Atom-optically synthetic gauge fields for a noninteracting Bose gas

AbstractSynthetic gauge fields in synthetic dimensions are now of great interest. This concept provides a convenient manner for exploring topological phases of matter. Here, we report on the first experimental realization of an atom-optically synthetic gauge field based on the synthetic momentum-state lattice of a Bose gas of 133Cs atoms, where magnetically controlled Feshbach resonance is used to tune the interacting lattice into noninteracting regime. Specifically, we engineer a noninteracting one-dimensional lattice into a two-leg ladder with tunable synthetic gauge fields. We observe the flux-dependent populations of atoms and measure the gauge field-induced chiral currents in the two legs. We also show that an inhomogeneous gauge field could control the atomic transport in the ladder. Our results lay the groundwork for using a clean noninteracting synthetic momentum-state lattice to study the gauge field-induced topological physics.

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Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: A density-matrix renormalization-group study

Physical Review A ◽

10.1103/physreva.89.063618 ◽

2014 ◽

Vol 89 (6) ◽

Cited By ~ 34

Author(s):

Marie Piraud ◽

Zi Cai ◽

Ian P. McCulloch ◽

Ulrich Schollwöck

Keyword(s):

Renormalization Group ◽

Density Matrix ◽

Optical Lattices ◽

Gauge Fields ◽

Density Matrix Renormalization Group ◽

Quantum Magnetism ◽

One Dimensional ◽

Density Matrix Renormalization ◽

Synthetic Gauge Fields

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Advances in synthetic gauge fields for light through dynamic modulation

Royal Society Open Science ◽

10.1098/rsos.172447 ◽

2018 ◽

Vol 5 (4) ◽

pp. 172447 ◽

Cited By ~ 5

Author(s):

Daniel Hey ◽

Enbang Li

Keyword(s):

Magnetic Field ◽

Gauge Field ◽

Time Reversal ◽

Higher Dimensions ◽

Gauge Fields ◽

Time Reversal Symmetry ◽

Topological Properties ◽

Dynamic Modulation ◽

Recent Developments ◽

Synthetic Gauge Fields

Photons are weak particles that do not directly couple to magnetic fields. However, it is possible to generate a photonic gauge field by breaking reciprocity such that the phase of light depends on its direction of propagation. This non-reciprocal phase indicates the presence of an effective magnetic field for the light itself. By suitable tailoring of this phase, it is possible to demonstrate quantum effects typically associated with electrons, and, as has been recently shown, non-trivial topological properties of light. This paper reviews dynamic modulation as a process for breaking the time-reversal symmetry of light and generating a synthetic gauge field, and discusses its role in topological photonics, as well as recent developments in exploring topological photonics in higher dimensions.

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Localization of quantum topology in the presence of matter and gauge fields

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887815500917 ◽

2015 ◽

Vol 12 (09) ◽

pp. 1550091

Author(s):

Farzaneh Atyabi

Keyword(s):

Boundary Condition ◽

Hilbert Space ◽

Gauge Field ◽

Quantum Particle ◽

Spectral Geometry ◽

Gauge Fields ◽

Fuzzy Topology ◽

One Dimensional ◽

Quantum Topology ◽

Large N

In this paper a toy model of quantum topology is reviewed to study effects of matter and gauge fields on the topology fluctuations. In the model a collection of N one-dimensional manifolds is considered where a set of boundary conditions on states of Hilbert space specifies a set of all topologies perceived by quantum particle and probability of having a specific topology is determined by a partition function over all the topologies in the context of noncommutative spectral geometry. In general the topologies will be fuzzy with the exception of a particular case which is localized by imposing a specific boundary condition. Here fermions and bosons are added to the model. It is shown that in the presence of matter, the fuzziness of topology will be dependent on N, however for large N the dependence is removed similar to the case without matter. Also turning on a particular background gauge field can overcome the fuzziness of topology to reach a localized topology with classical interpretation. It can be seen that for large N more opportunities can be provided for choosing the background gauge field to localize the fuzzy topology.

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Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

Light Science & Applications ◽

10.1038/s41377-020-00384-7 ◽

2020 ◽

Vol 9 (1) ◽

Cited By ~ 1

Author(s):

Yi Yang ◽

Bo Zhen ◽

John D. Joannopoulos ◽

Marin Soljačić

Keyword(s):

Quantum Hall ◽

Building Blocks ◽

Real Space ◽

Gauge Fields ◽

Spin Orbit ◽

Abelian Gauge ◽

Experimental Realization ◽

Integer Quantum Hall Effect ◽

Integer Quantum ◽

Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

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Nilpotent symmetries as a mechanism for Grand Unification

Journal of High Energy Physics ◽

10.1007/jhep05(2021)240 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Lars Andersson ◽

András László ◽

Błażej Ruba

Keyword(s):

Gauge Field ◽

Scalar Product ◽

Local Symmetry ◽

Matter Field ◽

Gauge Fields ◽

Spacetime Symmetries ◽

Invariant Scalar ◽

Spacetime Manifold ◽

Local Symmetries ◽

Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

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Correlations of stripe phase in one-dimensional spin-orbit coupled Bose gas

Physical Review Research ◽

10.1103/physrevresearch.3.023245 ◽

2021 ◽

Vol 3 (2) ◽

Author(s):

Clemens Staudinger ◽

Martin Panholzer ◽

Robert E. Zillich

Keyword(s):

Bose Gas ◽

Spin Orbit ◽

Stripe Phase ◽

One Dimensional

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Practical scheme for a light-induced gauge field in an atomic Bose gas

Physical Review A ◽

10.1103/physreva.79.011604 ◽

2009 ◽

Vol 79 (1) ◽

Cited By ~ 49

Author(s):

Kenneth J. Günter ◽

Marc Cheneau ◽

Tarik Yefsah ◽

Steffen P. Rath ◽

Jean Dalibard

Keyword(s):

Gauge Field ◽

Bose Gas ◽

Practical Scheme

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Non-Hermitian route to higher-order topology in an acoustic crystal

Nature Communications ◽

10.1038/s41467-021-22223-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

He Gao ◽

Haoran Xue ◽

Zhongming Gu ◽

Tuo Liu ◽

Jie Zhu ◽

...

Keyword(s):

Higher Order ◽

Order Topology ◽

Topological Phases ◽

Edge States ◽

Experimental Realization ◽

Artificial Materials ◽

Intrinsic Loss ◽

Topological Phases Of Matter ◽

Hierarchical Features ◽

Nontrivial Topology

AbstractTopological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.

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