Related papers: When geometric phases turn topological

The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…

Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a…

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner does not depend on the complicated…

Using Kaluza-Klein theory we discuss the quantum mechanics of a particle in the background of a domain wall (brane) embedded in extra dimensions. We show that the geometric phases associated with the particle depend on the topological…

We consider a wave packet of a spin-1/2 particle in a gravitational field, the effect of which can be described in terms of a succession of local inertial frames. It is shown that integrating out of the momentum yields a spin mixed state,…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…

In this article we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a…

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…

Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction…

We calculate the geometric phase of a spin-1/2 system driven by a one and two mode quantum field subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when…

Quantum mechanics allows the emergence of nonstatic quantum light waves in the Fock state even in a transparent medium of which electromagnetic parameters do not vary over time. Such wave packets become broad and narrow in turn periodically…

Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…

Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding…

High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. In electron spin resonance, manipulation of the quantum spin is usually achieved with time-dependent microwave fields. In contrast to…

Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system…

Geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can…

We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…