Time- and Site-Resolved Dynamics in a Topological Circuit

Abstract

From studies of exotic quantum many-body phenomena to applications in spintronics and quantum information processing, topological materials are poised to revolutionize the condensed-matter frontier and the landscape of modern materials science. Accordingly, there is a broad effort to realize topologically nontrivial electronic and photonic materials for fundamental science as well as practical applications. In this work, we demonstrate the first simultaneous site-and time-resolved measurements of a time-reversalinvariant topological band structure, which we realize in a radio-frequency photonic circuit. We control band-structure topology via local permutation of a traveling-wave capacitor-inductor network, increasing robustness by going beyond the tight-binding limit. We observe a gapped density of states consistent with a modified Hofstadter spectrum at a flux per plaquette of ϕ ¼ π=2. In situ probes of the band gaps reveal spatially localized bulk states and delocalized edge states. Time-resolved measurements reveal dynamical separation of localized edge excitations into spin-polarized currents. The radio-frequency circuit paradigm is naturally compatible with nonlocal coupling schemes, allowing us to implement a Möbius strip topology inaccessible in conventional systems. This room-temperature experiment illuminates the origins of topology in band structure, and when combined with circuit quantum electrodynamics techniques, it provides a direct path to topologically ordered quantum matter. [7], and 2DEGs [8,9]. In a condensed-matter context, such "topologically protected" properties include single-particle features of the band structure and many-particle ground-state degeneracies, with the latter typically emerging from the former in conjunction with strong interactions. To explore the nature of topologically derived material properties, it is desirable to develop materials that not only support conserved topological quantities but that may be precisely produced, manipulated, and probed. The aim, then, is to realize material test beds that marry favorable coherence properties, strong interactions, and topologically nontrivial single-particle dynamics.Metamaterials, where interaction strengths and length scales can be engineered, are a promising avenue for studying topological physics. Efforts are ongoing to produce the requisite topological single-particle dynamics in ultracold atomic gases [10][11][12][13][14][15][16], gyrotropic metamaterials [17,18], and photonic systems [17,[19][20][21][22][23][24][25][26].In cold atomic gases, gauge fields are generated either through spatially dependent Raman coupling of internal atomic states [10,14], or time-and space-periodic modulation of lattice tunneling rates [15,27,28]. In the optical domain, synthetic magnetic fields were realized via strain of a honeycomb lattice [29]. A Floquet topological insulator [30,31] was realized under a space-to-time mapping of an array of tunnel-coupled waveguides modulated along their propagation direction [21]. A photonic topologic...

Synthetic dimensions for cold atoms from shaking a harmonic trap

“…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].…”

Chiral Bogoliubov excitations in nonlinear bosonic systems

“…The robustness of the Hall conductance can be traced back to the nontrivial topology of the underlying electronic band structure [2], which ensures the existence of chiral edge states and thus eliminates backscattering. Recently there was a surge of interest in the possibility to exploit such topology to create chiral bosonic modes in driven-dissipative systemswith possible applications to one-way transport of photons [3][4][5][6][7][8][9][10][11][12][13], polaritons [14][15][16], excitons [16,17], magnons [18,19], and phonons [20,21]. A common thread through these seemingly diverse ideas has been to induce topology by external manipulations of a single-particle band structure, with interactions playing a negligible role.…”

Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

“…In addition, a very recent work [80] has reported on the observation of a point-like edge state, situated at the interface between two geometrically distinct regions, in a one-dimensional optical lattice reminiscent of the Su-Schrieffer-Heeger model [81]. Finally, we point out that topological structures were also identified in other engineered systems, such as photonic lattices [82][83][84][85][86][87], superconducting qubits [88,89], mechanical systems [90] and radio-frequency circuits [91,92]. In 2D systems, topological interfaces consist of boundary lines separating two distinct topologically-ordered regions, where topologically-protected "edge" modes are located and propagate [see Fig.…”