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Agenda

Agenda. Last class review Calculating < r >, including dephasing and relaxation Let’s build a laser : quantum atoms in a cavity ASIDE: Problem set #5 due November 24 th . Reading for next class: M.E. pp 283-287 . M.E.: 211-212. M.E.: 255-258. dipole. probability. E 2. E 1.

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Agenda

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  1. Agenda • Last class review • Calculating <r>, including dephasing and relaxation • Let’s build a laser : quantum atoms in a cavity ASIDE: Problem set #5 due November 24th. Reading for next class: M.E. pp 283-287 M.E.: 211-212 M.E.: 255-258 Laser Optics – Phys460

  2. dipole probability E2 E1 1. Last class review • Introduced density matrix: • Online Java demonstrations: • Matrix element rpq for transitions other than ground state to first excited state (1D SHO) Laser Optics – Phys460

  3. 1. Review, cont. 4. Atomic hydrogen: M.E.: pg 208 Calculating matrix element rpq for anything other than 1-d SHO beyond the scope of this course… Laser Optics – Phys460

  4. 2. <r>, including dephasing Include dephasing and energy relaxation: ~: collisions, other processes but no change to occupation probabilities • Rate of relaxation from upper to lower state • a.k.a. spontaneous emission • a.k.a. Einstein A coefficient Laser Optics – Phys460

  5. 2. <r>, cont. • Recall lecture 19: • We are far from Rabi flopping regime • Dipole terms reach steady-state much faster than probabilities change. 1/A21 s l o w FAST Laser Optics – Phys460

  6. 2. <r>, cont. • “Adiabatic following” regime • Requires “low” intensities and fast dephasing – almost always the case even in a laser • Can eliminate off-diagonal terms from equations and write everything in term of : • We will first return to atoms in a cavity as discussed with classical atoms The rest of the course! population equations! Laser Optics – Phys460

  7. What is the physical meaning of  in this formula? 3. Quantum atoms in a cavity Standing wave solutions: Quantum atom polarization P! 1. Check for consistency real Careful: consistent phasor notation Laser Optics – Phys460

  8. 3. Cavity, cont. 2. Assume steady-state solution Regime: fast dephasing! Laser Optics – Phys460

  9. 3. Cavity, cont. Define: Does this look familiar? Laser Optics – Phys460

  10. 3. Cavity, cont. Required for steady-state! Break into real and imaginary components: IMAG Threshold condition! g can be positive! Frequency pulling/pushing REAL Laser frequency does not match vacuum cavity modes! Reference: lecture 22 Laser Optics – Phys460

  11. Laser guide star – Lick Observatory We have “built” a laser! Require N2>N1 Laser Optics – Phys460

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