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The Bloch Vector

The Bloch Vector. Dan Li SUNY-Stony Brook 12/11/2002. Outline. Time-Dependent Perturbation Theory Two-Level Problem The Solution for the Problem Bloch Vector The Animations Acknowledgments References . Time-Dependent Perturbation Theory. ,. Two-Level Problem.

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The Bloch Vector

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  1. The Bloch Vector Dan Li SUNY-Stony Brook 12/11/2002

  2. Outline • Time-Dependent Perturbation Theory • Two-Level Problem • The Solution for the Problem • Bloch Vector • The Animations • Acknowledgments • References

  3. Time-Dependent Perturbation Theory , .

  4. Two-Level Problem • To truncate the summation to just two terms single ground and excited state Rabi Frequency Laser Detuning

  5. The Solution for the Problem • Equations: • Solutions:

  6. The Solution for the Problem (2) The probability for the atom to be in the ground and excited state for Ω=γ and δ=γ. Time is in unit of 1/ γ.

  7. Bloch Vector • Its Components:

  8. Bloch Vector (2) • The Bloch vector obeys The vector has the three components:

  9. Animations

  10. Acknowledgments I am very grateful to Professor Metcalf. I got much inspiration in the discussion with him. He is a strict but nice man. He gives much help as possible. I also want to thank to those guys in Prof. Metcalf’s group.

  11. References • 1, Review of Quantum Mechanics • 2, Geometrical Representation of the Schrodinger Equation for Solving Maser Problem, R. P. Feynman et.al. Journal of Applied Physics P49 Vol.28, No.1 Jan. 1957 • 3, Mathematica: A system for doing mathematics by computer. 2nd-Edition. Addison- Wesley Publishing Company, Inc. 1991 My Webpage: http://grad.physics.sunysb.edu/~dli/Courses/OpticsRotation/FinalReportBlochVector.htm

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