Constructing correlated spin states with neutral atoms in optical lattices

This thesis reports on the experimental investigation of controlled spin dependent interactions in a sample of ultracold Rubidium atoms trapped in a periodic optical potential. In such a situation, the most basic interaction between only two atoms at one common potential well, forming a micro laboratory for this atom pair, can be investigated. Spin dependent interactions between the atoms can lead to an intriguing time evolution of the system. In this work, we present two examples of such spin interaction induced dynamics. First, we have been able to observe and control a coherent spin changing interaction. Second, we have achieved to examine and manipulate an interaction induced time evolution of the relative phase of a spin 1/2-system, both in the case of particle pairs and in the more general case of N interacting particles. The first part of this thesis elucidates the spin-changing interaction mechanism underlying many fascinating effects resulting from interacting spins at ultracold temperatures. This process changes the spin states of two colliding particles, while preserving total magnetization. If initial and final states have almost equal energy, this process is resonant and leads to large amplitude oscillations between different spin states. The measured coupling parameters of such a process allow to precisely infer atomic scattering length differences, that e.g. determine the nature of the magnetic ground state of the hyperfine states in Rubidium. Moreover, a method to tune the spin oscillations at will based on the AC-Zeeman effect has been implemented. This allowed us to use resonant spin changing collisions as a quantitative and non-destructive particle pair probe in the optical lattice. This led to a series of experiments shedding light on the Bosonic superfluid to Mott insulator transition. In a second series of experiments we have been able to coherently manipulate the interaction induced time evolution of the relative phase in an ensemble of spin 1/2-systems. For two particles, interactions can lead to an entanglement oscillation of the particle pair. For the general case of N interacting particles, the ideal time evolution leads to the creation of spin squeezed states and even Schrödinger cat states. In the experiment we have been able to control the underlying interactions by a Feshbach resonance. For particle pairs we could directly observe the entanglement oscillations. For the many particle case we have been able to observe and reverse the interaction induced dispersion of the relative phase. The presented results demonstrate how correlated spin states can be engineered through control of atomic interactions. Moreover, the results point towards the possibility to simulate quantum magnetism phenomena with ultracold atoms in optical traps, and to realize and analyze many novel quantum spin states which have not been experimentally realized so far.

Patterns in and kinetics of phase separation in binary mixtures

This work focused mainly on two aspects of kinetics of phase separation in binary mixtures. In the first part, we studied the interplay of hydrodynamics and the phase separation of binary mixtures. A considerably flat container (a laterally extended geometry), at an aspect ratio of 14:1 (diameter: height) was chosen, so that any hydrodynamic instabilities, if they arise, could be tracked. Two binary mixtures were studied. One was a mixture of methanol and hexane, doped with 5% ethanol, which phase separated under cooling. The second was a mixture of butoxyethanol and water, doped with 2% decane, which phase separated under heating. The dopants were added to bring down the phase transition temperature around room temperature.rnrnAlthough much work has been done already on classical hydrodynamic instabilities, not much has been done in the understanding of the coupling between phase separation and hydrodynamic instabilities. This work aimed at understanding the influence of phase separation in initiating any hydrodynamic instability, and also vice versa. Another aim was to understand the influence of the applied temperature protocol on the emergence of patterns characteristic to hydrodynamic instabilities. rnrnOn slowly cooling the system continuously, at specific cooling rates, patterns were observed in the first mixture, at the start of phase separation. They resembled the patterns observed in classical Rayleigh-Bénard instability, which arises when a liquid continuously is heated from below. To suppress this classical convection, the cooling setup was tuned such that the lower side of the sample always remained cooler by a few millikelvins, relative to the top. We found that the nature of patterns changed with different cooling rates, with stable patterns appearing for a specific cooling rate (1K/h). On the basis of the cooling protocol, we estimated a modified Rayleigh number for our system. We found that the estimated modified Rayleigh number is near the critical value for instability, for cooling rates between 0.5K/h and 1K/h. This is consistent with our experimental findings. rnrnThe origin of the patterns, in spite of the lower side being relatively colder with respect to the top, points to two possible reasons. 1) During phase separation droplets of either phases are formed, which releases a latent heat. Our microcalorimetry measurements show that the rise in temperature during the first phase separation is in the order of 10-20millikelvins, which in some cases is enough to reverse the applied temperature bias. Thus phase separation in itself initiates a hydrodynamic instability. 2) The second reason comes from the cooling protocol itself. The sample was cooled from above and below. At sufficiently high cooling rates, there are situations where the interior of the sample is relatively hotter than both top and bottom of the sample. This is sufficient to create an instability within the cell. Our experiments at higher cooling rates (5K/h and above) show complex patterns, which hints that there is enough convection even before phase separation occurs. Infact, theoretical work done by Dr.Hayase show that patterns could arise in a system without latent heat, with symmetrical cooling from top and bottom. The simulations also show that the patterns do not span the entire height of the sample cell. This is again consistent with the cell sizes measured in our experiment.rnrnThe second mixture also showed patterns at specific heating rates, when it was continuously heated inducing phase separation. In this case though, the sample was turbid for a long time until patterns appeared. A meniscus was most probably formed before the patterns emerged. We attribute the reason of patterns in this case to Marangoni convection, which is present in systems with an interface, where local differences in surface tension give rise to an instability. Our estimates for the Rayleigh number also show a significantly lower number than that's required for RB-type instability.rnrnIn the first part of the work, therefore, we identify two different kinds of hydrodynamic instabilities in two different mixtures. Both are observed during, or after the first phase separation. Our patterns compare with the classical convection patterns, but here the origins are from phase separation and the cooling protocol.rnrnIn the second part of the work, we focused on the kinetics of phase separation in a polymer solution (polystyrene and methylcyclohexane), which is cooled continuously far down into the two phase region. Oscillations in turbidity, denoting material exchange between the phases are seen. Three processes contribute to the phase separation: Nucleation of droplets, their growth and coalescence, and their subsequent sedimentation. Experiments in low molecular binary mixtures had led to models of oscillation [43] which considered sedimentation time scales much faster than the time scales of nucleation and growth. The size and shape of the sample therefore did not matter in such situations. The oscillations in turbidity were volume-dominated. The present work aimed at understanding the influence of sedimentation time scales for polymer mixtures. Three heights of the sample with same composition were studied side by side. We found that periods increased with the sample height, thus showing that sedimentation time determines the period of oscillations in the polymer solutions. We experimented with different cooling rates and different compositions of the mixture, and we found that periods are still determined by the sample height, and therefore by sedimentation time. rnrnWe also see that turbidity emerges in two ways; either from the interface, or throughout the sample. We suggest that oscillations starting from the interface are due to satellite droplets that are formed on droplet coalescence at the interface. These satellite droplets are then advected to the top of the sample, and they grow, coalesce and sediment. This type of an oscillation wouldn't require the system to pass the energy barrier required for homogenous nucleation throughout the sample. This mechanism would work best in sample where the droplets could be effectively advected throughout the sample. In our experiments, we see more interface dominated oscillations in the smaller cells and lower cooling rates, where droplet advection is favourable. In larger samples and higher cooling rates, we mostly see that the whole sample becomes turbid homogenously, which requires the system to pass the energy barrier for homogenous nucleation.rnrnOscillations, in principle, occur since the system needs to pass an energy barrier for nucleation. The height of the barrier decreases with increasing supersaturation, which in turn is from the temperature ramp applied. This gives rise to a period where the system is clear, in between the turbid periods. At certain specific cooling rates, the system can follow a path such that the start of a turbid period coincides with the vanishing of the last turbid period, thus eliminating the clear periods. This means suppressions of oscillations altogether. In fact we experimentally present a case where, at a certain cooling rate, oscillations indeed vanish. rnrnThus we find through this work that the kinetics of phase separation in polymer solution is different from that of a low molecular system; sedimentation time scales become relevant, and therefore so does the shape and size of the sample. The role of interface in initiating turbid periods also become much more prominent in this system compared to that in low molecular mixtures.rnrnIn summary, some fundamental properties in the kinetics of phase separation in binary mixtures were studied. While the first part of the work described the close interplay of the first phase separation with hydrodynamic instabilities, the second part investigated the nature and determining factors of oscillations, when the system was cooled deep into the two phase region. Both cases show how the geometry of the cell can affect the kinetics of phase separation. This study leads to further fundamental understandings of the factors contributing to the kinetics of phase separation, and to the understandings of what can be controlled and tuned in practical cases. rn