Periodic Reporting for period 1 - LATIS (Local Addressing of Topological Interacting Systems)
Berichtszeitraum: 2022-10-01 bis 2025-03-31
It is the central theme of the LATIS project to build on the latest developments of optical-lattice technologies in view of revealing exquisite properties of interacting topological matter. While developing our understanding of topological phases from a theoretical perspective, the project will also establish practical methods by which FQH states of neutral atoms can be unambiguously detected in current experimental settings. The ever-growing interest of the scientific community for synthetic topological systems, both for their elegance in addressing fundamental concepts and for their potential applications, highly motivate the LATIS project.
The design of topological band structures in optical-lattice setups has led to the experimental observation of various geometric and topological properties. However, until now, ultracold topological matter has been explored in the non-interacting regime of quantum gases, so that the observed quantities are genuinely associated with single-particle states. While the exploration of (single-particle) topological band theory still constitutes an active field of research, continuously revealing surprising mathematical concepts and novel phenomena in condensed matter, exciting avenues would become accessible upon combining engineered band structures with tunable inter-particle interactions. In particular, this scenario would provide a concrete path towards the experimental realization of strongly-correlated topological states in ultracold gases. Such intriguing phases of matter are reminiscent of the fractional quantum Hall (FQH) states discovered in the solid state, and they are predicted to exhibit remarkable properties, such as emergent fractionally-charged quasiparticles satisfying fractional (anyonic) statistics. The observation and manipulation of these “anyons” represents one of the greatest challenges in condensed-matter physics, motivated by their central role in topological quantum computing.
Activating and controlling interactions between neutral atoms are routine operations in the realm of cold atoms. However, severe complications arise when engineering band structures in the interacting regime of quantum gases. Indeed, the driving schemes that are required to generate topological bands generally lead to heating and instabilities through inevitable interaction processes. A promising strategy to nevertheless load and stabilize interacting atoms in a FQH state would consist in manipulating a very small ensemble of atoms within a few lattice sites of an optical lattice. Such a local addressing of individual atoms is now made possible by quantum gas microscopes, which are currently developed by several groups. This setting not only has the appealing potential to realize FQH states of neutral atoms for the first time, but it would also allow for unprecedented control over these strongly-correlated states of matter through the local addressing and detection tools provided by quantum-gas microscopes. Importantly, this emerging physical framework offers the unique possibility of analyzing topological order, and related notions such as entanglement, in a local and dynamical manner. Altogether, interacting atomic gases in topological band structures offer a unique and promising framework for many-body quantum physics, where theorists and experimentalists join forces to unveil fundamental properties of quantum matter.
The design of topological band structures in optical-lattice setups has led to the experimental observation of various geometric and topological properties. However, until now, ultracold topological matter has been explored in the non-interacting regime of quantum gases, so that the observed quantities are genuinely associated with single-particle states. While the exploration of (single-particle) topological band theory still constitutes an active field of research, continuously revealing surprising mathematical concepts and novel phenomena in condensed matter, exciting avenues would become accessible upon combining engineered band structures with tunable inter-particle interactions. In particular, this scenario would provide a concrete path towards the experimental realization of strongly-correlated topological states in ultracold gases. Such intriguing phases of matter are reminiscent of the fractional quantum Hall (FQH) states discovered in the solid state, and they are predicted to exhibit remarkable properties, such as emergent fractionally-charged quasiparticles satisfying fractional (anyonic) statistics. The observation and manipulation of these “anyons” represents one of the greatest challenges in condensed-matter physics, motivated by their central role in topological quantum computing.
Activating and controlling interactions between neutral atoms are routine operations in the realm of cold atoms. However, severe complications arise when engineering band structures in the interacting regime of quantum gases. Indeed, the driving schemes that are required to generate topological bands generally lead to heating and instabilities through inevitable interaction processes. A promising strategy to nevertheless load and stabilize interacting atoms in a FQH state would consist in manipulating a very small ensemble of atoms within a few lattice sites of an optical lattice. Such a local addressing of individual atoms is now made possible by quantum gas microscopes, which are currently developed by several groups. This setting not only has the appealing potential to realize FQH states of neutral atoms for the first time, but it would also allow for unprecedented control over these strongly-correlated states of matter through the local addressing and detection tools provided by quantum-gas microscopes. Importantly, this emerging physical framework offers the unique possibility of analyzing topological order, and related notions such as entanglement, in a local and dynamical manner. Altogether, interacting atomic gases in topological band structures offer a unique and promising framework for many-body quantum physics, where theorists and experimentalists join forces to unveil fundamental properties of quantum matter.
The work performed so far can be partitioned in terms of the following topics:
1°) Engineering chiral spin liquids and fractional quantum Hall states in cold atoms
EXperimental realization of a fractional quantum Hall state with ultracold atoms
• Introduction of the cold-atom elevator, as a technique to prepare fractional Chern insulators
• Method to engineer and probe non-Abelian chiral spin liquids using periodically-driven ultracold atoms
• Method to grow extended Laughlin states in a quantum gas microscope using a patchwork construction
• Search for gapless Majorana edge modes in few-leg bosonic flux ladders
• Study of Floquet dynamical chiral spin liquids at finite frequency
2°) The Streda response as a local topological marker for correlated insulators and driven systems
• Connecting the many-body Chern number to Luttinger's theorem through Středa's formula
• The Streda formula for Floquet systems: Relating Floquet winding numbers to quantized anomalies and measurable observables through Cesaro summation
• Method to detect the quantized valley Hall response from local bulk density variations
3°) Exploring the edge physics of quantum Hall states with ultracold atoms
• Spectroscopy of edge and bulk collective modes in fractional Chern insulators
• Quantized circular dichroism on the edge of quantum Hall systems: A method to detect the many-body Chern number from the edge
• Scheme to detect topological chiral edge states in a synthetic dimension of atomic trap states
4°) Polaron physics in topological and strongly-interacting quantum matter
• Polaron spectroscopy of interacting Fermi systems: insights from exact diagonalization
• A unified theory of strong coupling Bose polarons: Connecting repulsive polarons to non-Gaussian many-body bound states
• Prediction of chiral polaron formation on the edge of topological quantum matter
• Elucidation of polaron formation in insulators and the key role of hole scattering processes, considering band insulators, charge density waves and the Mott transition
5°) Spontaneous time-reversal symmetry breaking in interacting bosonic quantum matter
• Study of chiral orbital order of interacting bosons without higher bands
• Scheme for Floquet-engineered pair-hopping processes, as a method to realize interaction-induced magnetic fluxes
• Fate of chiral order and impurity self-pinning in flat bands with local symmetry
6°) Quantum geometry and quantum metrology
• Experimental demonstration of topological bounds in quantum metrology
• Theoretical study of lasing in non-Hermitian flat bands: Quantum geometry, coherence, and the fate of Kardar-Parisi-Zhang physics
7°) Photonics: topological photonics, synthetic dimensions for light and nonlinear optics
• Experimental observation of Bloch oscillations of coherently-driven dissipative solitons in a synthetic dimension
• Experimental observation of nonlinear topological symmetry protection in a dissipative system
• Experimental observation of cavity soliton-induced topological edge states
• Theory proposal for Thouless pumping in a driven-dissipative Kerr resonator array
• Scheme for Floquet-engineered nonlinearities in Kerr cavities
1°) Engineering chiral spin liquids and fractional quantum Hall states in cold atoms
EXperimental realization of a fractional quantum Hall state with ultracold atoms
• Introduction of the cold-atom elevator, as a technique to prepare fractional Chern insulators
• Method to engineer and probe non-Abelian chiral spin liquids using periodically-driven ultracold atoms
• Method to grow extended Laughlin states in a quantum gas microscope using a patchwork construction
• Search for gapless Majorana edge modes in few-leg bosonic flux ladders
• Study of Floquet dynamical chiral spin liquids at finite frequency
2°) The Streda response as a local topological marker for correlated insulators and driven systems
• Connecting the many-body Chern number to Luttinger's theorem through Středa's formula
• The Streda formula for Floquet systems: Relating Floquet winding numbers to quantized anomalies and measurable observables through Cesaro summation
• Method to detect the quantized valley Hall response from local bulk density variations
3°) Exploring the edge physics of quantum Hall states with ultracold atoms
• Spectroscopy of edge and bulk collective modes in fractional Chern insulators
• Quantized circular dichroism on the edge of quantum Hall systems: A method to detect the many-body Chern number from the edge
• Scheme to detect topological chiral edge states in a synthetic dimension of atomic trap states
4°) Polaron physics in topological and strongly-interacting quantum matter
• Polaron spectroscopy of interacting Fermi systems: insights from exact diagonalization
• A unified theory of strong coupling Bose polarons: Connecting repulsive polarons to non-Gaussian many-body bound states
• Prediction of chiral polaron formation on the edge of topological quantum matter
• Elucidation of polaron formation in insulators and the key role of hole scattering processes, considering band insulators, charge density waves and the Mott transition
5°) Spontaneous time-reversal symmetry breaking in interacting bosonic quantum matter
• Study of chiral orbital order of interacting bosons without higher bands
• Scheme for Floquet-engineered pair-hopping processes, as a method to realize interaction-induced magnetic fluxes
• Fate of chiral order and impurity self-pinning in flat bands with local symmetry
6°) Quantum geometry and quantum metrology
• Experimental demonstration of topological bounds in quantum metrology
• Theoretical study of lasing in non-Hermitian flat bands: Quantum geometry, coherence, and the fate of Kardar-Parisi-Zhang physics
7°) Photonics: topological photonics, synthetic dimensions for light and nonlinear optics
• Experimental observation of Bloch oscillations of coherently-driven dissipative solitons in a synthetic dimension
• Experimental observation of nonlinear topological symmetry protection in a dissipative system
• Experimental observation of cavity soliton-induced topological edge states
• Theory proposal for Thouless pumping in a driven-dissipative Kerr resonator array
• Scheme for Floquet-engineered nonlinearities in Kerr cavities
Our research and results open the road for:
- the realization, detection and manipulation of fractional quantum Hall states and chiral spin liquids in quantum simulators
- the theoretical characterization of correlated topological quantum matter
- the use of mobile impurities (polarons) as a probe for topological quantum matter and strongly-correlated phases
- the development of local probes of topology based on circular dichroism
- the harnessing of spontaneous time-reversal-symmetry breaking in quantum matter
- connecting quantum geometry, topology and applications (e.g. in quantum metrology, but also optics)
- the observation of topological phenomena in driven-dissipative nonlinear optics
- the realization, detection and manipulation of fractional quantum Hall states and chiral spin liquids in quantum simulators
- the theoretical characterization of correlated topological quantum matter
- the use of mobile impurities (polarons) as a probe for topological quantum matter and strongly-correlated phases
- the development of local probes of topology based on circular dichroism
- the harnessing of spontaneous time-reversal-symmetry breaking in quantum matter
- connecting quantum geometry, topology and applications (e.g. in quantum metrology, but also optics)
- the observation of topological phenomena in driven-dissipative nonlinear optics