1. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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 16 Photon Number States (a basis of quantum theory of light) Reminder: Lecture notes taker HWK4 posted today, due next Wed 4/9

2. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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 16 (3/31/2014) 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/ Quantum Optics of Photons FQ’Chap5 Chap 7-8: coherent, squeezed, & number states FQ’Chap6

4. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Classification of Light by Photon Statistics (Nonclassical light) Poisson Statistics

5. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ single photons-> antibunching

6. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Fox FQ’Chap7

7. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Coherent State

8. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Photon Number States (FQ’8) Basis for quantum theory of light A simple form of “QFT”

9. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Review quantum operators for harmonic oscillator --- models for light quanta Ladder operators: Raising/creating operator Lowering/annilation operator Why? (dimensionless)

10. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Properties of raising/lowering operators Numbering operator

11. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Number (Eigen) States (can verify this for wave function of h.o.) (normalized) Photon number states (Fock states) |n> |0>=|vac> |n>= n photons

12. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Quadrature Fields of Light  X 1  X 2 >1/4 (classical) dimensionless Quantum uncertainty principle =1/16

13. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Number State in Phasor Diagram

14. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Coherent States (in number state representation) (check normalized: =1) = = Poisson distribution! Check: |  =0>=|0> =? =? etc.

15. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Coherent State Operator

16. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Quantum Theory of HBT Experiment (normal ordering) (vac) classical quantum input for |  1 >=|n> (number state) for |  1 >=|  > (coherent state) =1 (=0 “anti-bunching” for single photon)

17. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Squeezed State/Light Generate squeezed state/light: Degenerate parametric amplifier 2 nd harmonic generation (amplitude squeezing) Optomechanics … http://physics.aps.org/articles/v6/95

18. Purdue University Spring 2014 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 16 (3/31/2014) 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/ Next Lecture (16): Quantum Computing FQ Chap 13.