skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1]
  1. 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, Ji-Xuan. Effect of classical noise on the geometric quantum phase. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.024103.
Hou, Ji-Xuan. Effect of classical noise on the geometric quantum phase. United States. doi:10.1103/PHYSREVA.75.024103.
Hou, Ji-Xuan. 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, Ji-Xuan},
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}
}
  • We analyze two approaches to the quantum-classical 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 two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic statesmore » in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.« less
  • We introduce the nonadiabatic, or Aharonov-Anandan, 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 » gates that use the Berry phase instead of the dynamic phase.« less
  • We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal 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 Ornstein-Uhlenbeck noise, we determine the speed of convergence to the invariant measure. Finally, we determine an approximate one-dimensional diffusion equation for the transition probabilities. The proofs use both spectral-theoretic and probabilistic methods.
  • 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 second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free 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 » the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.« less