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arXiv:1403.5915 · Physical Review A

Generation of uniform synthetic magnetic fields by split driving of an optical lattice

C. E. Creffield, Fernando Sols

Published Aug 29, 2014• 21 citations
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Abstract

We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on quickly alternating two Hamiltonians to engineer the appropriate Aharonov-Bohm phases, and permits the simulation of a uniform tunable magnetic field. We explicitly demonstrate that our split-driving scheme reproduces the behavior of a charged quantum particle in a magnetic field over the complete range of field strengths, and obtain the Hofstadter butterfly band structure for the Floquet quasienergies.

DOI
10.1103/physreva.90.023636

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We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on quickly alternating two Hamiltonians to engineer the appropriate Aharonov-Bohm phases, and permits the simulation of a uniform tunable magnetic field. We explicitly demonstrate that our split-driving scheme reproduces the behavior of a charged quantum particle in a magnetic field over the complete range of field strengths, and obtain the Hofstadter butterfly band structure for the Floquet quasienergies.
We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential, we engineer spatially dependent complex tunneling amplitudes. Thereby, atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal-symmetric Hamiltonian underlying the quantum spin Hall effect; i.e., two different spin components experience opposite directions of the magnetic field.
We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the "dimension" provided by the internal atomic degrees of freedom, yielding a synthetic two-dimensional lattice. Suitable laser coupling between these internal states leads to a uniform magnetic flux within the two-dimensional lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter-butterfly spectrum and the chiral edge states of the associated Chern insulating phases.
A two-dimensional Fock-state lattice (FSL) is constructed from the many-body states of two interacting two-mode quantum gases. By periodically driving the interspecies interactions and pulsing the tunneling between the two modes of each gas, a synthetic gauge field is generated. We derive an effective Hamiltonian in the short pulse limit which resembles the Harper-Hofstadter Hamiltonian where the magnetic flux per plaquette is controlled by the ratio of the interaction energy and the driving frequency. The quasispectrum of the Floquet operator of the driving sequence shows the celebrated Hofstadter's butterfly pattern as well as the existence of edge states. From the calculation of the local Chern marker, we establish that the FSL has nontrivial topology and by simulating the dynamics of the edge states, show that they exhibit chirality. Finally, the inclusion of intraspecies interactions creates an overall harmonic trap in the lattice and introduces the nonlinear effect of macroscopic quantum self-trapping, which is shown to hinder movement along the edges of the lattice. This work introduces an avenue to explore synthetic gauge fields and the link between condensed matter systems and quantum gases.
Abstract Topological many-body phases of matter exhibit remarkable electronic properties and ultracold atoms in optical lattices constitute promising candidates to study them in a well-controlled environment. In two-dimensional (2D) electron gases topological phases may emerge in the presence of strong magnetic fields. This situation is not directly applicable to cold atoms because they are charge neutral. Therefore, novel experimental techniques have been developed to engineer novel lattice systems, whose Hamiltonian is formally equivalent to the one of charged particles in magnetic fields. In this Tutorial, we introduce a paradigmatic topological lattice model, the Hofstadter model, and explain how it can be implemented with ultracold atoms using laser-assisted tunneling. The technique is based on imprinting phases on the tunneling matrix elements using additional laser beams. These phases are reminiscent of Aharonov–Bohm phases and can be interpreted as a magnetic flux piercing the lattice unit cell. We present experimental results on the cyclotron-like dynamics of neutral atoms in isolated four-site square plaquettes and discuss the first measurement of a 2D topological invariant, the Chern number, in artificially generated Hofstadter bands. The work presented in this Tutorial was one of the four shortlisted finalists of the 2016 DPG SAMOP dissertation prize.
Synthetic gauge fields with ultracold atoms offer a route to quantum matter in which electromagnetic environments can be designed rather than merely imposed. While the Harper-Hofstadter model has been realized in several cold-atom systems, existing implementations are largely limited to spatially uniform magnetic fluxes. Here we experimentally realize a highly programmable two-dimensional momentum-state lattice of ultracold atoms with local control over the Peierls phase pattern, enabling direct implementation of Harper-Hofstadter Hamiltonians with tunable and spatially structured synthetic gauge fields. We observe a crossover from ballistic to strongly flux-modified bulk dynamics with suppressed transport. By introducing a synthetic electric field through site-dependent energy gradients, we further demonstrate Hall-type transverse drift arising from the interplay between electric and magnetic fields. In addition, we engineer a synthetic flux domain wall separating regions with opposite magnetic fluxes and observe anisotropic propagation guided along the interface. These results move cold-atom gauge-field engineering from uniform magnetic backgrounds toward designer gauge textures, providing an experimental setting for transport across programmable topological interfaces.