Geometric phase for an adiabatically evolving open quantum system

The University of Calgary, Calgary, Alberta, Canada
Physical Review A (Impact Factor: 2.81). 07/2004; 70(4). DOI: 10.1103/PhysRevA.70.044103
Source: arXiv


We derive a solution for a two-level system evolving adiabatically under the influence of a driving field, which includes open system effects. This solution, which is obtained by working in the representation corresponding to the eigenstates of the time-dependent Hermitian Hamiltonian, enables the dynamic and geometric phases of the evolving density matrix to be separated. The dynamic phase can be canceled in the limit of weak coupling to the environment, thereby allowing the geometric phase to be readily extracted both mathematically and operationally.

Download full-text


Available from: Barry C. Sanders, Dec 03, 2012
  • Source
    • "Several researches have noted [16] [17] [18], however, that this choice of gauge is not always possible globally, so that Berry phase may also appear in a noncyclic evolution . However, the Born-Fock gauge can cause the transformed vector potential to vanish if the curl of A(R) is zero. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The concept of Berry phase is included in an analysis of the intensity distribution in far wings of pressure-broadened spectral lines emitted or absorbed by atoms placed in an external cone-rotating electric field. Particular attention is focused on frequency regions where rainbow satellite bands appear. A classical-path treatment that employs the time-dependent Schrödinger equation is used to derive an expression for the line shape, and it uses a dipole transition moment calculated with quasimolecular wave functions given by the Berry version of the adiabatic approximation. It is found that in the presence of an external rotating electric field, the intensity distribution in far wings can be expressed in terms of the universal line shape function of the unified Franck-Condon theory once energy shifts due to Stark and Berry effects are taken into account. We show that the influence of Berry phase in the profiles of the far wings can be manifested either in the form of deviations of observed profiles from the quasistatic distribution or the appearance of additional features in the vicinity of the maximum of the rainbow satellite band. As an example, the modification of the rainbow satellite at 162.3 nm in the red wing of the self-broadened Lyman-α line of hydrogen, caused by an external rotating electric field, is considered.
    Full-text · Article · Sep 2015 · Physical Review A
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, e-print quant-ph/0404147). We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems [K.P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)] and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.
    Full-text · Article · Dec 2004 · Quantum Information Processing
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak coupling limit and it involves the phase information of the environment in general. In contrast with the geometric phase in dissipative systems, the geometric phase acquired by the system can be observed on a long time scale. We also show that with the system decohering to its pointer states, the geometric phase factor tends to a sum over the phase factors pertaining to the pointer states. Comment: 4 pages
    Preview · Article · Jan 2005 · Physical Review A
Show more