Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice

Aidelsburger, Monika; Atala, Marcos; Nascimbène, Sylvain; Trotzky, Stefan; Chen, Yu-Ao; Bloch, Immanuel

doi:10.1103/physrevlett.107.255301

Cited by 757 publications

(934 citation statements)

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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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“…Experimentally, cold atoms' unique controllability was employed to observe dynamical localisation and phase-coherence in strongly shaken bosonic systems [19][20][21][22][23][24] . This paved the way towards generating extremely strong artificial magnetic fields 25 in lattice models, which recently culminated in the realisation of the Harper-Hofstadter model 26,27 , the Quantum Spin Hall Effect 28,29 , and Floquet topological insulators 30,31 .…”

Section: Introductionmentioning

confidence: 99%

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

Bukov

Polkovnikov

2014

Phys. Rev. A

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We study the stroboscopic and non-stroboscopic dynamics in the Floquet realization of the HarperHofstadter Hamiltonian. We show that the former produces the evolution expected in the highfrequency limit only for observables which commute with the operator to which the driving protocol couples. On the contrary, non-stroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the number operator following a quantum cyclotron orbit on a 2 × 2 plaquette, as well as the chiral current operator flowing along the legs of a 2 × 20 ladder. The exact evolution is compared with its stroboscopic and non-stroboscopic counterparts, including finite-frequency corrections.

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“…A most exciting development are synthetic background gauge fields, in order to access, for example, the fractional quantum Hall effect or topological insulators with atoms. Such synthetic gauge fields can mimic an external magnetic field [41][42][43][44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

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Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

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Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice

Cited by 757 publications

References 32 publications

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

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

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

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