dependent off-axis holography is developed, and evaluate its robustness to technical noise and the magnetic field variations. The reconstruction and analysis pipeline is presented in detail, with special emphasis on the background noise suppression using an inpainting technique based on principal component analysis. In the final part, the method is applied to investigate dynamics in spin-1 ultracold atomic sodium. To that end, we introduce the theory of three-level spin systems and propose magnetization-preparation and precise Zeeman-sublevel readout schemes, which are experimentally verified. These tools are then used to investigate spin diffusion and spin mixing dynamics, and the formation and evolution of spin domains. This work establishes spin-dependent off-axis holography as a powerful tool for probing spinor quantum gases. The techniques developed here enable efficient and minimally destructive imaging of spin dynamics, and provide new opportunities for studying non-equilibrium spin phenomena and magnetism in ultracold atomic systems.
In this thesis, we develop, validate and apply a non-destructive, spin-sensitive probing method for ultracold gases of sodium. By exploiting the polarization dependence of the atom-light interaction, the method combines optical hardware with computational reconstruction to access spin-resolved density and magnetization distributions from a single, minimally destructive exposure. The thesis is structured in three parts; firstly, we describe the experimental platform for making, probing and manipulating sodium spinor Bose–Einstein condensates, including laser cooling, optical and magnetic trapping, and radio-frequency techniques for coherent spin preparation. In the second part, we develop the core measurement technique of spin-dependent off-axis holography is developed, and evaluate its robustness to technical noise and the magnetic field variations. The reconstruction and analysis pipeline is presented in detail, with special emphasis on the background noise suppression using an inpainting technique based on principal component analysis. In the final part, the method is applied to investigate dynamics in spin-1 ultracold atomic sodium. To that end, we introduce the theory of three-level spin systems and propose magnetization-preparation and precise Zeeman-sublevel readout schemes, which are experimentally verified. These tools are then used to investigate spin diffusion and spin mixing dynamics, and the formation and evolution of spin domains. This work establishes spin-dependent off-axis holography as a powerful tool for probing spinor quantum gases. The techniques developed here enable efficient and minimally destructive imaging of spin dynamics, and provide new opportunities for studying non-equilibrium spin phenomena and magnetism in ultracold atomic systems.
This thesis features fundamental experiments on the coherence properties of Bose-Einstein condensates (BEC) and atom lasers, made possible by a newly developed apparatus combining a Bose-Einstein condensate with an ultrahigh nesse optical cavity.Using the cavity as a single atom detector, atoms extracted from a trapped cloud are detected with unprecedented sensitivity, and the rst time-resolved counting of single atoms from a quantum degenerate source was demonstrated.O-diagonal long-range order is a dening property of a BEC and equivalent to longrange phase coherence.Its formation is a complex process accompanied by spontaneous symmetry breaking.We witnessed this formation in an ultracold cloud of 87 Rb atoms crossing the phase transition of BEC.Two overlapping atomic beams originating from dierent positions inside the condensate propagated downwards into the cavity.They showed a matter wave interference pattern with a visibility determined by the coherence of the probed regions.The modulation of the ux of atoms, recorded with single-atom resolution, yields the visibility, whereas its mean value gives information about the density of the sample.By shock cooling, a cloud of atoms was prepared in a highly nonequilibrium state slightly above the phase transition.While the ensemble subsequently relaxed, it crossed the phase transition into an equilibrium with a small condensate fraction.Employing our minimally invasive measurement method, the growth of both the rst-order coherence and the density of the sample was tracked in real time while the system crossed the phase transition.The growth of the coherence was found to start later, proceed faster and nish earlier than the increase in density.The coherent region increased at one fth of the speed of sound.Employing time-resolved single atom counting with the cavity detector, the full counting statistics of an atom laser beam was recorded.In a Hanbury Brown and Twiss type experiment, the second-order correlation function was found to be constant g (2) (τ ) = 1.00±0.01,proving the atom laser's second-order coherence and the absence of excess intensity uctuations that were observed in a pseudothermal beam.An analysis of the time interval distributions of atoms in the beam conrmed these ndings.The iii
Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
This thesis is primarily a comprehensive discussion of the development of two experimental studies: the quantum transport and effects of heating of ultracold atoms. It specifically provides details of the manipulation and control of ultracold atoms in magnetic waveguides, optical lattices, and optical billiards. The design, construction, and implementation of experimental apparati are also outlined and additional experimental tests are summarized, including the realization of a macroscopic transport (> 20 cm) system for ultracold atoms and transmission of ultracold atoms through a random optical potential. The first experiment is a study of the quantum transport for atoms confined in a periodic potential. These results include a comparison made of thermal and BEC initial conditions. Here, observation of ballistic transport is made for all values of well depth and initial conditions, and the expansion rates for thermal atoms are shown to be in excellent agreement with a singleparticle model. For weak wells (V0/ER ≤ 6), the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature model based on single (non-interacting) particle theory. For deep wells (V0/ER ≥ 6), a crossover is observed to a new regime for the BEC case, indicating the importance of interactions on quantum transport. The second experiment is a study of the effect of different heating rates on a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the BoseEinstein condensate fraction and an exponential decay in phase space density.
In this habilitation-thesis a collection of 14 experiments is presented. In these experiments we have developed and used novel techniques to control ultracold gases on the quantum level. In brief, Bose-Einstein condensates (BEC) and degenerate Fermi gases of laser-cooled alkali atoms are subjected to specially designed optical and magnetic fields. The fields influence in a coherent way the behavior, properties and dynamics of the gases. On this basis we developed tools to prepare, coherently manipulate, and analyze pre-defined quantum states. With this high level of control, it was possible to investigate interesting physics phenomena, and we were able to achieve several breakthroughs in the field of ultracold atoms. Highlights of our experimental results include the demonstration of phase engineering of a BEC wavefunction where we created solitons in a BEC and studied their propagation. In another experiment we constructed a spatially resolved matter wave interferometer with which we mapped out the phase distribution on a condensate. Illuminating the BEC with a periodic pattern, i.e. an optical lattice, allowed us to study solid states physics phenomena. In a second set of experiments we demonstrated optically tuning of the interaction between atoms with optical Feshbach resonances. Employing either magnetically tunable Feshbach resonances or laser radiation, we were able to produce ground state molecules in well defined quantum states. This led to the production of the first molecular BEC. By tuning the coupling of atom pairs in a Fermi gas of atoms, we could for the first time investigate the so-called BEC-BCS crossover which describes the continuous change from a BEC superfluid to a Bardeen-Cooper Schrieffer (BCS) superfluid. Due to the excellent control on the quantum level, the developed cold atom techniques open up intriguing prospects for future applications and experiments. They represent a general tool box to investigate fundamental physical phenomena in a pure and undisturbed environment. In the future, cold atoms might serve as a testing ground for fundamental theories or as quantum simulators for complex systems.