28p-L-3 Motion of an Electron Wave Packet in a Scalar Potential and a Magnetic Field

Thai Quang

F. Suekane

Hideo Tsuru, Takeshi Kobayashi

Wave packet motions of a single electron in harmonic potentials or a magnetic field are obtained analytically. The phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the electron changes its width and central position periodically. These results are visualized using computer animation techniques.

Hideo Tsuru

A motion of a Gaussian wave packet of a single electron in a uniform magnetic field is obtained by solving the time dependent Schrödinger equation analytically. The wave packet moves changing its width and central position periodically. The period of the change of the width is the same as that of the central position. The interpretation of these periodic changes in terms of the Green's function which can be derived by the path integration formulation is also discussed.

K.-J. KIM

F. Yılmaz, Mehmet Özgür Oktel

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 wave packet 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 wave packet splits into a number of smaller packets moving with different velocities. Both the weights and the number of packets depend on the implemented gauge. If an initial packet, prepared under zero flux in an $n$-leg ladder, is quenched to Hamiltonian with a vector potential parallel to the ladder, it splits into at most $n$ smaller wave packets. The same initial wave packet splits into up to ${n}^{2}$ packets if the vector potential is implemented to be along the rungs. Even a trivial difference in the gauge choice such as the addition of a constant to the vector potential produces observable effects. We also calculate the packet weights for arbitrary initial and final fluxes. 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.