We began with a project on observing non-ergodic dynamics in a Stark system. During the project p[eriod, we designed, implemented and calibrated a magnetic field gradient to simulate a tilted lattice potential. We also developed and implemented a technique to count atoms separately for different spin (i.e. internal state) and the parity of their occupied lattice site (i.e. even or odd). With these developments, we were able to observe a long-time non-ergodicity in a tilted Fermi-Hubbard system. The results were published in [1].
As a second project, we turned towards a possible application of quantum simulators. Many-body physics presents some of the most computationally challenging problems. Many of these problems can be addressed using classical approximation algorithms. The bottleneck in developing such approximate algorithms is their benchmarking. In order to benchmark, the approximation needs to be compared with an exact calculation, which, by definition, is beyond the limits of classical computation. We showed that a quantum simulator can be used for this purpose. We developed an efficient approximation algorithm for Fermi-Hubbard systems and we used our experiment to benchmark it. We call such approximations as quantum certified approximations (see attached figure). These results were published in [2].
Finally, we developed our work on the tilted Fermi-Hubbard system further, by studying a novel phenomenon known as Hilbert space fragmentation. In the limit of large tilts, the Hamiltonian admits an effective description based on a Schreiffer-Wolff transformation. Some of these effective Hamiltonians feature the phenomenon of Hilbert space fragmentation. By releasing this regime in the lab, we experimentally observed some of the properties of a fragmented Hamiltonian. A paper with these results is currently under review [3].
[1.] Sebastian Scherg et al. Nature Communications 12 (1), 1-8
[2.] Bharath Hebbe Madhusudhana et. al. PRX Quantum 2, 040325.
[3.] Thomas Kohlert et al. arXiv:2106.15586
[4.] Bharath Hebbe Madhusudhana arXiv:2210.04330
[5.] Bharath Hebbe Madhusudhana, manuscript under preparation
