Lect10_TwoLevel - General Study of Two-Level Systems Goals...

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General Study of Two-Level Systems Goals: Study ‘Quantum Resonance’ behavior Discuss ‘Avoided Crossings’ and ‘Adiabatic Passage’ Study connection between Spin-1/2 and general two-level systems Examples of two level systems: A Spin 1/2 particle A ‘two-level atom’ An atom driven with an oscillating E-field whose frequency closely matches one of the atomic transition frequencies Particle in a double-well potential Tunneling couples the lowest level on the left side with the lowest level on the right side Generic Two-level Hamiltonian Consider a system with two quantum energy levels, and a Hamiltonian H 0 The eigenstates satisfy: So that: In the { | ! 1 " , | 2 " } basis, H 0 is represented by the matrix: The evolution of the system is then: 2 2 2 0 1 1 1 0 h h = = H H H 0 = h " 1 1 1 + h 2 2 2 H 0 = h 1 0 0 2 # $ % & ( ( t ) = # 1 e $ i 1 t 1 (0) + 2 e $ i 2 t 2 (0)
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Adding a Perturbation Suppose we suddenly change the Hamiltonian, e.g. by turning on an external field So that H # H 0 + W
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.

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Lect10_TwoLevel - General Study of Two-Level Systems Goals...

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