Atomic Quantum Simulation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold">U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>Non-Abelian Lattice Gauge Theories

Banerjee, Debasish; Bögli, Michael; Dalmonte, Marcello; Rico, E.; Stebler, Pascal; Wiese, U.‐J.; Zoller, P.

doi:10.1103/physrevlett.110.125303

Cited by 282 publications

(274 citation statements)

References 45 publications

(69 reference statements)

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“…Using higher-order processes, plaquette interactions have also been constructed in this way. An alternative proposal is based on the rishon formulation of U(N) and SU(N) quantum link models [71]. This construction uses fermionic alkaline-earth atoms [102][103][104], such as 87 Sr or 173 Yb, hopping in an optical superlattice [105].…”

Section: Analog Quantum Simulators For U (N ) and Su (N ) Gauge Theoriesmentioning

confidence: 99%

“…Similarly, due to a severe sign problem, the deep interior of neutron stars, which may contain color superconducting quark matter [60,61] can currently not be addressed nonperturbatively from QCD first principles either. While it is difficult to predict when full QCD quantum simulations with cold atoms might become experimentally feasible, it is timely to work towards this long-term goal [62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Analog Quantum Simulators For U (N ) and Su (N ) Gauge Theoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2013

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“…An alternative analog proposal embodies the rishons of quantum link models with fermionic 87 Sr or 173 Yb alkalineearth atoms moving in an optical superlattice (c.f. Fig.3) [41]. The interactions between the atoms can be engineered Depending on its position in the optical lattice, an alkaline-earth atom either embodies a "quark" or a rishon.…”

Section: Quantum Simulators For Non-abelian Gauge Theoriesmentioning

confidence: 99%

“…Gauge invariance is protected by the internal S U(2I + 1) symmetry of the nuclear spin I of the atoms. Right: Real-time τ evolution of the chiral order parameter profile (ψψ) x in a U(2) gauge theory, mimicking the expansion of a hot "quark-gluon" plasma [41].…”

Section: Quantum Simulators For Non-abelian Gauge Theoriesmentioning

confidence: 99%

Towards quantum simulating QCD

Wiese

2014

Nuclear Physics A

103

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Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.

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“…Stimulated by the enormous progress made in experimental ultra-cold atomic systems, theoretical proposals have been made for quantum simulations of various physical systems and associated phenomena [2,3]. One such proposal is atomic quantum simulation of lattice gauge theories (LGTs) [4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

et al. 2016

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In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gaugeHiggs model at zero temperature, we perform Monte-Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time-evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.

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Atomic Quantum Simulation ofU(N)andSU(N)Non-Abelian Lattice Gauge Theories

Cited by 282 publications

References 45 publications

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

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

Towards quantum simulating QCD

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

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