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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
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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
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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
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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
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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
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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
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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
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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”
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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)
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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
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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
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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
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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
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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.
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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
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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)
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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
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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.
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