1. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 1yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Lecture 4 Review of Quantum Physics & Basic AMO Physics How to “do” quantum mechanics QO tries to “understand” it (partly)

2. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 2yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Course Outline Part 1: basic review: Optics+Quantum; Part 2: Basic Light- matter interaction; laser; Part 3: Quantum Optics of photons Part 4: More advanced light-matter interaction Part 5: Quantum information/photonics/ applications Subject to change; Check updates on course web/wiki

3. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 3yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ This Lecture Review key concepts from quantum mechanics & AMO (cf. *FQ Chap3; also of interests: *FS Appendix; *Ken Krane “Modern Physics” *D. Griffiths: intro quantum mechanics * (AMO): Chris Foot, atomic physics

4. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 4yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Some most important model systems in QM 2-state QM (d=2, simplest hilbert space) –spin-1/2 (  &  ) –photon 2-polarization (  &  ) Particle in box /1D Schrodinger Harmonic oscillator Hydrogen atom  AMO physics Periodic potential  solid state physics

5. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 5yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Conceptual/theory Matter wave; wave-particle duality (De Broglie) –Energy, momentum, wavelength, for free particle [dispersion] Uncertainty principle (Heisenberg) –Fourier transform picture

6. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 6yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Theory/Formulation Schordinger equation/wavefuction Matrix formulation (Heisenberg) Dirac “bra-ket” … quantum state/Hilbert space –Wave function vector in Hilbert space QED and QFT: Feynman diagram

7. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 7yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Particle in a box/1D Schrodinger Infinite square well (uncertainty) Finite square well 1D scattering state (refection & transmission --- “quantum reflection” & tunneling, even “resonant tunneling”)

8. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 8yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Energy-momentum-wavelength Wave-particle duality Massless particle (photon) Massive particle (eg. electron) Phase vs group velocity Dirac vs Schrodinger eq. (E  H)

9. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 9yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ AMO (Atomic and Molecular & Optical Physics) Some Key Concepts Not really…

10. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 10yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Hydrogen Atom (Z=1) Bohr model Schrodinger equation “Hydrogenic” atom /ion Dopant in semiconductor..

11. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 11yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ (quantum) Angular Momentum Orbital Spin (intrinsic angular momentum) Angular momentum addition, S-O coupling

12. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 12yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Hydrogen atom wavefunction (for the electron orbit)

13. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 13yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ 11/24/201513 Nomenclature

14. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 14yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ 11/24/2015 14 Probability Functions for a few states of H

15. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 15yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/

16. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 16yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/

17. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 17yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ n=1,l=0

18. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 18yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Finer structures Fine structure Hyperfine structure Zeeman effect (B field) Stark effect (E field) “21cm”

19. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 19yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Periodic Table of Elements “each column have similar properties”

20. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 20yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Order of filling atomic orbitals K (n=1) shell L (n=2) shell M (n=3) shell subshell by l (s, p, d, f), each can accommodate 2(2l+1) electrons Why filling the orbitals: Pauli exclusion principle 4s before 3d [draw levels on board]

21. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 21yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ 3s 3p 3d ---- turns out 4s will come lower! for n>=3 …. s & p orbitals more “penetrating” (can get closer to nucleus) ---- lower in energy d, f orbitals less penetrating (cannot get as close to nucleus) ---- higher in energy consequence in filling order, (4s, 3d, 4p), (5s, 4d, 5p), (6s, 4f/5d, 6p) etc. [with few exceptions]

22. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 22yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Periodic Table of Elements “each column have similar properties” alkali Alkaline earth inert gas halogen Transition metal (elements) (rare earth) f f

23. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 23yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ A few concepts Outer electrons (most important for usual chemical/physical properties, & optical transition), screening of nucleus charge by inner electrons (Z eff ) [example 8.3 --- excited state approach hydrogenic atom]

24. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 24yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ (K absorption edge) (K  ) Inner electron (“core” electron) --- much more tightly bound, X-ray absorption edge and X-ray transition [K, L x-rays, etc.], Morseley’s law to determine atomic Z # “not periodic behavior”!

25. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 25yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Molecules How do molecules form (bonding) Molecular spectra

26. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 26yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Molecular bonding Atomic orbitals interact and form molecular orbitals Bonding and anti-bonding orbitals Covalent bond –H2+, H2 molecule, s-s bond –P-p bond, eg. N2, O2 –S-p bond, HCl, etc. –Sp hybrid, involving C, Si etc. Ionic bond

27. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 27yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Vibration and Rotation quantum states vibration rotation hf BJ(J+1) 2B(J+1)

28. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 28yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Molecular potentials, ro-vibration levels & spectra HCl hf 2B

29. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 29yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Some Modern Areas in AMO Physics Atomic/molecular structure and spectroscopy Few-body physics, chemical physics Precision measurements, fundamental constants, “beyond standard model” physics, atomic clocks Ultracold atoms/molecules, quantum gases ---BEC, fermi gas etc. Ultrafast science (from fs to as), quantum dynamics “quantum” physics & technology: quantum information/computing/communication, quantum control, quantum optics Laser physics: ultra-intense/fast lasers, light-matter interaction etc. http://www.physics.purdue.edu/research/amo.shtml http://www.nap.edu/catalog.php?record_id=11705

30. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 30yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Electrons in Crystalline Solids Some Key Concepts

31. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 31yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/

32. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 32yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/

33. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 33yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ ©2008 by W.H. Freeman and Company

34. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 34yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/

35. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 35yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ ©2008 by W.H. Freeman and Company

36. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 36yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ ©2008 by W.H. Freeman and Company

37. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 37yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ If band varies with space Junction, quantum well/wire/dot 1D quantum mechanics! Interband tunneling

38. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 38yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ ©2008 by W.H. Freeman and Company

39. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 39yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ ©2008 by W.H. Freeman and Company

40. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 40yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Back to 2-state QM (d=2 Hilbert space)

41. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 41yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Stern Gerlach Experiment -1 0 +1 Spins (m f ) (Stern-Gerlach: separate BECs with different spins) B-field gradient

42. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 42yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Next Lecture : Quantum Information 1: Cryptography FQ Chap 12

43. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 43yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Quantum Information Science 1: quantum (secure) communication & quantum cryptography (photon based) (cf. *FQ Chap12) Shapiro-Wang Group: http://www.rle.mit.edu/qoptics/ MIT 6.453 course on quantum communication http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-453-quantum-optical-communication-fall-2008/ Learn more: Chuang & Nielson, QCQI

44. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/27/2014) Slide 44yongchen@purdue.edu Introduction to Quantum Optics & Quantum Photonics PHYS522 ECE695 (“Coherent Optics & Quantum Electronics”) http://www.physics.purdue.edu/academic_programs/courses/phys522/ Classical Cryptography (Secure Communication) ENIGMA RSA RSA-100 = 15226050279225333605356183781326374297180681149613 80688657908494580122963258952897654000350692006139 RSA-100 = 37975227936943673922808872755445627854565536638199 × 40094690950920881030683735292761468389214899724061 RSA-100=37975227936943673922808872755445627854565536638199 × 40094690950920881030683735292761468389214899724061 Earn $200,000 to factorize RSA-2048 Later quantum computing will break this