Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.
We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature
Tc(H) of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated
XY model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments.
Tc(H) is found to exhibit a largest peak at the fraction of a flux quantum $f=\ensuremath{\varphi}/{\ensuremath{\varphi}}_{0}=1/2$ and a second-largest one at
f=1/3, in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated
XY model.
In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014); Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [Mancini et al. Science 349, 1510 (2015)] with a uniform flux were studied and different interesting many-body states were observed. Motivated by these experiments, we extend the uniform synthetic magnetic field to a periodic case and show that a commensurate synthetic magnetic field offers an alternative scheme to realize topological phases in many-body systems of ultracold Fermi gases in ladderlike optical lattices. Using the exact diagonalization, we numerically determine the topological band structure, edge states, nonzero Chern numbers, Hofstadter-butterfly-like spectrum, and a complete phase diagram of noninteracting fermionic ladders.