Related papers: Sum rule for non-adiabatic geometric phases
We study quantum adiabatic dynamics, where the slowly moving field is influenced by system's state (feedback). The information for the feedback is gained from non-disturbating measurements done on an ensemble of identical non-interacting…
The monopole for the geometric curvature is studied for non-Hermitian systems. We find that the monopole contains not only the exceptional points but also branch cuts. As the mathematical choice of branch cut in the complex plane is rather…
A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is…
We derive the general formula giving the Berry phase for an arbitrary spin, having both magnetic-dipole and electric-quadrupole couplings with external time-dependent fields. We assume that the effective E and B fields remain orthogonal…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
The quantum adiabatic theorem incorporating the Berry phase phenomenon can be characterized as a factorization of the time evolution operator into a path-dependent geometric factor, a usual dynamical factor and a non-adiabatic factor that…
The non-adiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent years. Here, we propose the first scheme for realizing universal single-qubit gates based on an…
The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.
Based on the adiabatic geometric phase concerning with density matrix[1] , we extend it to the sub-geometric phase in the non-adiabatic case. It is found that whatever the real part or imaginary part of the sub-geometric phase can play an…
We study the constraints of supersymmetry on the non-Abelian holonomy given by U=P exp(i\int A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A satisfies the tt* equations if it is a…
In this work we study the geometrical and topological properties of non-equilibrium quantum systems driven by ac fields. We consider two tunnel coupled spin qubits driven by either spatially homogeneous or inhomogeneous ac fields. Our…
Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the…
The geometric phase has been proposed as a candidate for noise resilient coherent manipulation of fragile quantum systems. Since it is determined only by the path of the quantum state, the presence of noise fluctuations affects the…
We clarify that the nonadiabatic scheme based on a parallel extension of the adiabatic scenario cannot realize the desired goal of quantum computation.
It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with…
The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…
Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates.…
Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are…
We show that the definition of instantaneous eigenstate populations for a dynamical non-self-adjoint system is not obvious. The naive direct extension of the definition used for the self-adjoint case leads to inconsistencies; the resulting…