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

ABSTRACT 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.

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Available from: Barry C. Sanders, Dec 03, 2012
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    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.
    Quantum Information Processing 12/2004; 3:331. DOI:10.1007/s11128-004-7712-7 · 1.92 Impact Factor
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    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
    Physical Review A 01/2005; 71(4). DOI:10.1103/PhysRevA.71.044101 · 2.81 Impact Factor
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    ABSTRACT: We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analysed.
    Physical Review A 01/2005; 71:012331. DOI:10.1103/PhysRevA.71.012331 · 2.81 Impact Factor
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