Chapter 11-12

1. Chapter 11-12

2. 现在进入量子理论体系 量子光学 电磁光学 波动光学 非线性光学 几何光学 Photon Optics The study of the nature and effects of light as quantized photons

3. 书本上对QED的定义 Quantum Electrodynamics

4. 什么是photons Photons • According to quantum mechanics, light may be considered not only as an electro-magnetic wave but also as a "stream" of particlescalled photons. • These particles should not be considered to be classical billiard balls, but as quantum mechanical particles described by a wavefunction spread over a finite region. • This kind of use of statistical mechanics is the fundament of most concepts of quantum optics • Light is described in terms of field operators for creation and annihilation of photons—i.e. in the language of quantum electrodynamics.

5. 回顾历史发展 neither descriptions are sufficient EM waves? 光子的粒子-波动性的历史 • 17th century : Newton particle • (Ray Optics) • 19th century : Fresnel, Maxwell... wave • 1900s : Planck, Einstein particle • 1920s : Quantum mechanics • 1950s : Quantum Electrodynamics • 1960s : Quantum Optics

6. XIX-th century • Young (~1800) : interferences, a light wave can be added or substracted • Sinusoïdal wave • Fresnel (1814-20) : Mathematical theory of diffraction and interferences • Scalar wave • Fresnel - Arago(1820-30) : polarization phenomena • Transverse vectorial wave • Faraday - Maxwell (1850-64) : light as an electromagnetic phenomena • wave withwith Everything is understood but...

7. Some problems remain • The spectral behaviour of black body radiation is not understood : • why the decrease at high frequency ? 迈克尔逊-莫雷实验和黑体辐射实验称为十九世纪末叶飘在物理学晴朗天空的“两朵乌云”

8. Some more problems... • Photoelectric effect (Hertz and Hallwachs, 1887) • UV light removes charges on the surface while a visible light does not Planck : energy exchange occur with multiples of Bohr : atomic energy levels

9. Light is made of particles • Light is made of unbreakable “quanta” of energy (Einstein 1905) This was later checked by Millikan • The Compton effect (1923) The particle (“photon”) possesses a given momentum • Photomultiplier : light can be seen as a photon current pulses

10. 后续，随着激光器的发展…进一步推广 Time Table • 1899, Planck, blackbody radiation • 1905, Einstein, photoelectric effect • Bohr, atoms were also quantized • 1953, invention of maser • 1960, invention of laser • 1950s to 1960s, Dirac, Sudarshan, Glauberand Mandel, quantum field theory and applied quantum theory • The introduction of the coherent state and squeezed light Light Amplification by Stimulated Emission of Radiation

11. 除了光电效应及黑体辐射，后续的试验证明… Interferences and photons Taylor (1909) : Young's slits with an attenuated source ("a candle burning at a distance slightly exceeding a mile”) Photographic plate Exposure time "each photon then interferes only with itself”, Dirac This specific property of a single photon only by the behavior of a group of photons.

12. 量子理论体系刚开始… Quantum mechanics (~1925) • Complete quantum theory of matter : • energy levels, atomic collisions • Atom-field interaction : Classical electromagnetic waveQuantum atom « Semi classical theory : • Energy transfers only by units of • Momentum transfers by units of

13. Consequences of the semi-classical theory • Photoelectric, Compton effects can be understood with a classical wave • Pulses recorded in the photomultiplier are due to quantum jumps inside the material and not to the granular structure of light same for the photographic plate in Taylor ’s experiment Light remains a classical electromagnetic wave • Should Einstein be deprived of his (only) Nobel prize ? • And Compton ?

14. 最终量子化… Quantum electrodynamics (1925-30) • Quantum calculations are applied to light in the absence of matter • In the case of a monochromatic light, the energy is quantified : • contains n photons (quanta) : En • contains 0 photons (quanta) : E0 (Vacuum, absence of radiation, fundamental state of the system)

15. QED remains a marginal theory (1930-47) • Reasons 1) Problem of interpretation 2) Problem of formalism : many diverging quantities e.g. Vacuum energy : 3) Problem of "concurrence" : the more simple semiclassical theory gives (generally) the same results • 2) was solved in 1947 (Feynman, Schwinger & Tomonaga) : renormalization QED serves as a base and model for all modern theoretical physics (elementary particles…)

16. Toward new experiments • Large success of quantum electrodynamics to predict properties of matter “in the presence of vacuum”. • Agreement between theory and experiment 10-9 • Progress in optical techniques • lasers • better detectors • nonlinear optics

17. 到底有什么不同？ Difference between wave and corpuscle Wave Continuous Unlocalised, breakable Photons Discontinuous Localised, unbreakable A crucial experiment : the semitransparent plate 50% reflected (1) (2) 50% transmitted The plate does not cut the photon in two ! photons are – in the sense of energy quanta –indivisible.

18. Experimental result (1) (2) But a very faint source does not produce a true one photon state : the beam is a superposition of different states, e.g. A faint source does not give a clear result

19. Production of a state A single dipole (atom, ion…) emits a single photon at a time The classical concept of continuously distributed electromagnetic energy in space must be abandoned in the case of single photons. Kimble, Dagenais and Mandel, Phys. Rev. Lett. 39 691 (1977) First experimental proof of the particle nature of light

20. One photon interference To MZ2 To MZ1 Ca beam Grangier et al., Europhys. Lett1 173(1986)

21. What have we learned ? • Light can behave like a classical wave • Classical interferences • Light can behave like a classical particle • One photon interferences • Light can behave like a non-classical state • Two photon interferences “a photon interferes with itself” (Dirac, 1958)

22. Quantum Physics • All measurement results (up to now) are in agreement with the predictions of quantum electrodynamics • (including experiments of measurement and control of quantum fluctuations) • No more mysteries • the actual theory explains without ambiguity all phenomena • but still "strange" behaviours • Physical images • several may work wave and particle • only someworks wave or particle • none works neither wave nor particle 观察光子时应用的方法，将最终决定光子的行为是像粒子还是像波

23. Science 2 November 2012: Vol. 338 no. 6107 pp. 634-637 科学家同时观察到光的波粒二象性? 正弦振荡的波形，表示的是单光子干涉，是一种波动现象。 近处，观察不到振荡，说明只表现出粒子的特性 实现了光子从波的形式向粒子状态的连续转变

24. The Photon

25. Photon Quantum electrodynamics (QED) is today accepted as a theory that is useful for explaining almost all known optical phenomena.

26. In classical electromagnetic theory, the energy Eqcan assume an arbitrary nonnegative value, no matter how small. In Photon Optics the energy of a mode is quantized with onlyintegral units of this fixed energy permitted.

27. Photon Energy 一种自发的能量扰动

28. Zero-Point Energy • All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature • Zero-point energy is fundamentally related to the Heisenberg uncertainty principle • Energy Background---seems infinite and can be utilized as a energy source

29. Casimir effect • two uncharged metallic plates in a vacuum, placed a few micrometers apart as in a capacitor but without any external electromagnetic field • using the QED, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force - either an attraction or a repulsion depending on the specific arrangement of the two plates. • it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects.

30. Photon Energy 化学键的键能一般在10eV以内，紫外线的光子能量大于3.4eV。 不过对于能量高达KeV的X射线，则基本上所有化学键都会被打断

31. Photon Polarization

32. Photon Position

33. Transmission of a Single Photon Through a Beam-splitter A single photon incident on the device follows one of the two possible paths in accordance with the probabilistic photon-position rule

34. Photon Momentum m0=0 光子的质量都不会超过10的负54次方千克 地球:电子的质量比~1054

35. Spin and Orbit Angular Momentum • 与偏振相关：自旋角动量SAM • 与螺旋相位相关：轨道角动量OAM • 总角动量：SAM + OAM Intrinsic: ΔJz=0 for all r, e.g. SAM Otherwise: Extrinsic

36. Photon Interference Demonstrate the wave nature of light

37. Single Photon in a Mach-Zehnder Interferometer

38. Something need our attention 全同性和不可区分性，非常重要！ • A world with variables possessing well defined values which are not known precisely • It is forbidden to draw conclusions about certain physical properties before the measurement of those properties is complete. • Measurement: a “reduction” or “collapse” of the wave function takes place • it chose its behavior only in accordance with the experimental conditions it found at its moment of arrival at the given place. • No difference between the physical states of the individual atoms • Indistinguishable • The atoms are in the upper and lower levels simultaneously

39. Quantum Superposition or Classical Physics: “bit” + Quantum Physics: “qubit” Uncertainty & nonlocal

40. magnet B source magnet A Einstein–Podolsky–Rosen Paradox • Einstein was never reconciled to quantum theory being an essentially indeterministic description of natural processes • “God does not play dice” NonLocality in Quantum Mechanics Superlumina Hidden variables theories

41. Twin-photons are needed How to prepare entanglement • Parametric down-conversion (PDC) • twin daughter photons are produced simultaneously from a parent photon • the signal and idler photons have natural correlations in energy and momentum. • Type-I phase matching • The generated signal and idler photons have parallel polarizations. • Type-II phase matching • The signal and idler photons have perpendicular polarizations.

42. Applications • Quantum Communication • Quantum teleportation • Quantum logic gate • Quantum Computation

43. Time-Energy Uncertainty 满足量子力学的一些性质 其实，是波的基本特性！

44. Photon Streams

46. Mean Photon-Flux Density 人眼是非常敏感的探头，可以察觉100个光子能量！

47. Photon-Number Statistics • Coherent Light under the assumption that the registrations of photons are statistically independent

48. Coherent Light Signal-to-Noise Ratio increases linearly with the mean number of photon counts.

49. Thermal Light

50. behave like random quantities