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arXiv:1711.03777 · Physical Review A

Artificial magnetic-field quenches in synthetic dimensions

F. Yılmaz, Mehmet Özgür Oktel

Published Feb 7, 2018• 7 citations
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Abstract

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.

DOI
10.1103/physreva.97.023612

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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 nnn-leg ladder, is quenched to Hamiltonian with a vector potential parallel to the ladder, it splits into at most nnn smaller wave packets. The same initial wave packet splits into up to n2{n}^{2}n2 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.
Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.
Synthetic dimension is a potent tool in quantum simulation of topological phases of matter. Here we propose and demonstrate a scheme to simulate an anisotropic Harper-Hofstadter model with controllable magnetic flux on a two-leg ladder using the spin and motional states of a single trapped ion. We verify the successful simulation of this model by comparing the measured dynamics with theoretical predictions under various coupling strength and magnetic flux, and we observe the chiral motion of wave packets on the ladder as evidence of the topological chiral edge modes. We develop a quench path to adiabatically prepare the ground states for varying magnetic flux and coupling strength, and we measure the chiral current on the ladder for the prepared ground states, which allows us to probe the quantum phase transition between the Meissner phase and the vortex phase. Our work demonstrates the trapped ion as a powerful quantum simulation platform for topological quantum matter.
I will report on very recent experiments performed at LENS with ultracold 173Yb Fermi gases in artificial gauge fields. We have engineered Raman transitions between different 173Yb nuclear spin states to synthesize an effective lattice dynamics in a finite-sized “extra dimension”, which is encoded in the internal degree of freedom of the atoms [1]. By using this innovative approach, we have realized synthetic magnetic fields for effectively-charged fermions in ladder geometries with a variable number of legs. Direct imaging of the individual legs allowed us to demonstrate the emergence of chiral edge currents and to observe edge-cyclotron orbits propagating along the edges of the system [2], thus providing a direct evidence of a fundamental feature of quantum Hall physics in condensed-matter systems. A. Celi et al., Synthetic gauge fields in synthetic dimensions, Phys. Rev. Lett. 112, 043001 (2014). M. Mancini et al., Observation of chiral edge states with neutral fermions in a synthetic Hall ribbon, preprint arXiv:1502.02495 (2015). ∗Speaker †Corresponding author: fallani@lens.unifi.it sciencesconf.org:bec2015:67564
We describe a synthetic three-leg Hall ladder system with a tunable magnetic flux for neutral 173Yb^{173}\mathrm{Yb}173Yb atoms in a one-dimensional optical lattice. The ladder legs are formed by three hyperfine ground spin states of the atoms, and the complex interleg links are generated through Raman couplings between the spin states using multiple laser beams. The effective magnetic flux through a ladder plaquette $\ensuremath{\phi}$ is controlled by the angles of the Raman laser beams with the lattice axis. We investigate the quench dynamics of the Hall ladder system for $\ensuremath{\phi}\ensuremath{\approx}\frac{\ensuremath{\pi}}{3},\frac{\ensuremath{\pi}}{2},$ and $\frac{2\ensuremath{\pi}}{3}$ after a sudden application of the Raman coupling in various interleg link configurations. The semiclassical trajectory of the atoms in the plane of the spin composition and lattice position exhibits the characteristic motion of the effective magnetic field. In a tube configuration with the three legs cyclically linked, the quench evolution was observed to be substantially damped, which is attributed to the random flux threading the Hall tube.
Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long-range dipolar interactions on a two-leg ladder. We focus on the limit where the number of particles per site is large and the interactions are weak. Using two complementary variational approaches, we find rich physics driven by the long-range forces. Generically, long-range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. For example, nearest-neighbor interactions produce an interleg charge density wave phase, where the total density remains uniform but the density on each leg of the ladder is modulating in space, out of phase with one another. Next-nearest-neighbor interactions lead to a fully modulated biased ladder phase, where all of the particles are on one leg of the ladder. This state simultaneously breaks Z2{Z}_{2}Z2​ reflection symmetry and U(1)\mathrm{U}(1)U(1) translation symmetry. For values of the flux near $\ensuremath{\phi}=\ensuremath{\pi}$, we find a switching effect for arbitrarily weak interactions, where the density is modulated but the chiral current changes sign on every plaquette. Arbitrarily weak attractive interactions along the rungs destroy the Meissner phase completely, in favor of a modulated density wave phase. Remarkably, varying the rung to ladder hopping produces a cascade of first-order transitions between modulated density wave states with different wave vectors, which manifests itself as discrete jumps in the chiral current. Polarizing the dipoles along the ladder direction yields a region of phase space where a stable biased ladder phase occurs even at arbitrarily weak rung hopping. We discuss the experimental consequences of our work and draw connections between our work and recent experiments on cold atoms in synthetic dimensions.
The prospect of studying topological matter with the precision and control of atomic physics has driven the development of many techniques for engineering artificial magnetic fields and spin-orbit interactions. Recently, the idea of introducing nontrivial topology through the use of internal (or external) atomic states as effective "synthetic dimensions" has garnered attraction for its versatility and possible immunity from heating. We engineer tunable gauge fields through the local control of tunneling phases in an effective two-dimensional manifold of discrete atomic momentum states. We demonstrate the ability to create homogeneous gauge fields of arbitrary value, directly imaging the site-resolved dynamics of induced chiral currents. Furthermore, we engineer the first inhomogeneous artificial gauge fields for cold atoms, observing the magnetic reflection of atoms incident upon a step-like variation of an artificial vector potential. These results open new possibilities for the study of topological phases and localization phenomena in atomic gases.