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Manipulation of topological phases with cold atoms

Periodic Reporting for period 3 - TopoCold (Manipulation of topological phases with cold atoms)

Reporting period: 2020-02-01 to 2021-07-31

Topological states of matter constitute one of the hottest disciplines in quantum physics, demonstrating a remarkable fusion between elegant mathematical theories and technological applications. However, solid-state experiments only provide a limited set of physical systems and probes that can reveal non-trivial topological order. It is thus appealing to seek for alternative setups exhibiting topological properties. Cold atoms in optical lattices constitute an instructive and complementary toolbox, being extremely versatile, clean and controllable. In fact, cold-atom theorists and experimentalists have recently developed new tools providing the building blocks for the exploitation of topological atomic gases.
TopoCold will propose realistic optical-lattice setups hosting novel topologically-ordered phases, based on those technologies that are currently developed in cold-atom experiments. The central goal of the project consists in identifying unambiguous manifestations of topological properties that are specific to the cold-atom framework. We will establish concrete methods to experimentally visualize these signatures, elaborating efficient schemes to detect the unique features of topological phases using available manipulation and imaging techniques. This central part of the TopoCold project will deepen our understanding of topological phenomena and guide ongoing experiments. We also plan to elaborate simple protocols to exploit topological excitations, based on the great controllability of atom-light coupling methods. Moreover, by tailoring the geometry and laser-coupling of optical-lattice setups, we will explore topological systems that are not accessible in solid-state devices. Finally, we will study the properties of topological phases that arise in the strongly-correlated regime of atomic gases. TopoCold will build a bridge between several communities, deepening our knowledge of topological phases from an original and interdisciplinary perspective.
The general objectives of the TopoCold project can be listed as follows:

(A) Realization of topological properties in quantum-engineered systems (cold-atoms and photonics);
(B) Identification of novel topological phenomena and probes in ultracold atoms;
(C) Study the possibility of manipulating topological excitations in ultracold topological matter;
(D) Exploration of the classification of topological matter and higher-dimensional states;
(E) Stabilization and characterization of topological systems in the presence of interactions.

The works performed so far, which have all contributed to one or several of these topics, are indicated below:

(1) Analysis of instabilities in ultracold periodically-driven (Floquet-engineered) bosonic matter [Objectives A and E]:

- Parametric Instability Rates in Periodically-Driven Band Systems,
S. Lellouch, M. Bukov, E. Demler and N. Goldman,
Phys. Rev. X 7, 021015 (2017)

- Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates,
S. Lellouch and N. Goldman,
Quantum Sci. Technol. 3 024011 (2018)

- Parametric instabilities of interacting bosons in periodically-driven 1D optical lattices,
J. Näger, K. Wintersperger, M. Bukov, S. Lellouch, E. Demler, U. Schneider, I. Bloch, N. Goldman and M. Aidelsburger,
arXiv:1808.07462 (2018)

- Parametric instabilities in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime,
T. Boulier, J. Maslek, M. Bukov, C. Bracamontes, E. Magnan, S. Lellouch, E. Demler, N. Goldman and J. V. Porto,
arXiv:1808.07637 (2018)

(2) Artificial gauge fields and topology in periodically-driven photonic lattices [Objective A]:

- Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice,
S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. Ohberg, N. Goldman and R. R. Thomson,
Nature Communications 8,13918 (2017)

- Experimental observation of Aharonov-Bohm cages in photonic lattices,
S. Mukherjee, M. Di Liberto, P. Öhberg, R. R. Thomson, and N. Goldman,
Phys. Rev. Lett. 121, 075502 (2018)

- State-recycling and time-resolved imaging in topological photonic lattices,
S. Mukherjee, H. K. Chandrasekharan, P. Ohberg, N. Goldman and R. R. Thomson,
arXiv:1712.08145 (2018); to appear in Nature Communications

(3) Analysis of adiabatic loading into Floquet bands in view of probing topological transport properties [Objectives A and B]:

- Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses,
A. Dauphin, D.-T. Tran, M. Lewenstein and N. Goldman,
2D Materials 4, 024010 (2017)

(4) Novel methods for probing the geometry and topology of many-body quantum systems based on excitation-rate measurements (including experimental validation) [Objective B]:

- Probing topology by “heating”: Quantized circular dichroism in ultracold atoms,
D. T. Tran, A. Dauphin, A. G. Grushin, P. Zoller and N. Goldman,
Science Advances 3, e1701207 (2017)

- Extracting the quantum metric tensor through periodic driving,
T. Ozawa and N. Goldman,
Phys. Rev. B 97, 201117(R) (2018)

- Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems,
D. T. Tran, N. R. Cooper, and N. Goldman,
Phys. Rev. A 97, 061602(R) (2018)

- Measuring quantized circular dichroism in ultracold topological matter,
L. Asteria, D. T. Tran, T. Ozawa, M. Tarnowski, B. S. Rem, N. Fläschner, K. Sengstock, N. Goldman and C. Weitenberg, arXiv:1805.11077 (2018)

(5) Study of quench dynamics in strongly-interacting topological matter [Objectives B and C]

- Quenched dynamics and spin-charge separation in an interacting topological lattice,
L. Barbiero, L. Santos, and N. Goldman,
Phys. Rev. B 97, 201115(R) (2018)

(6) Study of artificial gauge fields in 3D (Weyl) semimetals, in view of optical-lattice implementations [Objectives A and D]:

- Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementations,
S. Roy, M. Kolodrubetz, N. Goldman and A. G. Grushin,
2D Materials 5, 024001 (2018)

(7) Exploration of higher-form (tensor) gauge fields in condensed-matter physics and their topological defects (tensor monopoles) [Objective D]:

- Revealing tensor monopoles through quantum-metric measurements,
G. Palumbo and N. Goldman,
arXiv:1805.01247 (2018)

Other results associated with Objectives [A-E] have been obtained recently, and will be reported soon.
The aim of the project is to identify novel manifestations of topology in condensed-matter and quantum-engineered quantum matter. The results obtained so far have already demonstrated novel schemes by which topological matter can be realized and probed. Until the end of the project, we expect to validate a series of theoretical predictions, but also, to further deepen our understanding of (interacting) topological systems based on quantum-engineered systems.