Topological Properties of Linear Circuit Lattices

Albert, Victor V.; Glazman, L. I.; Jiang, Liang

doi:10.1103/physrevlett.114.173902

Cited by 273 publications

(222 citation statements)

References 56 publications

Supporting

Mentioning

216

Contrasting

Order By: Relevance

“…As long as time reversal symmetry is preserved, these two modes are independent and do not scatter into each other (6,7). Much of the interest in condensed matter research involving topological states is driven by the use of these protected edge modes for technological applications such as spintronics (8,9), magnetic devices (10), or quantum information processing (11).…”

mentioning

confidence: 99%

Observation of phononic helical edge states in a mechanical topological insulator

Süsstrunk

Huber

2015

Science

937

766

View full text Add to dashboard Cite

A topological insulator, as originally proposed for electrons governed by quantum mechanics, is characterized by a dichotomy between the interior and the edge of a finite system: The bulk has an energy gap, and the edges sustain excitations traversing this gap. However, it has remained an open question whether the same physics can be observed for systems obeying Newton's equations of motion. We conducted experiments to characterize the collective behavior of mechanical oscillators exhibiting the phenomenology of the quantum spin Hall effect. The phononic edge modes are shown to be helical, and we demonstrate their topological protection via the stability of the edge states against imperfections. Our results may enable the design of topological acoustic metamaterials that can capitalize on the stability of the surface phonons as reliable wave guides.

show abstract

mentioning

confidence: 99%

Observation of phononic helical edge states in a mechanical topological insulator

Süsstrunk

Huber

2015

Science

937

766

View full text Add to dashboard Cite

show abstract

“…Although first studied in solid-state materials, there has been great progress in exploring QH physics also with ultracold atoms [5][6][7][8][9][10], photons [11][12][13], classical circuits [14,15] and mechanical systems [16][17][18], where the magnetic field effects must be engineered artificially [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Synthetic dimensions for cold atoms from shaking a harmonic trap

2017

View full text Add to dashboard Cite

We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time-modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realisation of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.

show abstract

“…We have further assumed that the total bandwidth of the features under consideration is a small fraction of the center frequency, allowing us to assume the losses κ are frequencyindependent; more sophisticated techniques are required for truly broadband experiments [25,26], or for dissipation into structured continua. To extract the coupling strengths κ α,β c , we must also measure the 1-port reflections S αα (ω) and S ββ (ω).…”

Section: Theory Of Lattice Spectroscopy a Formulae For Arbitrarymentioning

confidence: 99%

Hamiltonian tomography of photonic lattices

Owens

LaChapelle

et al. 2017

Phys. Rev. A

View full text Add to dashboard Cite

In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tightbinding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from S αβ (ω), the (suitably normalized) two-port measurement between sites α and β at frequency ω. This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band-projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in-between.

show abstract

Topological Properties of Linear Circuit Lattices

Cited by 273 publications

References 56 publications

Observation of phononic helical edge states in a mechanical topological insulator

Observation of phononic helical edge states in a mechanical topological insulator

Synthetic dimensions for cold atoms from shaking a harmonic trap

Hamiltonian tomography of photonic lattices

Contact Info

Product

Resources

About