Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms

Jaksch, Dieter; Zoller, P.

doi:10.1088/1367-2630/5/1/356

Cited by 776 publications

(1,128 citation statements)

References 24 publications

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“…This is precisely what Lin and colleagues 2 achieved in their ingenious experimental set-up, which is an inspired realization of earlier proposals [3][4][5][6] . Using a pair of laser beams, they first imprinted the equivalent of a river's uniform flow -a uniform vector potential -on their ultracold cloud of atoms 7,8 .…”

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confidence: 70%

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Neutral atoms put in charge

Zwierlein¹

2009

Nature

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An elegant experiment shows that atoms subjected to a pair of laser beams can behave like electrons in a magnetic field, as demonstrated by the appearance of quantized vortices in a neutral superfluid.Ultracold gases of atoms -a million times thinner than air and a million times colder than interstellar space -allow the observation and control of many-body quantum physics at macroscopic scales. They can thus serve as model materials 1 for condensed-matter systems where such quantum behaviour dominates. From frictionless flow in superfluids to inhibited transport in insulators and from weakly to strongly interacting systems, an extreme variety of fundamental states of matter can be realized in ultracold atomic gases in real time and with the precision of atomic physics. But there seems to be one obvious limitation: atoms are neutral, a fact that in principle precludes the observation of a wealth of phenomena tied to the behaviour of charged particles, for example their behaviour in a magnetic field. On page 000 of this issue, Lin et al. 2 get round this problem and demonstrate in a striking fashion their ability to create synthetic magnetic fields for a neutral ultracold atomic system -A collective state of matter termed a Bose-Einstein condensate develops mini-tornadoes known as quantized vortices. velocity (blue arrows) does not rotate. b, If the water flows non-uniformly and in a different direction on one side of the paddle wheel from that on the other, the wheel rotates (green arrow). The flow pattern is analogous to the 'vector potential' created in Lin and colleagues' experiment 2 to generate a synthetic magnetic field for an ultracold cloud of atoms known as a Bose-Einstein condensate. The rotation axis (purple arrow) and the speed with which the paddle wheel rotates correspond respectively to the direction and strength of the magnetic field. c, d, Images of the BoseEinstein condensate before (c) and after (d) application of the synthetic magnetic field. The appearance of quantized vortices (d) is a direct demonstration of a synthetic magnetic field.

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confidence: 70%

“…Future applications of their method might include the measurement of the superfluid fraction in ultracold atomic gases 11 and the realization of unusual quantum states in two-dimensional optical lattices at high effective fields 5 . The demonstration of quantum Hall physics in such lattices 6 using the authors' approach might also be within reach.…”

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confidence: 99%

Neutral atoms put in charge

Zwierlein¹

2009

Nature

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“…The discovery of the integer and fractional quantum Hall effects in the 1980s has led to a new paradigm, where quantum phases of matter are characterized by the topology of their ground-state wavefunctions. Since then, topological phases have been identified in physical systems ranging from condensed-matter [2][3][4][5][6][7][8][9] and high-energy physics 10 to quantum optics 11 and atomic physics [12][13][14][15] .…”

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Observation of topologically protected bound states in photonic quantum walks

et al. 2012

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Topological phases exhibit some of the most striking phenomena in modern physics. much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems-notably in photonics, where wavefunctions can be observed directly-provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations-a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

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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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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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Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms

Cited by 776 publications

References 24 publications

Neutral atoms put in charge

Neutral atoms put in charge

Observation of topologically protected bound states in photonic quantum walks

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

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