Measuring<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>topological invariants in optical lattices using interferometry

Grusdt, Fabian; Abanin, Dmitry A.; Demler, Eugene

doi:10.1103/physreva.89.043621

Cited by 64 publications

(59 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method can readily be applied to a variety of optical lattices and other physical settings such as polariton condensates [29]. Multiband extensions of this work can enable measurements of Wilson loops and off-diagonal (non-Abelian) Berry connections and thus provide a framework for the full determination of the geometric tensor of Bloch bands in periodic structures [30]. Controlled application of non-Abelian Berry phases would furthermore constitute a key step towards holonomic quantum computation [31].…”

mentioning

confidence: 99%

An Aharonov-Bohm interferometer for determining Bloch band topology

Duca

Reitter

et al. 2015

Science

274

281

View full text Add to dashboard Cite

The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular π Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space.More than thirty years ago, Berry [1] delineated the effects of the geometric structure of Hilbert space on the adiabatic evolution of quantum mechanical systems. These ideas have found widespread applications in science [2] and are routinely used to calculate the geometric phase shift acquired by a particle moving along a closed path-a phase shift that is determined only by the geometry of the path and is independent of the time spent en route. Geometric phases provide an elegant description of the celebrated Aharonov-Bohm effect [3], where a magnetic flux in a confined region of space influences the eigenstates everywhere via the magnetic vector potential. In condensed-matter physics, an analogous Berry flux in momentum space is responsible for various anomalous velocities and Hall responses [4] and lies at the heart of many-body phenomena ranging from quantum Hall physics [5] to topological insulators [6]. The Berry flux density (Berry curvature) is indeed essential to the characterization of an energy band and determines its topological invariants. However, mapping out the geometric structure of an energy band [7][8][9] has remained a major unresolved challenge for experiments.Here, we demonstrate a versatile technique for measuring geometric phases in reciprocal space using spin-echo interferometry with ultracold atoms [9, 10]. In contrast to typical solid state experiments, where all geometric effects are averaged over the Fermi sea, the use of a Bose-Einstein condensate (BEC) enables measurements with high momentum resolution. We exploit this resolution to directly detect the singular topological properties of an individual Dirac cone [11] in a graphene-type hexagonal optical lattice (see Fig. 1). Concentrated at the Dirac point is a π Berry flux, which is analogous to a magnetic flux generated by an infinitely narrow solenoid [12]. This localized flux gives rise to several striking properties of graphene, including the half-integer shift in the positions of quantum Hall plateaus [13,14], the phase of Shubnikov-de Haas oscillations [13,14], and the polarization dependence in photoemission spec...

show abstract

mentioning

confidence: 99%

An Aharonov-Bohm interferometer for determining Bloch band topology

Duca

Reitter

et al. 2015

Science

274

281

View full text Add to dashboard Cite

show abstract

“…4). Wilson loops can be directly measured [42,44] to experimentally test our prediction. Our scheme can also be applied to add SOC to the Haldane model [48,49] more closely resembling the situation considered in the Kane-Mele model [3].…”

Section: Soc In the Presence Of Magnetic Fieldsmentioning

confidence: 99%

“…The second leg of the Raman transition between bands |+ and |− of the same spin state is realized by near-resonant lattice shaking with frequency ω. This coupling is described by [42][43][44] …”

Section: General Proceduresmentioning

confidence: 99%

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

Grusdt

Bloch

et al. 2017

Phys. Rev. A

View full text Add to dashboard Cite

Spin-orbit coupling (SOC) is at the heart of many exotic band-structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of 2D SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with non-trivial spin textures closely related to the Kane-Mele model.

show abstract

“…In addition, our scheme can also realize complex operation, such as one spin state is pinned and the other spin state is moved to obtain Zak phase. Therefore, it provides a newly possible idea to detect the Z 2 topological invariants [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Interferometric detection of Chern numbers of Haldane model on bosonic optical lattices

Xu¹

2015

EPL

View full text Add to dashboard Cite

Topological states of matter emergent as a new type of quantum phases, which can be distinguished by their associated topological invariants, e.g., Chern numbers. Currently, there has increasing interests toward the physically detection of the new predicted topological phases. Here, we propose an interferometric approach to directly measure the Chern number in a topological optical lattice via detecting the associated Zak phases. We show that this interferometric approach can distinguish Zak phases of ±2π from 0 in the first Brillouin zone, and thus provides a new tool to directly detect the Chern number of topological systems. In addition, we demonstrate that this method is feasible under realistic experimental conditions and may generalize to detect topological systems with higher Chern numbers.

show abstract

MeasuringZ2topological invariants in optical lattices using interferometry

Cited by 64 publications

References 63 publications

An Aharonov-Bohm interferometer for determining Bloch band topology

An Aharonov-Bohm interferometer for determining Bloch band topology

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

Interferometric detection of Chern numbers of Haldane model on bosonic optical lattices

Contact Info

Product

Resources

About