Related papers: Identifying non-Hermitian critical points with qua…
Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian…
Quantum computing's potential for exponential speedup is fundamentally limited by decoherence, a phenomenon arising from environmental interactions. Non-Hermitian quantum mechanics, particularly $PT$-symmetric systems, offers a novel…
Topological physics has broadened its scope from the study of topological insulating phases to include nodal phases containing band structure singularities. The geometry of the corresponding quantum states is described by the quantum metric…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising…
The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena -- topological phases and…
Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that, under equilibrium conditions, the management of quantum noise becomes extremely flexible around the quantum critical point of a…
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…
When a quantum state traverses a path, while being under the influence of a gauge potential, it acquires a geometric phase that is often more than just a scalar quantity. The variety of unitary transformations that can be realised by this…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
Non-Hermitian quasicrystal forms a unique class of matter with symmetry-breaking, localization and topological transitions induced by gain and loss or nonreciprocal effects. In this work, we introduce a non-Abelian generalization of the…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
We systematically study the non-Hermitian version of the one-dimensional anisotropic XY model, which in its original form, is a unique exactly solvable quantum spin model for understanding the quantum phase transition. The distinguishing…
Non-Hermitian topological systems have attracted a lot of research activities in recent times, both theoretically and experimentally, due to their unique physical properties and association with open quantum systems. We show that modular…
Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian due to spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase…
In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution…