The quantum geometric tensor represents a central and ubiquitous concept in quantum mechanics, by characterizing the geometric structure of the Hilbert space. It is responsible to a number of striking phenomena, such as quantum phase transitions and novel topological matters, and has a wide range of applications in the area of quantum information and quantum metrology. The imaginary part of the quantum geometric tensor is corresponding to the well-known Berry curvature, while the real part is corresponding to Riemannian metric which defines the distance of quantum states in parameter space through the overlap of wavefunctions.
Recently, a team led by Jianming Cai and Shaoliang Zhang at Huazhong University of Science and Technology in collaboration with Tomoki Ozawa (Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN), Nathan Goldman (Universite? Libre de Bruxelles), Martin B. Plenio and Fedor Jelezko (Ulm University) have made breakthrough in experimentally measuring the complete quantum geometric tensor in solid-state spin system. This work has been published on National Science Review.
The experiment was performed in a two-level system of color center in diamond: Firstly, they make use of the coupling between an engineered microwave field and a nitrogen-vacancy (NV) center in diamond to simulate a monopole in parameter space; Secondly, they exploit the technique of parametric driving to add external periodic modulations to the corresponding Hamiltonian parameters: as shown in the figures below, (a) and (b) correspond to the linear parameters modulation, while (c) corresponds to the elliptical parameters modulation.
Finally, they measure the dynamical processes (i.e. Rabi transitions between the dressed eigenstates) induced by parametric modulation. Since the frequencies of Rabi transitions are related to the transition matrix elements that are dependent on the corresponding matrix elements of the quantum geometric tensor, the team is able to achieve the measurement of the full quantum geometric tensor.
This is the first experimental demonstration of direct measurement of the Riemannian metric in solid-state spin system. The technique can also be used to precisely measure the other matrix elements of the quantum geometric tensor, such as Berry curvature.
Furthermore, the researchers have applied this method to an interacting two-qubit system, which consists of an NV center electron spin coupled to a C13 nuclear spin located in the vicinity of the NV center. And they realize the direct measurement of the full quantum geometric tensor in such an interacting quantum system.
These results demonstrate that coherent dynamical responses can serve as a powerful tool to access the geometric and topological properties of quantum systems and open a way to explore the fundamental role of the QGT in various scenarios, ranging from many-body systems to open quantum systems.
See the article:
Min Yu, Pengcheng Yang, Musang Gong, Qinyun Cao, Qiuyu Lu, Haibin Liu, Shaoliang Zhang, Martin B. Plenio, Fedor Jelezko, Tomoki Ozawa, Nathan Goldman and Jianming Cai.
Experimental measurement of the quantum geometric tensor using coupled qubits in diamond.
Natl Sci Rev: