Artificial Magnetic Field Quenches in Synthetic Dimensions

Recent cold atom experiments have realized models where each hyperfine state at an optical lattice site can be regarded as a separate site in a synthetic dimension. In such synthetic ribbon configurations, manipulation of the transitions between the hyperfine levels provide direct control of the hopping in the synthetic dimension. This effect was used to simulate a magnetic field through the ribbon. Precise control over the hopping matrix elements in the synthetic dimension makes it possible to change this artificial magnetic field much faster than the time scales associated with atomic motion in the lattice. In this paper, we consider such a magnetic flux quench scenario in synthetic dimensions. Sudden changes have not been considered for real magnetic fields as such changes in a conducting system would result in large induced currents. Hence, we first study the difference between a time varying real magnetic field and an artificial magnetic field using a minimal six site model. This minimal model clearly shows the connection between gauge dependence and the lack of on site induced scalar potential terms. We then investigate the dynamics of a wavepacket in an infinite two or three leg ladder following a flux quench and find that the gauge choice has a dramatic effect on the packet dynamics. Specifically, a wavepacket splits into a number of smaller packets. Both the weights and the number of packets depend on the implemented gauge. If an initial packet, prepared under zero flux in a n--leg ladder, is quenched to Hamiltonian with a vector potential parallel to the ladder; it splits into at most $n$ smaller wavepackets. The same initial packet splits up to $n^2$ packets if the vector potential is implemented to be along the rungs. Finally, we show that edge states in a thick ribbon are robust under the quench only when the same gap supports an edge state for the final Hamiltonian.