Related papers: Geometric Phase in Quantum Synchronization
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…
We formulate a geometric framework for quasistatic thermodynamics in open quantum systems by parameterizing the dynamics on a control manifold. In the quasistatic limit, the system follows a manifold of stationary states, and the work…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
Geometric quantum gates are performed by using the geometric phase, making them particularly robust to the pulse amplitude error due to the intrinsic global property. However, in many systems, such as the silicon-based spin qubits, the…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a…
We make use of a superconducting qubit to study the effects of noise on adiabatic geometric phases. The state of the system, an effective spin one-half particle, is adiabatically guided along a closed path in parameter space and thereby…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable…
We report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
Scalable methods for detecting and quantifying the nonclassical nature of a quantum state in noisy environments are challenging due to a complex relationship between noise and quantum coherence. In particular, identifying experimentally…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
Trapped-ion systems are a leading platform for quantum computing. The M{\o}lmer-S{\o}rensen (MS) gate is a widely used method for implementing controlled interactions in multipartite systems. However, due to unavoidable interactions with…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
We study how quantum and thermal noise affects synchronization of two optomechanical limit-cycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either in-phase or anti-phase. Taking into…
We show that by examining the global geometric entanglement it is possible to identify "elusive" or hard to detect quantum phase transitions. We analyze several one-dimensional quantum spin chains and demonstrate the existence of…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…