Related papers: Direct probing the quantum geometric tensor for bo…
The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical…
The Berry connection encodes the momentum-space geometry of occupied Bloch states in gapped insulators and plays a central role in topological materials. While gauge-invariant quantities can be evaluated from overlap matrices between…
The quantum geometric properties of topological materials underpin many exotic physical phenomena and applications. Quantum nonlinearity has emerged as a powerful probe for revealing these properties. The Berry curvature dipole in…
The effective quantum field theory description of gravity, despite its non-renormalizability, allows for predictions beyond classical general relativity. As we enter the age of gravitational wave astronomy, an important and timely question…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
The characterization of the dynamics of quantum systems is a task of both fundamental and practical importance. A general class of methods which have been developed in quantum information theory to accomplish this task is known as quantum…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The gravitational wave perturbation is then considerd as a sum of discrete Fourier modes in the momentum space. Coming to an operatorial…
The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of "direct measurement" was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While…
This study presents a unified description of the thermodynamics of ideal quantum gases under nanoscale confinement using a Quantum Phase Space (QPS) formalism. We show that the statistical momentum variances B_ll capture quantum degeneracy:…
In this paper, making use of the global one-dimensionality conjecture, we discuss the reduction of the Wheeler-DeWitt quantum geometrodynamics to the Klein-Gordon equation describing the scalar bosonic particle. The method of second…
The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…
The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are…
This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it $N$-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the $N$-bein behaves like a ``square root'' of the…
Correlations in quantum systems exhibit a rich phenomenology under the effect of various sources of noise. We investigate theoretically and experimentally the dynamics of quantum correlations and their classical counterparts in two nuclear…
Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in…
The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting…