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spin + An electron in a quantum dot between magnetic pole pieces is subjected to an external magnetic field B. At zero field, the spin-up and spin-down states are degenerate. At nonzero field, they split by an energy Delta E Z equal to mu B times B. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Zeeman Splitting of an Electron Spin + An external magnetic field lifts the degeneracy of the two spin states + + + + + Magnetic pole + Magnetic pole + N + S + + + External magnetic field + B + + + + + electron + + + + No magnetic field + B = 0 + + + Energy + + E0 + spin up + spin down + degenerate spin states + Eup = Edown = E0 + + + + Applied magnetic field + B > 0 + + + Energy + + E0 + + + + spin up + spin down + E0 + ½ μBB + E0 − ½ μBB + + + ΔEZ + = μBB + + + + + The energy separation increases linearly with the field strength B + From 64fe976d5b63619e20e071a33a75b5fb1caaf3e4 Mon Sep 17 00:00:00 2001 From: Kiro Date: Mon, 20 Jul 2026 05:42:46 +0000 Subject: [PATCH 2/2] Simplify Zeeman splitting figure --- zeeman_splitting.png | Bin 83996 -> 25760 bytes zeeman_splitting.svg | 138 +++++++++++++++---------------------------- 2 files changed, 49 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a quantum dot between magnetic pole pieces is subjected to an external magnetic field B. At zero field, the spin-up and spin-down states are degenerate. At nonzero field, they split by an energy Delta E Z equal to mu B times B. + + Simplified Zeeman splitting diagram + At B equals zero the electron spin states are degenerate at E zero. At nonzero B the states split symmetrically, with energy separation Delta E sub Z equal to mu sub B times B. - - - - - - - - - - - - - - - - - - - - - - - - - - + + - - Zeeman Splitting of an Electron Spin - An external magnetic field lifts the degeneracy of the two spin states - - - - - Magnetic pole - Magnetic pole - N - S - - - External magnetic field - B - - - - - electron + - - - No magnetic field - B = 0 + + + B = 0 + + E - - Energy - - E0 - spin up - spin down - degenerate spin states - Eup = Edown = E0 + + E0 + + Eup + = Edown + = E0 + - - - Applied magnetic field - B > 0 + + + B > 0 + + E - - Energy - - E0 + + E0 - - - spin up - spin down - E0 + ½ μBB - E0 − ½ μBB + + + Eup + = E0 + + ½ μBB + - - ΔEZ - = μBB + + + Edown + = E0 + − ½ μBB + - - + + + ΔEZ + + + = μBB + - The energy separation increases linearly with the field strength B + + +