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DATE | 2009-05-11 |

TIME | 12:00 |

PLACE | R49223, Second Physics Building , NCKU |

FIELD | Quantum Information Science |

SPEAKER | Mr. Dong-Bang Tsai(蔡東邦) - 中研院應用科學研究中心 |

TITLE | Numerical Propagator for Time-Periodic Hamiltonians |

ABSTRACT | Time-periodic Hamiltonians are an important intermediate case between stationary and arbitrarily time-dependent systems, encountered for instance in the presence of ac driving. These are often handled by the Floquet method—the time counterpart of the Bloch-function approach for systems with a spatially periodic potential. One then has to deal with numerous Fourier components, dramatically increasing the dimension of the equations. This is not only computationally inefficient, but can also be less transparent physically than a more compact formulation. Here we provide an alternative by numerically integrating the Schrödinger evolution operator over one time period, and diagonalizing the ensuing unitary matrix. Thus, we avoid extended Hilbert space (with an additional index labeling the Fourier components) entirely. We have tested our method on the one-qubit NMR problem, and find perfect agreement with the analytical solution. Applications will include the voltage-biased single-Cooper-pair transistor, where the time-periodicity is due to Josephson oscillations. In a real-world system, the effect of damping must be considered, so that the propagator is no longer unitary. Therefore, we are trying to extend our approach to the trace-preserving superoperator describing the evolution of the density matrix in open quantum systems. |