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Synthetic magnetic fields for atoms and photons

Tena Dubček, Colin J. Kennedy, Ling Lü, Karlo Lelas, Dario Jukić, Robert Pezer, Wolfgang Ketterle, Marin Soljacic A, Hrvoje Buljan

Published Oct 28, 2016• 0 citations
OpenAlex

Abstract

We present our recent results in the rapidly developing field of synthetic magnetic fields for atoms and photons, in optical lattices and photonic structures, respectively. First, we show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three- dimensional optical lattices [1]. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions [1], which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected 'Fermi arc' surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well-within experimental reach with an extension of techniques recently used in ultracold gases [2]. We also present a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices [2]. The synthetic fields emerge from the nontrivial phases of the resulting tunneling matrix elements. The scheme is straightforward to implement at optical frequencies in optically induced one- and two- dimensional dielectric photonic lattices. We propose the implementation of the Harper- Hofstadter Hamiltonian in these photonic lattices [2]. [1] Dubcek et al., Phys. Rev. Lett. 114, 225301 (2015). [2] Dubcek et al., New Journal of Phys., New J. Phys. 17, 125002 (2015).

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We present our recent results in the rapidly developing field of synthetic magnetic fields for atoms and photons, in optical lattices and photonic structures, respectively. First, we show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three- dimensional optical lattices [1]. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions [1], which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected 'Fermi arc' surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well-within experimental reach with an extension of techniques recently used in ultracold gases [2]. We also present a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices [2]. The synthetic fields emerge from the nontrivial phases of the resulting tunneling matrix elements. The scheme is straightforward to implement at optical frequencies in optically induced one- and two- dimensional dielectric photonic lattices. We propose the implementation of the Harper- Hofstadter Hamiltonian in these photonic lattices [2]. [1] Dubcek et al., Phys. Rev. Lett. 114, 225301 (2015). [2] Dubcek et al., New Journal of Phys., New J. Phys. 17, 125002 (2015).
We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases.
Although Weyl semimetals have been extensively studied for exploring rich topological physics, the direct observation of the celebrated chiral magnetic effect (CME) associated with the so-called dipolar chiral anomaly has long intrigued and challenged physicists, still remaining elusive in nature.Here we propose a feasible scheme for experimental implementation of ultracold atoms that may enable us to probe the CME with a pure topological current in an artificial Weyl semimetal.The paired Weyl points with the dipolar chiral anomaly emerge in the presence of the well-designed spin-orbital coupling and laser-assisted tunneling.Both of the two artificial fields are readily realizable and highly tunable via current optical techniques using ultracold atoms trapped in threedimensional optical lattices, providing a reliable way for manipulating Weyl points in the momentum-energy space.By applying a weak artificial magnetic field, the system processes an auxiliary current originated from the topology of a paired Weyl points, namely, the pure CME current.This topological current can be extracted from measuring the center-of-mass motion of ultracold atoms, which may pave the way to directly and unambiguously observe the CME in experiments.
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.
The recent discovery of the Lorentz symmetry-violating ``type-II'' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed-matter systems. However, tuning the exceptional properties of this novel state has remained a challenge. Optical lattices, created using standing laser beams, provide a convenient platform to tune tunneling parameters continuously in time. In this paper, we propose a generalized two level system exhibiting type-II Weyl points that can be realized using ultracold atoms in an optical lattice. The system is engineered using a three-dimensional lattice with complex $\ensuremath{\pi}$ phase tunneling amplitudes. Various unique properties of the type-II Weyl semimetal such as open Fermi surface, anomalous chirality, and topological Fermi arcs can be probed using the proposed optical lattice scheme.
We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002)], as well as Meissner phases and vortex phases in double wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e., the Harper-Hofstadter model and the two-leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous Harper-Hofstadter model accessible with cold-atom experiments. For the minimal setup of a double wire, we explore how a subwavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar geometries such as cylinders, disks, and tori.
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.