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Einstein on the Nature of Light Brief History of Quantum Optics

Zhe-Yu Jeff Ou Department of Physics Indiana University-Purdue University Indianapolis. Einstein on the Nature of Light Brief History of Quantum Optics. • One Hundredth Anniversary of Photon. Outline:. • Einstein’s light quanta and its wave-particle duality .

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Einstein on the Nature of Light Brief History of Quantum Optics

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  1. Zhe-Yu Jeff Ou Department of Physics Indiana University-Purdue University Indianapolis Einstein on the Nature of Light Brief History of Quantum Optics

  2. • One Hundredth Anniversary of Photon Outline: • Einstein’s light quanta and its wave-particle duality • Hanbury-Brown and Twiss’ photon bunching • Glauber’s quantum theory of optical coherence • Mandel’s anti-bunched photons • Mandel’s two-photon interference —photon entanglement

  3. Nobel Prize in Physics Glauber Hall Haensch Happy One Hundredth Birthday, Photon!

  4. Happy One Hundredth Birthday, Photon! • Max Planck’s Blackbody Radiation Formula (1900) Model: 1-d harmonic oscillators with En = nhn in thermal equilibrium with radiation (light) • Einstein’s light quanta (1905)  Birth of the Photon  Compton first named “photon” (1923)

  5. • Kirchhoff from Thermodynamics (1859) independent of materials  • Wien’s radiation Law (1893) • Rayleigh-Jeans Law (1900) Blackbody Radiation Laws  short wavelength  long wavelength

  6. • Probability argument for photon: Einstein’s 1905 paper on Light • Photo-electric effect Particles in a box of V : pDV(1) = DV/V  pDV(n) = (DV/V)n

  7. • Einstein used the Wien’s radiation law high frequency limit from Planck’s formula  Einstein’s Probability Argument For radiation in a box: • Principles of thermodynamics for the probability  n = E/hn p(all E in DV) = (DV/V)E/hn

  8. •A. Einstein, Ann. Physik, 4th Ser. 17, 132-148 (1905). Photo-electric Effect • A. Einstein, Phys. Z. 10, 185-193 (1909). Wave-particle duality • A. Einstein, Phys. Z. 18, 121-128 (1917). Stimulated and spontaneous emission • A. Einstein, Preuss. Akad. D. Wissenschaften, 1924, pp.261-267; 1925, pp.3-14. Bose-Einstein Statistics Einstein’s Four Papers on Light

  9. • Einstein’s approach is from the aspect of the energy fluctuations in (n, n+dn) in a sub-volume of a box. Einstein’s Wave-Particle Duality •In 1909, Einstein published a paper on radiation: Planck’s radiation law  wave-particle duality

  10. where with Einstein’s Wave-Particle Duality •Using the principles of thermodynamics, Einstein derived

  11. wave particle Einstein’s Final Result

  12. Einstein’s Wave for Light •Assuming plane waves for radiation of different amplitude, phase, directions, and polarizations •This formula can be derived from Rayleigh-Jeans law  Long wavelength approximation

  13. •Poisson Statistics for random particles: •With Einstein’s photon formula of E = nhn, Einstein’s Particle for Light •This formula can be derived from Wien’s radiation law  short wavelength approximation

  14. Einstein’s Duality of Light •Similar argument for momentum of light (radiation pressure): p = nhn/c = nh/l

  15. Einstein’s Duality of Light It cannot be denied that there is a broad group of facts concerning radiation, which show that light has certain fundamental properties that can be much more readily understood from the standpoint of Newtonian emission theory than from the standpoint of the wave theory. It is, therefore, my opinion that the next stage of the development of theoretical physics will bring us a theory of light which can be regarded as a kind of fusion of the wave theory and the emission theory … a profound change in our views of the nature and constitution of light is indispensable. A. Einstein, 1909

  16. Quantum Theory of Light •Dirac first formulated the quantum theory of light in 1927. •Schwinger, Tomonaga, and Feymann in late 1940’s  Quantum Electrodynamics (QED) •Lamb shift in Hydrogen (1947). Individual Behavior! Collective Behavior???

  17. Hg I2 I1 t Nc(t) x t N ( ) / I I c 1 2 Wave has well defined amplitude and phase 2 1 <I1I2> = I1I2 t Hanbury-Brown Twiss Experiment 1956 Excess coincidence!!

  18. •Optical waves are described by •Thermal fields  Normal (Gaussian) Distribution Born and Wolf in late 1940s and early 1950s developed a coherencetheory for optical fields. Classical Coherent Theory with A(t) and j(t) as random variables

  19. Mandel, 1956 Need for Quantum Theory? Semi-classical theory of light -- Janes (Hot debate in early 1970s)  Treat vacuum as white random noise •Explain photo-electric effect •Spontaneous emission •Lamb shift!!

  20. 1 2 Photo-detection Theory  photo electric pulse Joint detection

  21. 1 2 Glauber, 1963 Quantum Photo-detection Theory

  22. If we use Classical Field ? Quantum Field Glauber’s Quantum Coherence Theory  coherent state

  23. Coherent source: laser has well defined A and j Amplitude + phase For multi-mode:  Glauber’s Quantum Coherence Theory

  24. For coherent state, Glauber’s Quantum Coherence Theory Multi-photon detection probability is proportional to

  25. For arbitrary fields, {ak} are random variables: For thermal source, Glauber’s Quantum Coherence Theory P({ak}) > 0 is some probability distribution How to describe a thermal source quantum mechanically?

  26. Furthermore, for an arbitrary source of light Glauber-Sudarshan’s P-representation Thermal source described by a density matrix:

  27. Need for Quantum Theory? Semi-classical theory of light -- Janes (Hot debate in early 1970s)

  28. with Glauber-Sudarshan’s P-representation But there is one caveat: P({ak}) can be negative! P({ak}) is only a quasi-probability density

  29. is called a classical state of light --- same as wave theory describes a nonclassical state of light --- a true quantum state Classical vs Nonclassical State of Light • IfP({ak}) >= 0, thenP({ak}) is a true probability density • IfP({ak}) < 0, for some {ak}, thenP({ak}) is not a probability density

  30. Bunching Anti-Bunching t N ( ) / I I c 1 2 1 t Schwartz inequality: t N ( ) / I I c 1 2 2 1 t Mandel’s Anti-Bunched Photons

  31. only look at the fluorescence Mandel’s Anti-Bunched Photons •Immediately after the emission of one photon, atom is in the ground state and cannot emit a second photon. •Atom has to wait until being re-pumped to the excited state to be able to emit another photon.

  32. Single atom, ion, molecule, artificial atom (quantum dot) Single Photon on Demand •If the pump pulse is short enough, each pulse can only make atom emit one photon only --- single photon source •Applications in quantum cryptography and computing

  33. Wave theory A List of Nonclassical Phenomena •Photon anti-bunching •Sub-Poissonian photon statistics •Squeezed state of light  quantum noise reduction •Nonclassical two-photon interference

  34. Two-photon entanglement Multi-photon entanglement and interference Quantum information Mandel’s Two-Photon Interference Two-photon interference

  35. j1 - j2 = constant for short observation time Interference between Independent Lasers Mandel and Magyor (1963) L a s e r 2 L a s e r 1

  36. Dirac’s Statement on Photon Interference

  37. L/2 Mandel and Pfleegor (1969) Interference between Independent Lasers Attenuator

  38. negative correlation! Mandel and Pfleegor (1967) Interference between Independent Lasers for x1- x2 = l/2

  39. x1- x2 = L/2=l/2 Mandel and Pfleegor (1967) Interference between Independent Lasers

  40. C Mandel and Pfleegor (1967) Two-Photon Interference

  41. Always exist for classical sources Mandel (1983): Two-photon: Quantum Two-Photon Interference

  42. Ou and Mandel (1989) Quantum Two-Photon Interference

  43. Photon Bunching   Photon Bunching as a Two-Photon Interference Effect •Spontaneous emission •Stimulated emission

  44. Thank You! Happy New Year!

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