Ch3 - Two Level System

Ch3 - Two Level System - Chapter 3 Two-state systems Spin...

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Two-state systems Chapter 3
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Spin states of an electron An electron is a spin ½ particle, which has only two values: /2 ± = The particle carries (intrinsic) angular momentum and magnetic moment. A general internal state of an electron is described by 22 || | | 1 αβ + = ψα β = ↑+ ↓ Remark: A full quantum state vector of an electron must include the external degree of freedom: () , , d ppp pp Ψ= + Question: Under what conditions can we ignore the external part? http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach /SternGerlach.html
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Polarization states of a single photon { H , V } or { L , R } H V ψ αβ = + () , k kH k k V k Ψ= + G GG G G A complete state vector of a photon
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Two-level atoms g e Laser L e g EE ω = e E g E Optical resonance • The atomic states and can be effectively coupled by the laser. It is unlikely that the atom can make transitions to non-resonant states (assuming that the field is not too strong and the level spacing differences are large. g e eg ψ αβ = + LL dE << =
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e.g. Sodium D2 line http://steck.us/alkalidata/
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1-photon input Artificial two-state systems Output Mode 1 Output Mode 2 Beam splitter 0 "0 1 "" 1 1 0 " output ψα β α =+ + N No photon in mode 1 One photon in mode 2 N One photon in mode 1 No photon in mode 2 e.g.
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A classical bit has a state: Either 0 or 1 What is a qubit? 22 || | | 1 αβ + = • The state of a qubit is generally a superposition state other than just or 0 1 • The number α and β can be any complex numbers satisfying the normalization condition: • The values of α and β (assuming unknown) cannot be determined if you have only one copy of the qubit, because a measurement would destroy the original state.
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Ch3 - Two Level System - Chapter 3 Two-state systems Spin...

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