Lect7_RabiModel - 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 E.g. electron in a double quantum dot Tunneling couples the lowest level on the left side with the lowest level on the right side
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Generic Two-level Hamiltonian Consider a system with two quantum energy levels, and a Hamiltonian H 0 – The eigenstates satisfy: – So that: – In the { | ω 1 , | 2 } basis, H 0 is represented by the matrix: – The evolution of the system is then: 2 2 1 1 2 0 1 0 h h = = H H 2 2 1 1 2 1 0 h h + = H = 2 1 0 0 0 h H ) 0 ( 2 2 ) 0 ( 1 1 ) ( 1 1 ψ t i t i e e t + =
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Lect7_RabiModel - General Study of Two-Level Systems Goals...

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