Detection of quantum geometric tensor by nonlinear optical response

Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor

We study the role of the quantum geometric tensor (QGT) in the evolution of quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wavepacket in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the non-adiabaticity is determined by the quantum metric (the real part of the tensor) and allows to determine corrections in the regimes where Landau-Zener approach is inapplicable. The particular case of a planar mi…

On chiral responses to geometric torsion

We show that geometric torsion does not lead to new chiral dissipationless transport effects. Instead apparent response to torsion can be viewed as a manifestation of the chiral vortical effect.

Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals

We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and reveals the crossover between the orthogonal and unitary critical states in weak random magnetic fields. The flow of the QGT near the critical points determines the critical exponents. Critical distributions of the QGT are universal and exhibit a remarkable isotropy even in a homogeneous magnetic field. We predict universal and isotropic Hall conductance fluctuati…

具有可调量子几何张量的周期性铺砌族

Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor

本研究提出了一种可调的非周期性铺砌族，通过实空间几何调节量子几何张量，实现拓扑相和量子度量的连续调控。

Experimental measurement of the quantum geometric tensor using coupled qubits in diamond

Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a …

从子丛几何角度获取量子几何张量

Quantum geometric tensors from sub-bundle geometry

本文从子丛几何角度提出量子几何张量的新定义，通过引入通用连接和子丛投影器，扩展了量子几何张量的描述，并展示了其在Dirac场和双曲平面中的应用。

利用量子几何张量对复SSH模型进行拓扑分析

Topological analysis of the complex SSH model using the quantum geometric tensor

该研究提出贝里相位和拓扑数据分析两种基于量子几何张量的方法，对复厄米SSH模型开展拓扑分析，得到对应参数相对大小的拓扑平庸与非平庸相区，为复杂SSH类模型的拓扑分析奠基。

非厄密特量子几何张量与非线性电响应

Non-Hermitian quantum geometric tensor and nonlinear electrical response

研究非厄密特量子几何张量如何调控具有谱线间隙系统的非线性电响应，揭示量子度量与波包宽度对非厄密特传输的影响。

有限温度混合态的Sjöqvist量子几何张量

Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states

本文基于Sjöqvist距离将量子几何张量推广到有限温度混合态，揭示其规范不变性、实部度规分解及虚部与Berry曲率的关系，并通过实例展示温度依赖特性。

Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems

Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to access. In non-Abelian systems this accessibility to geometric properties can be even more restrictive due to the degeneracy of the states. We propose universal protocols to determine quantum geometric properties in non-Abelian systems. First, we show that for a weak resonant driving of the local parameters the coherent Rabi oscillations are related to the quan…

Geometric response of quantum Hall states to electric fields

Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the characteristic geometry of electronic motion in the presence of magnetic and electric fields. The geometric picture we provide motivates the following conjecture: non-uniform electric fields mimic the presence of spatial curvature. Consequently, the gravitational coupling constant also appears in the charge response to non-uniform electric fields.

量子几何张量在野：通过Floquet-单值谱学解决Stokes现象

Quantum Geometric Tensor in the Wild: Resolving Stokes Phenomena via Floquet-Monodromy Spectroscopy

通过Floquet-单值谱学解决Stokes现象，揭示非微扰物理的拓扑分类方法。