Rigorous Born approximation and beyond for the spin-boson model

David P. DiVincenzo and Daniel Loss
Phys. Rev. B 71, 035318 – Published 14 January 2005
PDFHTMLExport Citation

Abstract

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the Ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by α, where α is the coupling strength to the environment. We also explore the calculation of the next-order Born approximation: we show that, at the expense of very large computational complexity, interesting physical quantities can be rigorously computed at fourth order using computer algebra, presented completely in an accompanying MATHEMATICA file. We compute the O(α) corrections to the long time behavior of the system density matrix; the result is identical to the reduced density matrix of the equilibrium state to the same order in α. All these calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.

  • Figure
  • Figure
  • Received 24 May 2004

DOI:https://doi.org/10.1103/PhysRevB.71.035318

©2005 American Physical Society

Authors & Affiliations

David P. DiVincenzo1 and Daniel Loss2

  • 1IBM Research Division, T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA
  • 2Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 71, Iss. 3 — 15 January 2005

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×