Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices

Aidelsburger, Monika; Atala, Marcos; Lohse, Michael; Barreiro, Julio T.; Paredes, B.; Bloch, Immanuel

doi:10.1103/physrevlett.111.185301

Cited by 1,365 publications

(1,810 citation statements)

References 51 publications

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“…Such artificial magnetic fields have been used in quantum gases confined to optical lattices to realize two showcase models of topologically insulating phases, the Hofstadter model in two-dimensions [4][5][6][7] or on a ladder geometry [8] and the Haldane model [9].…”

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confidence: 99%

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

et al. 2016

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We show how a fermionic quantum gas in an optical lattice and coupled to the field of an optical cavity can self-organize into a state in which the spontaneously emerging cavity field amplitude induces an artificial magnetic field. The fermions form either a chiral insulator or a chiral liquid carrying edge currents. The feedback mechanism via the cavity field enables robust and fast switching of the edge currents and the cavity output can be employed for non-destructive measurements of the atomic dynamics. The controlled generation of topologically non-trivial quantum phases is of greatest interest since they possess special properties such as extended edge states that can be well protected against destructive environmental effects[1]. Thus, materials with topological non-trivial properties have the prospect to be utilized for quantum devices and quantum computing. Well known are topological insulators with protected edge currents created in quantum Hall devices [2] by strong magnetic fields.For neutral atoms strong artificial magnetic fields can be created [3] which act similarly as magnetic fields for charged particles. Such artificial magnetic fields have been used in quantum gases confined to optical lattices to realize two showcase models of topologically insulating phases, the Hofstadter model in two-dimensions [4][5][6][7] or on a ladder geometry [8] and the Haldane model [9].Yet, the dynamic control and detection of topologically non-trivial quantum states remains a great challenge. In order to overcome this difficulty, in this work the dynamical feedback between atoms and an optical cavity is employed to reach a self-organization of topologically non-trivial phases. One fascinating example for a selforganization of a coupled atom-cavity system has been realized recently by placing a bosonic quantum gas into an optical high-finesse resonator subjected to a perpendicular off-resonant pump beam [10][11][12][13][14]. Above a critical pump strength, the occupation of the cavity mode is stabilized and the bosonic atoms organize into a checkerboard density pattern [12]. Many different proposals have been put forward to realize the self-organization of more complex quantum phases [13] reaching from the Mott-insulator [15] over fermionic phases [16][17][18][19][20] and disordered structures [21][22][23][24] to phases with spin-orbit coupling [25][26][27].In this work, we engineer a direct coupling mechanism of the cavity photons to the tunneling of atoms in an optical lattice. This is achieved using a Raman transition induced by the combination of a transverse pump beam and the cavity field (Fig. 1). The frequencies of the pump beam and the cavity mode are chosen such that the energy transfer is close to the energy offset between neigh- boring lattice sites. The resulting process represents an effective tunneling of the atoms. Due to the running-wave nature of the pump beam, a phase ϕ can be imprinted onto the tunneling of the atoms around a plaquette in the presence of cavity photons. We demonstrate that due t...

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Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

et al. 2016

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“…Treating interactions in such a non-perturbative way is difficult in periodically-driven systems [5][6][7][8][9][10], which have received unprecedented attention following the realisation of dynamical localisation [11][12][13][14][15], artificial gauge fields [16][17][18][19][20][21][22], models with topological [23][24][25][26][27][28] and statedependent [29] bands, and spin-orbit coupling [30,31]. In this paper, we consider strongly-interacting periodicallydriven systems and show how the SWT can be extended to derive effective static Hamiltonians of non-equilibrium setups.…”

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confidence: 99%

“…2, inset), where φ j = φ mn = Φ (m + n), σ ∈ {↑, ↓} ≡ {1, −1}, and we denote the square-lattice position by r j = (m, n). Such spin-sensitive drives are realised in experiments via the Zeeman effect using a periodically-modulated [29] and static [19,20] magnetic-field gradients which couple to atomic hyperfine states. For this protocol,…”

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confidence: 99%

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

2016

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We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.

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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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confidence: 99%

“…Bialas and colleagues investigated previously established mouse models of lupus in which there is activation of the type I interferon response 6 . The authors observed that such mice show significant neurological deficits, including poor performance on cognitive and behavioural tasks compared with wildtype animals.…”

Section: S a R A H M C G L A S S O N And Dav I D H U N Tmentioning

confidence: 99%

Interactions propel a magnetic dance

LeBlanc

2017

Nature

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Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices

Cited by 1,365 publications

References 51 publications

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

Interactions propel a magnetic dance

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