Periodic Reporting for period 1 - MBL-Fermions (Probing many-body localization dynamics using ultracold fermions in an optical lattice)
Reporting period: 2020-07-01 to 2022-06-30
Nature and properties of materials have continued to be both intriguing and challenging questions in physics for the last several decades. A material is composed of a very large number of atoms, and is often referred to as a “many-body system”. The study of its properties therefore requires handling a very large number of variables. Such a task is computationally very challenging and at the same time, it has the potential to uncover new and exciting properties of materials. The advent of quantum devices such as digital quantum computers and analog quantum simulators has opened a new pathway to study material properties at the quantum level. In this work, we use a neutral atom quantum simulator to study properties of materials. In particular, we focus on Fermionic quantum many-body systems and study their properties out of equilibrium.
Understanding the properties of materials at the quantum level can potentially boost their technological applications. Moreover, study of quantum many-body systems are among the first set of problems that can be potentially tackled using quantum devices. Therefore, they can help unleash the power of quantum devices.
In this work, we study many-body localization in 1D and 2D fermionic systems. We plan to
1. Stark many-body localization and Hilbert space fragmentation: Observing localization in an analytically tractable model — a Stark Hamiltonian, and studying non-ergodicity resulting from Hilbert space fragmentation.
2. Bipartite fluctuations in an MBL system of > 100 lattice sites: Characterizing the localization properties using bipartite fluctuations which is a proxy for the Entanglement entropy.
3. Approximate theories for fermionic MBL systems: Using a quantum simulator to develop efficient approximate theories to describe fermionic MBL systems.
4. Develop a new protocol for benchmarking analog quantum computers.
Understanding the properties of materials at the quantum level can potentially boost their technological applications. Moreover, study of quantum many-body systems are among the first set of problems that can be potentially tackled using quantum devices. Therefore, they can help unleash the power of quantum devices.
In this work, we study many-body localization in 1D and 2D fermionic systems. We plan to
1. Stark many-body localization and Hilbert space fragmentation: Observing localization in an analytically tractable model — a Stark Hamiltonian, and studying non-ergodicity resulting from Hilbert space fragmentation.
2. Bipartite fluctuations in an MBL system of > 100 lattice sites: Characterizing the localization properties using bipartite fluctuations which is a proxy for the Entanglement entropy.
3. Approximate theories for fermionic MBL systems: Using a quantum simulator to develop efficient approximate theories to describe fermionic MBL systems.
4. Develop a new protocol for benchmarking analog quantum computers.
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
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
In the projects carried out during this period, we made the following scientific contributions beyond the state of the art.
Studying slow dynamics and non-ergodicity in a tilted lattice system: We performed the first experimental simulations of a tilted Fermi-Hubbard system with >200 lattice sites and demonstrated non-ergodic behavior – a feature of fundamental importance, refs [1, 3].
Establishing quantum certified approximations as promising near term applications of quantum simulators and computers (see attached figure for a schematic). While the field of quantum computation has gathered a lot of interest recently, the hardware technology is expected to take several years before it is useful for practical applications, which have been previously identified. In this work, we identified and demonstrated new applications that can be implemented already with state-of-the art devices, ref[2]. That is, certifying new classical approximation algorithms using quantum simulators . Moreover, we also developed a new way of benchmarking analog quantum computers refs [4,5].
Studying slow dynamics and non-ergodicity in a tilted lattice system: We performed the first experimental simulations of a tilted Fermi-Hubbard system with >200 lattice sites and demonstrated non-ergodic behavior – a feature of fundamental importance, refs [1, 3].
Establishing quantum certified approximations as promising near term applications of quantum simulators and computers (see attached figure for a schematic). While the field of quantum computation has gathered a lot of interest recently, the hardware technology is expected to take several years before it is useful for practical applications, which have been previously identified. In this work, we identified and demonstrated new applications that can be implemented already with state-of-the art devices, ref[2]. That is, certifying new classical approximation algorithms using quantum simulators . Moreover, we also developed a new way of benchmarking analog quantum computers refs [4,5].