We investigate the ground state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction ν = 1/2. We find that our system supports topologically ordered states by calculating the topological entanglement entropy, and its value is in good agreement with the theoretical value for the ν = 1/2 Laughlin state. By exploring the behaviour of the density profiles, edge currents and single-particle correlation functions, we find that the ground state on the cylinder shows all signatures of a fractional quantum Hall state even for large values of the magnetic flux density. Furthermore, we determine the dependence of the correlation functions and edge currents on the interaction strength. We find that depending on the magnetic flux density, the transition towards Laughlin-like behaviour can be either smooth or happens abruptly for some critical interaction strength.arXiv:1901.03595v2 [cond-mat.mes-hall]

We use state-of-the-art density matrix renormalization group calculations in the canonical ensemble to determine the phase diagram of the dipolar Bose-Hubbard model on a finite cylinder. We consider several observables that are accessible in typical optical lattice setups and assess how well these quantities perform as order parameters. We find that, especially for small systems, the occupation imbalance is less susceptible to boundary effects than the structure factor in uncovering the presence of a periodic density modulation. By analysing the non-local correlations, we find that the appearance of supersolid order is very sensitive to boundary effects, which may render it difficult to observe in quantum gas lattice experiments with a few tens of particles. Finally, we show how density measurements readily obtainable on a quantum gas microscope allow distinguishing between superfluid and solid phases using unsupervised machine-learning techniques. arXiv:1909.09099v1 [cond-mat.quant-gas]

We study the influence of photons on the dynamics and the ground state of the atoms in a Bosonic Josephson junction inside an optical resonator. The system is engineered in such a way that the atomic tunneling can be tuned by changing the number of photons in the cavity. In this setup the cavity photons are a new means of control, which can be utilized both in inducing selftrapping solutions and in driving the crossover of the ground state from an atomic coherent state to a Schrödinger's cat state. This is achieved, for suitable setup configurations, with interatomic interactions weaker than those required in the absence of cavity. This is corroborated by the study of the entanglement entropy. In the presence of a laser, this quantum indicator attains its maximum value (which marks the formation of the cat-like state and, at a semiclassical level, the onset of self-trapping) for attractions smaller than those of the bare junction.