Time-of-flight patterns of ultracold bosons in optical lattices in various Abelian artificial magnetic field gauges

Abstract

We calculate the time-of-flight patterns of strongly interacting bosons confined in two-dimensional square lattice in the presence of an artificial magnetic field using quantum rotor model that is inherently combined with the Bogolyubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method let us to study cases of the artificial magnetic field being uniform, staggered or forming a checkerboard configuration. Effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The presented time-of-flight patterns may serve as a verification of chosen gauge in experiments, but also provide important hints on unconventional, non-zero momentum condensates, or possibility of observing graphene-like physics resulting from occurrence of Dirac cones in artificial magnetic fields in systems of ultra-cold bosons in optical lattices. Also, we elucidate on differences between effects of magnetic field in solids and the artificial magnetic field in optical lattices, which can be controlled on much higher level leading to effects not possible in condensed matter physics.

Spin-Orbit Coupling and Quantum Spin Hall Effect for Neutral Atoms without Spin Flips

“…Time-of-flight pictures will reveal the enlarged magnetic unit cell due to the synthetic magnetic field [48,[53][54][55]. Hall plateaus can be discerned in the density distribution [56].…”

Single-site-resolved measurement of the current statistics in optical lattices

“…These systems can be used to realize states that support equilibrium currents. Various methods have by now been proposed to detect interesting aspects of such systems, e.g., quantum Hall edge states and Chern numbers in topological insulators, using time-of-flight expansion [22][23][24][25][26], light scattering [27,28], or the time evolution of the real space density after a quench in the potential [29][30][31]. The protocol discussed below has similarities with the latter approach.…”

Real and Imaginary Part of Conductivity of Strongly Interacting Bosons in Optical Lattices

“…Next, the unimodular fields ζ i (τ ) = e i φi(τ ) can be introduced. Then, by relaxing the constraint of the unitary modulus [17,18], which introduces a Lagrange multiplier λ, the equation of state [12,19] and also the current-current correlation functions [13,[20][21][22][23] can be calculated.…”