Periodic Reporting for period 1 - DInTopF (Disorder and Interactions in Topological Floquet Systems)
Periodo di rendicontazione: 2021-04-01 al 2023-03-31
The DInTopF project aimed at experimentally exploring the topological properties of Floquet systems with ultracold atoms in modulated hexagonal optical lattices. The project was based on an existing experimental setup where the topology of the bulk of such a system had already been studied. The objectives of the project were the following:
1. Improve the experimental setup to be able to directly observe edge states in these systems and gain an innovative tool to characterize the topology of a system.
2. Improving how the optical lattice is generated and controlled in order to add a sublattice energy in the hexagonal lattice and be able to probe new regions of the phase diagram, including a phase with Chern number 2.
3. Adding tools to the experiment to generate disorder in the energy landscape of the optical lattice, and study the interplay between topology and disorder. There are two specific questions that had been anticipated: (a) How can the addition of disorder change the topology of a band; (b) How can an anomalous phase have localized states in the bulk and chiral edge states on the border of the material (WP2)
4. Add a stronger vertical confinement to the atoms in order to increase the interactions between particles and, in combination to the natural Feshbach resonance of the potassium atoms that are used, bring the system to a strongly interacting regime. The goals there are two-fold: (a) Investigate whether there is a phase where disorder brings the bulk of the system in a many-body-Anderson-localized state, and at the same time where chiral edge states still sustain transport on the border of the material. (b) Without disorder, the statistics of strongly interacting bosons in the Floquet system can be transformed into one similar to a fermionic statistics.
1. Improve the experimental setup to be able to directly observe edge states in these systems and gain an innovative tool to characterize the topology of a system.
2. Improving how the optical lattice is generated and controlled in order to add a sublattice energy in the hexagonal lattice and be able to probe new regions of the phase diagram, including a phase with Chern number 2.
3. Adding tools to the experiment to generate disorder in the energy landscape of the optical lattice, and study the interplay between topology and disorder. There are two specific questions that had been anticipated: (a) How can the addition of disorder change the topology of a band; (b) How can an anomalous phase have localized states in the bulk and chiral edge states on the border of the material (WP2)
4. Add a stronger vertical confinement to the atoms in order to increase the interactions between particles and, in combination to the natural Feshbach resonance of the potassium atoms that are used, bring the system to a strongly interacting regime. The goals there are two-fold: (a) Investigate whether there is a phase where disorder brings the bulk of the system in a many-body-Anderson-localized state, and at the same time where chiral edge states still sustain transport on the border of the material. (b) Without disorder, the statistics of strongly interacting bosons in the Floquet system can be transformed into one similar to a fermionic statistics.
During the full length of the project, the following steps have been achieved:
A tool to produce sharp edges on the optical lattice has been developed and added to the experiment. An optical tweezer that traps a few hundreds of atoms in a small region and brings them to the desired position has also been installed. With these tools, direct observation of chiral edge states has been performed, and the characteristics of these edge states across the phase diagram of the system have been studied. In particular it has been shown that the height and the sharpness of the engineered edge have an important influence on the velocity of these edge states. All these observations are backed by simple numerical simulations of the system. This has led to the writing of an article which is pre-published (arxiv.org/abs/2304.01980) and has been submitted for publication.
A tool to add a sublattice energy to the hexagonal lattice has been developed independently from the experiment. This consists in the independent control of the intensity and the dephasing of the two polarizations of the light coming out of a fibre. This control can be performed with an excellent precision and a large bandwidth. This tool need to be duplicated for the three beams generating the lattice and to be installed on the experiment for operation.
A speckle beam with variable disorder landscape and controllable strength has been installed. Very promising preliminary results have been obtained on the interplay between topology and disorder: the point where topology can be broken by disorder has been observed for different regions of the phase diagram, and in addition, the displacement of the boundaries of ths phase diagram has been observed. This last effect is a manifestation of disorder-induced topology, as the addition of disorder changes the Chern number of the material. This study is still ongoing and will lead to a publication. This will also be coupled to measurements of localization of a small wavepacket to bring answers to question (b) of the previous paragraph.
An accordion lattice has been developed independently from the experiment. This will allow the vertical confinement to be increased in a dynamical way. The implementation of this setup on the experiment still has to be done when some time can be allocated to it. This sill probably happen when the measurements on disorder will be finished.
The dissemination of this work has been done by myself on two occasions: the workshop "Topology and non-equilibrium dynamics in engineered quantum systems" at Max-Planck Institute for the Physics of Complex Systems in Dresden in October 2022, and the workshop FOR 2414 in Hamburg in March 2023 in the framework of the corresponding DFG project. It has also been done by the two PhD students working on the experiment: at the March meeting of the APS in March 2023, at the DPG Spring meetings of 2022 and 2023, and in internal meetings in the framework of their respective PhD programs. Finally, it has been done by the many visits in international groups by Monika Aidelsburger during the last two years.
I could also disseminate in a broader way the work performed in the laboratory at the occasion of the international students competition PLANCKS2022: I have presented the activities in the labs to a group of participating students.
A tool to produce sharp edges on the optical lattice has been developed and added to the experiment. An optical tweezer that traps a few hundreds of atoms in a small region and brings them to the desired position has also been installed. With these tools, direct observation of chiral edge states has been performed, and the characteristics of these edge states across the phase diagram of the system have been studied. In particular it has been shown that the height and the sharpness of the engineered edge have an important influence on the velocity of these edge states. All these observations are backed by simple numerical simulations of the system. This has led to the writing of an article which is pre-published (arxiv.org/abs/2304.01980) and has been submitted for publication.
A tool to add a sublattice energy to the hexagonal lattice has been developed independently from the experiment. This consists in the independent control of the intensity and the dephasing of the two polarizations of the light coming out of a fibre. This control can be performed with an excellent precision and a large bandwidth. This tool need to be duplicated for the three beams generating the lattice and to be installed on the experiment for operation.
A speckle beam with variable disorder landscape and controllable strength has been installed. Very promising preliminary results have been obtained on the interplay between topology and disorder: the point where topology can be broken by disorder has been observed for different regions of the phase diagram, and in addition, the displacement of the boundaries of ths phase diagram has been observed. This last effect is a manifestation of disorder-induced topology, as the addition of disorder changes the Chern number of the material. This study is still ongoing and will lead to a publication. This will also be coupled to measurements of localization of a small wavepacket to bring answers to question (b) of the previous paragraph.
An accordion lattice has been developed independently from the experiment. This will allow the vertical confinement to be increased in a dynamical way. The implementation of this setup on the experiment still has to be done when some time can be allocated to it. This sill probably happen when the measurements on disorder will be finished.
The dissemination of this work has been done by myself on two occasions: the workshop "Topology and non-equilibrium dynamics in engineered quantum systems" at Max-Planck Institute for the Physics of Complex Systems in Dresden in October 2022, and the workshop FOR 2414 in Hamburg in March 2023 in the framework of the corresponding DFG project. It has also been done by the two PhD students working on the experiment: at the March meeting of the APS in March 2023, at the DPG Spring meetings of 2022 and 2023, and in internal meetings in the framework of their respective PhD programs. Finally, it has been done by the many visits in international groups by Monika Aidelsburger during the last two years.
I could also disseminate in a broader way the work performed in the laboratory at the occasion of the international students competition PLANCKS2022: I have presented the activities in the labs to a group of participating students.
The achievements reported above constitute important steps in the understanding of Floquet systems. The tools developed during this project and implemented on the experiment bring it to a unique condition for the study of disordered topological systems with ultracold atoms. Cutting-edge studies are being performed, such as the observation of the evolution in real space of edge states, and their fate when disorder is being added. In the future, the adding of the phase-control of the optical lattice and the vertical confinement that has been developed will provide even greater capabilities to include interactions. The two PhD students that are still working on this experiment will continue pursuing these objectives in the next years.