By means of a diffusion Monte Carlo technique, we study one-dimensional unbalanced mixtures of fermionic ytterbium atoms (
173Yb and
171Yb). This means clusters in which the total number of
173Yb particles is different from the sum of all the atoms belonging to the
171Yb isotope. Our aim will be to check the possibility of having self-bound arrangements beyond the balanced compositions reported in previous literature rather than exploring all the situations in which that could be possible. In that vein, we focused mainly on mixtures in which the atoms belonging to one isotope are spin polarized, while the spins of the particles in the other isotope are evenly distributed in two sets. What we found was that, even though self-bound droplets are possible for different compositions, the most stable ones are clusters with a slight excess of attractively interacting
171Yb particles with different spins with respect to the number of spin-polarized
173Yb atoms. Clusters in which the number of repulsively interacting unequal-spin
173Yb atoms are in excess with respect to the spin-polarized
171Yb particles have a very narrow stability range.
A classical charged particle moves along a straight line and interacts with a silver atom in its ground state fixed at the origin of coordinates through Biot-Savart coupling. If the silver atom initially lies in a spin superposition state of valence electron, in the co-moving reference frame the projected measurements of the spin of silver’s valence electron along the z direction determine the moving direction of the charged particle. The projected measurements of that spin along the x or the y direction yield straight line motion versions of Schrödinger’s cat state for the charged particle. When the spin coherence state of the silver atom suffers from its environment decoherence, as long as the silver atom’s spin is entangled with the trajectories of the moving charged particle, the measurements on the silver atom’s spin also yield the partial superpositions of different trajectories of the moving charged particle. It is possible to control mechanical motion up to quantum level by the means of quantum measurements.
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 \nachieved to examine and manipulate an interaction\ninduced 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\noscillations 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.\nMoreover, 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 \ncollisions 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.\nIn 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\ninteractions 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.\nThe presented results demonstrate how correlated spin states can be engineered through \ncontrol of atomic interactions. Moreover, the results point towards the possibility to simulate quantum\nmagnetism 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.