Quantum optics - Tran Thi Ngoc Dung

Nội dung text: Quantum optics - Tran Thi Ngoc Dung

1. QUANTUM OPTICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. Contents • Thermal Radiation • Spectral irradiance r,T, r,T, • Total irradiance R,T, • Spectral absorbance a,T, a,T, • Kirchhoff ‘s law of equilibrium thermal radiation • Laws of Blackbody Radiation • Stefan-Boltzmann’s law • Wien’s Displacement law • Planck’s Quantum theory • Einstein’s Photon Theory • Compton Effect
3. THERMAL RADIATION 1. The fundamental sources of all electromagnetic radiation are electric charges in accelerated motion. 2. All bodies emit electromagnetic radiation as a result of thermal motion of their molecules; this radiation, called thermal radiation, is a mixture of different wavelengths.
4. Spectral irradiance r(,T), r(,T) • Consider an object of temperature of T. • The object emits electromagnetic waves dW(,T) of many different frequencies dS (wavelengths) • Let dW(,T) the energy emitted per area dS per unit time, and transmitted by T electromagnetic waves of frequencies in the range (,+d). • Spectral irradiance which is the energy dW( ,T) W emitted per unit area per unit time per unit r( ,T) [ ] frequency is defined as: dS.d m2.Hz Spectral irradiance is dependent on: - Absolute temperature T - Frequency  - and The nature of the object ( glass, metal )
5. b) Total Irradiance RT the energy emitted by a unit area of the surface per unit time and transmitted by electromagnetic waves of all frequencies: R(T) r(,T)d r(,T)d [W/m2] 0 0 Total Irradiance is dependent on : - Absolute temperature T - The nature of the object ( glass, metal, balckbody )
6. c) Spectral absorbance a(,T), a(,T) dW(,T) • Consider an object of dS temperature T . T • Let dW(,T) the energy of electromagnetic waves of frequencies between dW'(,T) (,+d) , sent to the area a(,T) dS, per unit time. dW(,T) • Let dW’(,T) the energy absorbed a(,T) 1 • Spectral absorbance is Spectral absorbance is dependent on: defined as: - Absolute temperature T - Frequency  - and The nature of the object ( glass, metal )
7. Blackbody (Vật đen tuyệt đối) Definition: a(,T) =1 for all , at all T Blackbody A black body is an ideal system that absorbs all radiation incident on it. The electromagnetic radiation emitted by the black body is called blackbody radiation. A good approximation of a black body is a small hole leading to the inside of a hollow object as shown in Figure 40.1. Any radiation incident on the hole from outside the cavity enters the hole and is reflected a number of times on the interior walls of the cavity; hence, the hole acts as a perfect absorber. The nature of the radiation leaving the cavity through the hole depends only on the temperature of the cavity walls and not on the material of which the walls are made.
8. KIRCHHOFF ‘S LAW OF THERMAL RADIATION IN THERMAL EQUILIBRIUM • Consider a thermal insulated cavity, containing B 3 different objects A, B, C • These objects radiate and absorp electromagnetic waves. A C Atinitialstate : TA TB TC At thermal equilibrium state :TA TB TC T rA (,T) rB (,T) rC (,T) aA (,T) aB (,T) aC (,T) Maintaining the equilibrium state requires that an object which radiate strongly, absorps strongly. r (,T) r (,T) r (,T) r(,T) A B C f (,T) KIRCHHOFF ‘S LAW aA (,T) aB (,T) aC (,T) a(,T) “ In equilibrium thermal radiation, the ratio between spectral irradiance and spectral absorbance is not dependent on the nature of the object, it depends only on the temperature T and the given frequency  . Function f(,T) is called universal function or common function.
9. The meaning of the universal function : • Applying the Kirchhoff’s law for a blackbody r ( ,T) r ( ,T) Blackbody Blackbody f ( ,T) aBlackbody ( ,T) 1 • Universal function f(,T) is the spectral irradiance of the blackbody Consequences of Kirchhoff’s law of thermal radiation r(,T) a(,T)f (,T) a(,T)rBlackbody(,T) a(,T) 1 r(,T) rB.B(,T) r(,T) 0 if a(,T) 0 and rBb (,T) 0 a) Spectral irradiance of a real object is smaller than Spectral irradiance of a blackbody b) A real object of temperature T radiates electromagnetic wave of frequency  if this object of temp. T can absorp the EM wave of frequency  and the blackbody of temperature T radiates electromagnetic wave of frequency 
10. Spectral Irradiance of Blackbody O F T1 Grating T2 Detector 2. The universal function f(,T) - Has a peak - At higher temperature, the peak of the curve moves to a higher frequency m , or a shorter wavelenth m - The area limitted by the function f(,T) and the horizontal axis is the total irradiance of the black body.
11. PLANCK‘s QUANTUM THEORY 1. Ultraviolet catastrophe 2. PLANCK‘s QUANTUM THEORY 3. Planck‘s formula 4. Stefan-Boltzman‘s law 5. Wien‘s law
12. Ultraviolet Catastrophe Based on classical theory : The atoms, molecules can emit or absorp radiation energy of any value, (continuous values) Rayleigh –Jeans derived the formula for the spectral radiation of blackbody: 2  2 f (,T) kBT c2 This formula is approximately correct for the region of long wavelengths, low frequencies, but not for the region of short wavelengtsh, high frequencies. This is known as the Ultraviolet Catastrophe (Sự khủng hoảng ở vùng tử ngoại)
13. 2. Planck‘s quantum theory The concept of quantization of radiation was discovered in 1900 by Max Planck, who had been trying to understand the emission of radiation from heated objects, known as black-body radiation. Planck assumed: a) Energy can only be absorbed or released in tiny discrete packets, which are an integer multiple of a quantum energy E n n 1,2,3 b) Quantum energy of an electromagnetic wave of frequency , (wavelength  ) is c  h h  Planck derived the spectral irradiance of the black body , called Planck’s formula: 8  2 h f ( ,T) c2 h e kBT 1
14. Stefan – Boltzmann law The Stefan – Boltzmann law states that the power emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature 4 2 R T T (W / m ) 2 RT: Total power emitted per unit area (W/m ) T: Absolute temperature of the object (K)  = 5.67x10-8 W/(m2.K4): Stefan- Boltzmann constant
15. Wien‘s Displacement Law The peak in the spectral irradiance occurs at a wavelength m which is inversely proportional to the absolute temperature of the blackbody. b  m T Wien constant b=2.898x10-3 (m.K)
16. b Wien’s law  m T 2.898 10-3 a)Skin T 35 273 308K, λ 9.41m m 308 2.898 10-3 b)filamentT 2000K λ 1.45m m 2000 2.898 10-3 c)SunsurfaceT 5800K;λ 0.5m m 5800
17. An FM radio transmitter has a power output of 150 kW and operates at a frequency of 99.7 MHz. How many photons per second does the transmitter emit? P hN P 150 103 J / s N 2.27 1030 photons / s h 6.625 10 34 J.s 99.7 106 s 1
18. P T4 4 r2 1/ 4 1/ 4 P 3.85 1026 T 5783K 2 8 8 2 4 r 5.67 10 4 (6.96 10 ) 2.898 10 3  0.5m m 5783
19. Einstein’s Photon Theory Einstein suggested that: - Light is composed of tiny particles called photons - Each photon has energy E=h=hc/ - The speed of photon is c=3x10^8m/s - An object emits or absorps electromagnetic waves An object emits or absorps photons hc Photon Energy : ε hν λ ε h Photon mass : m c2 λc h Photon Momentum : p mc λ m relativisticmass : m o v2 1 c2 for a photon:v c mo 0 : rest massof photon
20. Compton Scattering • Arthur H. Compton observed the scattering of x-rays from electrons in a carbon target and found scattered x-rays with a longer wavelength than those incident upon the target. • The shift of the wavelength increased with scattering angle according to the : h 2   (1 cos)  '  2c sin m c 2 e h 12 Compton wavelength of the electron λc 2.4 10 m mec X-ray ’  10-910-12m Carbon  target 
21. EXPLAINATION • The shifted peak at ’ is caused by the scattering of x-rays from free electron, weakly bound to the target atoms. • The unshifted peak at  is caused by x-rays scattered from electrons tightly bound to the target atoms.  ’
22. Compton Scattering Data At a time (early 1920's) when the particle (photon) nature of light suggested by the photoelectric effect was still being debated, the Compton experiment gave clear and independent evidence of particle-like behavior. Compton was awarded the Nobel Prize in 1927 for the "discovery of the effect named after him".
23. Compton Scattering in radiography
24.  Derive  '  2 sin2 c 2 In an elastic collision,There are conservation of the system momentum and conservation of the system energy Weakly bound X rays Interaction of and electrons Incident Free electrons Ellastic collision of photons and
25. Energy Momentum particle Before After Before After collision collision collision collision photon hc/ hc/’ p=h/ p’=h/’ 2 m v 2 mec e electron E =m c E 0 pe o e 2 v2 v 1 1 c2 c2
26. 2 2 2 h c 2  hc hc Conservation of Energy (5)c (6) 2 (2sin ) 2Eo (8) ' 2  ' hc hc 2 2 EEo (1) h c 2  3 '  ' 2 (2sin ) 2mehc (8) ' 2 ' h  hc hc 2 (sin 2 )  (8) EE o (1') ' mec 2 Conservation of Momentum h 12  2.4 10 m o m c p 0 p ' pe (2) e p p ' pe (3) 2 2 '2 2 (3)p p 2 pp ' pe (4) h2 h 2 h 2 EE22 2 cos o (5) 2 '' 2  c 2 hc hc (1')2 EE (1') ' o h2 c 2 h 2 c 2 h 2 c 2 (1')2 2 E 2 E 2 2 EE (6) 22 ''  oo hc22 (5)c22 (6) 2 (1 cos ) 2 EE 2 E 2 E ( E E )(7)  ' o o o o
27. The shift of the wavelength conservatio n of momentum 2   '  2 sin ( ) p 0 p' pe o 2 h h p ;p'  ' Conservation of energy : hc hc E E λ o λ' hc hc d E Eo λ λ'  Kineticenergy Energy of Energy of of the electron incident photon scattered photon hc hc hc hc E ’:wavelength of incident X-ray KE _ electron   '   2 sin2( ) ’: wavelength of scattered X-ray o 2 o: Compton wavelength of 2  E if sin ( ) 1or  electron KE _ electron _ max 2 : scattering angle , the angle between the incident and scattered x rays
28.  45o  '  2 sin2 2 2.4 10 12 sin2 6.4 10 13 c 2 2 '   0.2 10 9 6.4 10 13m 28. X-rays with a wavelength of 120.0 pm undergo Compton scattering. (a) Find the wavelengths of the photons scattered at angles of 30.0°, 60.0°, 90.0°, 120°, 150°, and 180°. (b) Find the energy of the scattered electron in each case. (c) Which of the scattering angles provides the electron with the greatest energy? Explain whether you could answer this question without doing any calculations.