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Manipulation of topological phases with cold atoms

Periodic Reporting for period 4 - TopoCold (Manipulation of topological phases with cold atoms)

Reporting period: 2021-08-01 to 2022-09-30

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, over the last few years, cold-atom theorists and experimentalists have developed new tools, which provide the building blocks for the exploitation of topological atomic gases.
TopoCold proposed realistic optical-lattice setups hosting novel topologically-ordered phases, based on those technologies that are developed in cold-atom experiments. The central goal of the project consisted in identifying unambiguous manifestations of topological properties that are specific to the cold-atom framework. We established concrete methods to experimentally visualize these signatures, elaborating efficient schemes to detect the unique features of topological phases using available manipulation and imaging techniques. Moreover, by tailoring quantum-engineered systems, we explored topological systems that were not accessible in solid-state devices. Finally, we studied the properties of topological phases that arise in the strongly-correlated regime of atomic gases. TopoCold built 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 main contributions of TopoCold 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,
Phys. Rev. X 7, 021015 (2017)

- Parametric instabilities of interacting bosons in periodically-driven 1D optical lattices,
Physical Review X 10, 011030 (2020)

- Parametric instabilities in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime,
Phys. Rev. X 9, 011047 (2019)

(2) Realizing artificial gauge fields and topological modes in periodically-driven photonic lattices [Objective A]:

- Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice,
Nature Communications 8,13918 (2017)

- Experimental observation of Aharonov-Bohm cages in photonic lattices,
Phys. Rev. Lett. 121, 075502 (2018)

- State-recycling and time-resolved imaging in topological photonic lattices,
Nature Communications, 9, 4209 (2018)

(3) 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,
Science Advances 3, e1701207 (2017)

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

- Measuring quantized circular dichroism in ultracold topological matter,
Nature Physics 15, 449 (2019)

- Experimental measurement of the quantum geometric tensor using coupled qubits in diamond,
National Science Review 7, 254 (2020)

(4) 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,
Phys. Rev. Lett. 121, 170401 (2018)

- A synthetic monopole source of Kalb-Ramond field in diamond,
Science 375, 1017 (2022)

(5) Cold-atom implementations of lattice gauge theories [Objective A and E]:

- Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theories,
Science Advances 5, eaav7444 (2019)

- Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices,
Nature Physics 15, 1168 (2019)

(6) Anomalous Floquet systems in quantum gases [Objectives A and B]:

- Realization of an anomalous Floquet topological system with ultracold atoms,
Nature Physics (2020);

(7) Non-Abelian Bloch oscillations as novel probes for higher-order topological systems [Objective B and D]:

- Non-Abelian Bloch oscillations in higher-order topological insulators,
Nature Communications 11, 5942 (2020) + Editors’ Highlights

(8) Realization and probing of fractional Chern insulators in cold atoms [Objective E]:

- Detecting fractional Chern insulators through circular dichroism,
Phys. Rev. Lett. 122, 166801 (2019); PRL Editors’ Suggestion

- Fractional Chern insulators of few bosons in a box:
Hall plateaus from center-of-mass drifts and density profiles,
Phys. Rev. A 102, 063316 (2020)

(9) Quantum Fisher information measurements in NV centers [Objective B]:

- Experimental estimation of the quantum Fisher information from randomized measurements,
M. Yu, D. Li, J. Wang, Y.Chu P. Yang, M. Gong, N. Goldman and J. Cai,
Phys. Rev. Research 3, 043122 (2021)

- Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit,
M. Yu, Y. Liu, P. Yang, M. Gong, Q. Cao, S. Zhang, H. Liu, M. Heyl, T. Ozawa, N. Goldman, and J. Cai,
npj Quantum Information 8, 56 (2022)

(10) Non-linear topological excitations [Objective C]

- Quantized transport of solitons in nonlinear Thouless pumps:
From Wannier drags to ultracold topological mixtures,
Nature Communications 13, 5997 (2022)
The project aimed at identifying novel manifestations of topology in condensed-matter and quantum-engineered quantum matter. The results obtained have demonstrated novel phenomena stemming from topological matter and have established novel schemes by which topological matter can be realized and probed in a broad class of quantum systems.