Visualizing edge states with an atomic Bose gas in the quantum Hall regime

Stuhl, Benjamin; Lu, Hsin I; Aycock, Lauren; Genkina, Dina; Spielman, I. B.

doi:10.1126/science.aaa8515

Cited by 635 publications

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“…The HH model arises after time averaging the Floquet Hamiltonian, but it is an open question to what extent finite interactions and micromotion lead to transitions between Floquet modes and therefore heating [21][22][23][24]. Bose-Einstein condensation has been achieved in staggered flux configurations [15,25] and in small ladder systems [26,27] further highlighting its noted absence in the uniform field configuration.In this article, we report the first observation of BoseEinstein condensation in Hofstadter's butterfly. The presence of a superfluid state in the HH lattice allows us to analyze the symmetry of the periodic wavefunction by self-diffraction of coherent matter waves during ballistic expansion -analogous to a von Laue x-ray diffraction pattern, which reveals the symmetry of a lattice.…”

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Observation of Bose–Einstein condensation in a strong synthetic magnetic field

et al. 2015

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Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using gauge fields created by magnetic fields or spin orbit interactions which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created which are strong enough to realize the Harper-Hofstadter model. Despite many proposals and major experimental efforts, so far it has not been possible to prepare the ground state of this system. Here we report the observation of BoseEinstein condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution on the wavefuction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.Topological states of matter are an active new frontier in physics. Topological properties at the single particle level are well understood; however, there are many open questions when strong interactions and correlations are introduced [1, 2] as in the ν = 5/2 state of the fractional quantum Hall effect [3] and in Majorana fermions [4][5][6]. For neutral ultracold atoms, new methods have been developed to create synthetic gauge fields. Forces analogous to the Lorentz force on electons are engineered either through the Coriolis force in rotating systems [7][8][9], by phase imprinting via photon recoil [10][11][12][13][14], or lattice shaking [15,16]. Much of the research with ultracold atoms has focused on the paradigmatic HarperHofstadter (HH) Hamiltonian, which describes particles in a crystal lattice subject to a strong homogeneous magnetic field [17][18][19]. For magnetic fluxes on the order of one flux quantum per lattice unit cell, the radius of the smallest possible cyclotron orbit and the lattice constant are comparable, and their competition gives rise to the celebrated fractal spectrum of Hofstadfer's butterfly whose sub-bands have non-zero Chern numbers [20] and Dirac points.So far, it has not been possible to observe the ground state of the HH Hamiltonian, which for bosonic atoms is a superfluid Bose-Einstein condensate. It is unknown whether this is due to heating associated with technical noise, non-adiabatic state preparation, or inelastic collisions. These issues are complicated, since all schemes for realizing the HH Hamiltonian use some form of temporal lattice modulation and therefore are described by a time-dependent Floquet formalism. The HH model arises after time averaging the Floquet Hamiltonian, but it is an open question to what extent finite interactions and micromotion lead to transitions between Floquet modes and therefore heating [21][22][23][24]. Bose-Einstein condensat...

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Observation of Bose–Einstein condensation in a strong synthetic magnetic field

et al. 2015

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“…Some aspects of the current work have been explored in previous experiments, including the first atomic-gas simulations of the HarperHofstadter model 6,7 and observations of the chiral motion of particles in effective magnetic fields using synthetic dimensions [8][9][10][11] . But Tai and colleagues' study deepens our understanding of the interplay between interaction effects and the effective magnetic fields.…”

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Interactions propel a magnetic dance

LeBlanc

2017

Nature

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“…The synthetic implementation of this mechanism in cold atomic systems has been envisaged since the early days of quantum gases [1][2][3][4][5][6][7], and has been realized successfully during recent years [8][9][10][11][12][13]. Current quantum simulations with artificial gauge potentials are exploring the variety of interesting physics related to background gauge fields: spin liquid phases [14], topological phases evidenced by nonzero Chern numbers [15], or quantum Hall phases with edge currents [16,17]. A long-term goal is the simulation of quantum electromagnetism or chromodynamics, that is, of models where matter interacts with dynamical fields, as described in Refs.…”

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confidence: 99%

Topological phases of lattice bosons with a dynamical gauge field

et al. 2016

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Optical lattices with a complex-valued tunneling term have become a standard way of studying gauge-field physics with cold atoms. If the complex phase of the tunneling is made density dependent, such a system features even a self-interacting or dynamical magnetic field. In this paper we study the scenario of a few bosons in either a static or a dynamical gauge field by means of exact diagonalization. The topological structures are identified computing their Chern number. Upon decreasing the atom-atom contact interaction, the effect of the dynamical gauge field is enhanced, giving rise to a phase transition between two topologically nontrivial phases.

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Visualizing edge states with an atomic Bose gas in the quantum Hall regime

Cited by 635 publications

References 36 publications

Observation of Bose–Einstein condensation in a strong synthetic magnetic field

Observation of Bose–Einstein condensation in a strong synthetic magnetic field

Interactions propel a magnetic dance

Topological phases of lattice bosons with a dynamical gauge field

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