Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

Miyake, Hirokazu; Siviloglou, Georgios A.; Kennedy, Colin J.; Burton, William Cody; Ketterle, Wolfgang

doi:10.1103/physrevlett.111.185302

Cited by 1,073 publications

(928 citation statements)

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“…Other values of ϕ are also realizable. In contrast to previous setups [4][5][6][7], here the artificial magnetic field is not a static field imprinted by external laser beams, but dynamically emerges due to off-resonant scattering of pump light into the cavity mode. The resulting feedback mechanism between the rung tunneling process and the cavity field population leads to a selforganization of the system into a state in which the atoms are subjected to a strong artificial magnetic field.…”

mentioning

confidence: 97%

“…From the x-direction two different contributions can play an important role depending on the exact geometry of the optical lattices [4][5][6][7]. The first one is given by the direct overlap integral between the Wannier functions of the two wells and the cavity mode function cos (k c x):…”

Section: Bogolioubov Transformationmentioning

confidence: 99%

“…The quantum nature of the extended cavity field could lead to an effective (dissipative) long-range interaction between the fermions which could accelerate and stabilize the formation of the correlations. A generalization of the discussed setup to a two-dimensional system [5,6] and to interacting fermionic atoms can be envisaged and will be the subject of further investigations.…”

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confidence: 99%

“…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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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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confidence: 97%

Section: Bogolioubov Transformationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

et al. 2016

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“…The realization of the Hofstadter model in two dimensions [66][67][68][69] or on a ladder geometry [70] and of the Haldane model [71] have enabled the investigation of topological insulators in quantum gases.…”

Section: Introductionmentioning

confidence: 99%

Cavity-induced chiral states of fermionic quantum gases

2016

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We investigate ultra-cold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.

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Quanten‐Hall‐Physik mit ultrakalten Atomen

Aidelsburger

2015

Physik in unserer Zeit

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Der Quanten‐Hall‐Effekt bezeichnet das Auftreten großer stabiler Plateaus in einer Hall‐Widerstands‐Messung. Die Werte dieser Plateaus sind aufgrund der topologischen Eigenschaften des Systems außerordentlich robust und werden durch ganze Zahlen, sogenannte Chern‐Zahlen, beschrieben. In unserer Arbeitsgruppe wurde erstmals eine solche Chern‐Zahl in einem nicht‐elektronischen System aus ultrakalten Atomen experimentell bestimmt.

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Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

Cited by 1,073 publications

References 45 publications

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

Cavity-induced chiral states of fermionic quantum gases

Quanten‐Hall‐Physik mit ultrakalten Atomen

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