Related papers: The non-Abelian geometric phase in the diamond nit…
We propose an approach for an optical qubit rotation in the negatively charged nitrogen-vacancy (NV) center in diamond. The qubit is encoded in the ground degenerate states at the relatively low temperature limit. The basic idea of the…
We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a…
Based only on the parallel transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic…
Topological phases and transitions are of fundamental importance in physics, which provide a deep insight into the understanding of materials. Recently, non-Abelian topological transitions have been investigated in Hermitian systems,…
In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further…
We consider a periodically driven quantum system described by a Hamiltonian which is the product of a slowly varying Hermitian operator $V\left(\boldsymbol{\lambda}\left(t\right)\right)$ and a dimensionless periodic function with zero…
Nitrogen-vacancy center in diamond is a solid state defect qubit with favorable coherence time up to room temperature which could be harnessed in several quantum enhanced sensor and quantum communication applications, and has a potential in…
For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and…
Fast quantum spin manipulation is needed to design spin-based quantum logic gates and other quantum applications. Here, we construct exact evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields…
We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.
A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an 'orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi- great circles. Since the dynamical…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
The non-Abelian geometric phase possesses the capability of enabling robust and fault-resilient unitary transformations, making it a cornerstone of holonomic quantum computation. This "all-geometric" approach has successfully advanced the…
We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical…
The phase relation between quantum states represents an essential resource for the storage and processing of quantum information. While quantum phases are commonly controlled dynamically by tuning energetic interactions, utilizing geometric…
Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized,…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical…
We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing…
We present a theoretical study of vibrational and vibronic properties of a point defect in the dilute limit by means of first-principles density functional theory calculations. As an exemplar we choose the negatively charged…