Effect of classical noise on the geometric quantum phase
Abstract
We consider the effect of classical noise applied to the geometric quantum phase of a spin 1/2 in a revolving magnetic field. The Berry phase shows some sensitivity to the noise because the Bloch vector cannot return to its original direction, and the variance caused by noise is proportional to the evolution time.
 Authors:
 Department of Physics, Beijing Institute of Technology, Beijing 100081 (China)
 Publication Date:
 OSTI Identifier:
 20982195
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.024103; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLOCH THEORY; EVOLUTION; MAGNETIC FIELDS; NOISE; SENSITIVITY; SPIN
Citation Formats
Hou, JiXuan. Effect of classical noise on the geometric quantum phase. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.024103.
Hou, JiXuan. Effect of classical noise on the geometric quantum phase. United States. doi:10.1103/PHYSREVA.75.024103.
Hou, JiXuan. Thu .
"Effect of classical noise on the geometric quantum phase". United States.
doi:10.1103/PHYSREVA.75.024103.
@article{osti_20982195,
title = {Effect of classical noise on the geometric quantum phase},
author = {Hou, JiXuan},
abstractNote = {We consider the effect of classical noise applied to the geometric quantum phase of a spin 1/2 in a revolving magnetic field. The Berry phase shows some sensitivity to the noise because the Bloch vector cannot return to its original direction, and the variance caused by noise is proportional to the evolution time.},
doi = {10.1103/PHYSREVA.75.024103},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
Other availability
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Analysis of geometric phase effects in the quantumclassical Liouville formalism
We analyze two approaches to the quantumclassical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a twodimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the WignerthenAdiabatic (WA) QCL approach captures GP effects, whereas the AdiabaticthenWigner (AW) QCL approach does not. Moreover, the Wigner transform in AWQCL leads to an illdefined Fourier transform of doublevalued functions. The doublevalued character of these functions stems from the nontrivial GP of adiabatic electronic statesmore » 
Effect of noise on geometric logic gates for quantum computation
We introduce the nonadiabatic, or AharonovAnandan, geometric phase as a tool for quantum computation and show how this phase on one qubit can be monitored by a second qubit without any dynamical contribution. We also discuss how this geometric phase could be implemented with superconducting charge qubits. While the nonadiabatic geometric phase may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on nonadiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantummore » 
The effect of classical noise on a quantum twolevel system
We consider a quantum twolevel system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the offdiagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine the invariant measure of the system and prove its uniqueness. In the case of OrnsteinUhlenbeck noise, we determine the speed of convergence to the invariant measure. Finally, we determine an approximate onedimensional diffusion equation for the transition probabilities. The proofs use both spectraltheoretic and probabilistic methods. 
Quantum noise and squeezing in an optical parametric oscillator with arbitrary outputmirror coupling. III. Effect of pump amplitude and phase fluctuations
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the secondharmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noisefree pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution ofmore »