Detection of topological matter with quantum gases

Spielman, I. B.

doi:10.1002/andp.201300110

Cited by 21 publications

(17 citation statements)

References 50 publications

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“…A similar π flux also plays a crucial role in the nuclear dynamics of molecules featuring conical intersections of energy surfaces [2]. Our direct detection of the paradigmatic π flux demonstrates the capability to reveal even singular Berry flux fea- tures that are not observable by alternative techniques based on transport measurements [7,8,[17][18][19] and thereby paves the way to full topological characterization of optical lattice systems [18][19][20][21][22][23][24][25]. The effect of Berry curvature in our interferometer is analogous to the Aharonov-Bohm effect, where an electron wavepacket is split into two parts that encircle a given area arXiv:1407.5635v1 [cond-mat.quant-gas] 21 Jul 2014 The duration of the interferometer sequence is 2τ = 1.6 ms for all measurements.…”

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confidence: 87%

An Aharonov-Bohm interferometer for determining Bloch band topology

Duca

Reitter

et al. 2015

Science

274

281

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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...

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confidence: 87%

An Aharonov-Bohm interferometer for determining Bloch band topology

Duca

Reitter

et al. 2015

Science

274

281

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“…By comparing to what would have happened in the symmetric gauge, we showed that the gauge choice can make a significant difference in the experimental outcome. In the future, techniques that match a system's geometry to the artificial field's natural gauge might be used to selectively excite edge modes in cold-atom quantum-Hall-like systems [18][19][20].…”

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confidence: 99%

Gauge matters: observing the vortex-nucleation transition in a Bose condensate

et al. 2015

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The order parameter of a quantum-coherent many-body system can include a phase degree of freedom, which, in the presence of an electromagnetic field, depends on the choice of gauge. Because of the relationship between the phase gradient and the velocity, time-of-flight measurements reveal this gradient. Here, we describe such measurements of initially trapped Bose-Einstein condensates (BECs) subject to an artificial magnetic field. Vortices nucleated in the BEC for artificial field strengths above a critical value, which represented a structural phase transition. By comparing to superfluidhydrodynamic and Gross-Pitaevskii calculations, we confirmed that the transition from the vortexfree state gives rise to a shear in the released BECʼs spatial distribution, representing a macroscopic method to measure this transition, distinct from direct imaging of vortex entry. Shear is also affected by an artificial electric field accompanying the artificial magnetic field turn-off, which depends on the details of the physical mechanism creating the artificial fields, and implies a most natural choice of gauge. Measurements of this kind offer opportunities for studying phase in less-well-understood quantum gas systems.

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“…In condensed matter physics, the topological charge pumping is not easily observed because of the challenging requirement for flexible Hamiltonian engineering. Ultracold atom systems, with the highly controllable properties, provide a perfect platform to observe these topological phenomena [6,7]. The charge pumping has already been observed experimentally in ultracold atom systems by driving a superlattice adiabatically [8,9].…”

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confidence: 95%

Topological quantum pumping in spin-dependent superlattices with glide symmetry

2020

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Topological charge pumping represents an important quantum phenomenon that shows the fundamental connection to the topological properties of dynamical systems. Here, we introduce a pumping process in a spin-dependent double-well optical lattice with glide symmetry. In the dynamic process, the glide symmetry protects the band touching points and topological properties of the system are characterised by the non-Abelian Berry curvature. By engineering suitable form of interaction between different spin components, the model not only demonstrates topological phase transition, but also shows hybridisation between the spatial and temporal domain with novel topological features captured by the Wilson line along the synthetic directions. Our work provides a new model based on ultracold atoms towards the implementation of versatile topological matters and topological phenomena. arXiv:1909.06488v1 [cond-mat.quant-gas]

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Detection of topological matter with quantum gases

Cited by 21 publications

References 50 publications

An Aharonov-Bohm interferometer for determining Bloch band topology

An Aharonov-Bohm interferometer for determining Bloch band topology

Gauge matters: observing the vortex-nucleation transition in a Bose condensate

Topological quantum pumping in spin-dependent superlattices with glide symmetry

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