# Quantized interlevel character in quantum systems

@article{Xu2018QuantizedIC,
title={Quantized interlevel character in quantum systems},
author={Chao Xu and Jianda Wu and Congjun Wu},
journal={Physical Review A},
year={2018},
volume={97},
pages={032124}
}
• Published 30 November 2017
• Physics
• Physical Review A
For a quantum system subject to external parameters, the Berry phase is an intra-level property, which is gauge invariant module $2\pi$ for a closed loop in the parameter space and generally is non-quantized. In contrast, we define a inter-band character $\Theta$ for a closed loop, which is gauge invariant and quantized as integer values. It is a quantum mechanical analogy of the Euler character based on the Gauss-Bonnet theorem for a manifold with a boundary. The role of the Gaussian curvature…
2 Citations

## Figures from this paper

Nonadiabatic nonlinear optics and quantum geometry — Application to the twisted Schwinger effect
• Physics
SciPost Physics
• 2021
We study the tunneling mechanism of nonlinear optical processes in solids induced by strong coherent laser fields. The theory is based on an extension of the Landau-Zener model with nonadiabatic
Nonreciprocal Landau–Zener tunneling
• Physics
• 2019
Application of strong dc electric field to an insulator leads to quantum tunneling of electrons from the valence band to the conduction band, which is a famous nonlinear response known as

## References

SHOWING 1-10 OF 89 REFERENCES
Quantal phase factors accompanying adiabatic changes
• M. Berry
• Mathematics
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
• 1984
A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar
SU (2) non-Abelian holonomy and dissipationless spin current in semiconductors
• Physics
• 2004
Following our previous work [S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003)] on the dissipationless quantum spin current, we present an exact quantum-mechanical calculation of
Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: a new approach to quantum computation.
A new approach to quantum phase gates via the adiabatic evolution, where it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided.
Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
It is shown that the "geometrical phase factor" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem
Experimental study of the validity of quantitative conditions in the quantum adiabatic theorem.
• Physics, Medicine
Physical review letters
• 2008
The standard criterion for adiabatic evolution experimentally and theoretically is examined, and it is shown that the standard criterion is neither sufficient nor necessary.
Dissipationless Quantum Spin Current at Room Temperature
• Physics, Medicine
Science
• 2003
Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this
Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the "parity anomaly"
• Haldane
• Physics, Medicine
Physical review letters
• 1988
A two-dimensional condensed-matter lattice model is presented which exhibits a nonzero quantization of the Hall conductance in the absence of an external magnetic field, and exhibits the so-called "parity anomaly" of (2+1)-dimensional field theories.
Digital quantum simulation of fermionic models with a superconducting circuit
Digital methods are used to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit, and reach fidelities that are consistent with a simple model of uncorrelated errors.
Colloquium : Quantum annealing and analog quantum computation
• Physics
• 2008
The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive
Geometric quantum computation with NMR
• Physics
• 1999
An exciting recent development has been the discovery that the computational power of quantum computers exceeds that of Turing machines [1]. The experimental realisation of the basic constituents of