| Summary: | Motivated by the famous physicist Richard Feynman, we are eager to create a universal quantum simulator with ultracold atoms. Because of it's versatile controllability and clean environment, ultracold atomic system serves as a versatile plateform for imitating quantum systems with energy scale, time scale and length scale which is many orders of magnitude different. Oftentimes, it's very difficult to conduct direct experiment on the system to be simulated. Through the universality of the physics law, one could reproduce the same physical phenomena in another system which could be tested in a more convenience energy scale, time scale and length scale.
In this thesis, we demonstrate three different examples of quantum simulation. With the help of optical lattices, we measure the equation of states of two-dimensional Bose gases, create effective ferromagnetic domains, and also create roton quasi-particle in the atomic superfluid. The last two items rely on the technique of lattice shaking, and we are able to engineer atomic dispersion and create a double-well structure in the momentum space by dynamically modulating the lattice potential. We take advantage of the high resolution imaging system to study the effective ferromagnetism and many-body excitation in this system. The essential techniques we use include \textit{in situ} imaging, optical projection, Feshbach resonance, and optical lattice. An 1-$\mu$m imaging resolution is achieved by implementing an aberration-compensated objective which also allows projecting optical potentials crafted with a digital micromirror device. The Feshbach resonance and optical lattice, on the other hand, allows us tuning the interaction strength to a strongly interacting regime while keeping the gas stable. We first characterize the performance of static optical lattices by using it to enhance atomic interaction strength. From the weakly interacting regime to the strongly interacting regime, we study the critical behavior of two-dimensional Bose gas in the Berezinskii-Kosterlitz-Thouless transition and vacuum-to-superfluid transition. We compared the measurements of the critical points with different theoretical predictions. The scaling of the critical point deviates from the mean-field prediction but is still captured by the classical field theory in the strongly interacting regime.
Through dynamically modulating the phase of the optical lattice, we create an effective ferromagnetic system where the quasi-momentum of the atoms represents the pseudo-spin in the corresponding effective ferromagnetism. Using a shallow optical lattice and tuning the atomic scattering length to a small value help the system remain stable. The lifetime of the system is long enough for us to measure the susceptibility and observe formation of domains. We present the analysis of spin correlation function. From the spin correlation function, we find domain walls tend to align along the short axis of the cloud. We further investigate the many-body excitation spectrum with projection Bragg spectroscopy. The measurement reveals the existence of roton and maxon signatures in the dispersion. The roton and maxon energies scale with the chemical potential linearly which is an indication of many-body effect. The existence of roton leads to suppression of critical velocity of the system and is proved by a moving speckle experiment.
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