Quantum Optics email: ygu@pku.edu.cn Tel: 67588 354 Quantum mechanics +Optics PPT 1
1 λ ħ Planck λ 0 ħ 0 3
λ 0 ħ 0. Maxwell 4
λ 0 ħ 0 m=0) 5
Ψ Ψ = LΨ I dx matter -di=αidx α I I=I 0 e - αl 6
Maxwell D= ε E+ P 0 NL E E E µσ µε µ + + = t t t P NL P NL (1) () (3) PNL = P + P + P +... P = εχ E, P = χ EE, P = χ EEE (1) (1) () () (3) (3) 0 χ 1, χ 10, χ 10 (1) () 4 (3) 8 ω 7
国家自然科学基金委员会 Hamiltonian + Schrodinger Equations ω 数理学部实验物理讲习班 8
1 1900-1930 A 100% ν 9
Planck 1901 quanta ħω ħ Planck 10
B 1888 H.Hertz ν e ν>ν 0 ν 0 1 ν<ν 0, e ν 3 ν>ν 0, Eienstein: quanta photon 1905 light particle 11
Quantum theory= discrete 1901 Max Planck quanta 1905 A. Einstein photon 1913 Bohr 193 Compton scattering theory E=ħω 194 DeBrogli 197 Quantum mechanics 194 DeBrogli 1930 QED, Feyman 1940---1960 World War Radar Enhanced signal Maser high frequency Laser 1
Quantum Optics 1 Maxwell Laser 13
W.Lamb M.O.Scully M.Surgent III Laser theory H.Haken H.Walther F.Hakke 60 90 90 QO splitting W.Louiswell J.R.Glauber D.F.Walls Quantum information Quantum computation Atom Optics BEC Coherence 14
10 13 ---10 18 Hz 10 14 Hz c/10, P- Q- 15
Quantom Optics M.O. Scully, M.S.Zubairy Quantom Optics D. Walls, G.J. Milburn 0, 04 16
, Fock state 17
Motivation of quantization: Zero-point energy + SCT Spontaneous emission Lamb shift Laser width Photon statistics Quantum beat phenomena -photon interferometer, HBT exp. Entangle state exp. Observations of squeezed state Photon antibunching? 18
1 Hamiltonian H 1D 1 Η= + V 0 x 0 y dv ( ε E µ H ) pˆ 1 Η= + m ω qˆ [q,p]=iħ [a,a + ]= iħ 19
国家自然科学基金委员会 EM field 1D Maxwell 数理学部实验物理讲习班 id= ρ ( ρ= 0) ib= 0 H= D t+ J ( J= 0) E= B t D= ε0e+ P ( P= 0) B= µ H 0 B E 0
Cavity E B figure Ex 0 By 0 for z 0 or L ( E ) = i( ie ) E 1 E E x = x Ex E u( r) e iωt c x c ω t 0 1 ur () + ur () = 0 1
π u() z = Asin( kz) for = 1,,3 k = L V ν m u ( z) u ( z) dz = δ A = ( ) ν = πc/ L 1/ i i V ε 0 Ex(z,t) Hy(z,t) E (,) z t = A q ()sin( t k z) x H= D/ t ε0 q () t H y(,) zt = Acos( kz ) k
Hamiltonian 1 Η= + p ( m ν q m q ) = mq p ( m ν q ) m 1 Η = + Mode of EM fields Harmonic oscillators Classical results 3
3 [ q, p ] = i δ [ q, q ] = 0 [ p, p ] = 0 ' ' ' ' iħ iν 1 t ae = ( m ν q + ip ) m ν + iν 1 t a e = ( m ν q ip ) m ν a a + + + [ a, a ] = δ [ a, a ] = 0 [ a, a ] = 0 ' ' ' ' 4
EM field 国家自然科学基金委员会 iν t x E = ε a e sin( k z) + H. c. iν t y H = (-iε c) a e cos( k z) + H. c. ε ν = ( ) ε V 0 1/ 数理学部实验物理讲习班 H 1 Η= ν ( a + a + ) 5
4 Heisenberg equations i q i p = [ q, Η] = [ p, Η] Maxwell 4 6
Fock state a a H 1 ν + Η = ( a a + ) H H Fock state coherent state squeezed stae 7
Fock state H E>=E n E> n a a [H,n]=0 H n n> H n>=ħν(a a+1/)=e n n> [a,a + ]=1, Η a n = ( E ν ) a n n Η a + n = ( E + ν ) a + n n a n>, n>, a + n> H (E n - ħν), E n, (E n +ħν) H n-1>, n>, n-1> H 8
Ha n> n, (E 0 - ħν)<e 0 Ha 0> =(E 0 - ħν) 0> a 0>=0 H0 (1/) ħν, Fock state a n>= n n 1> + a n>= n+ 1 n+ 1> + n ( a ) n >= 0> n! 9
Fock state i ν t E x = ε ae sin( kz ) + HC.. = + E E E n E n = 0 n = = 0, E ε 0 n E n n = ε ( + 1) 30
1 A B x f ( x) = exp( xa) Bexp( xa) 1 x = B+ x[ A, B] + [ A,[ A, B]] +...! [A,B]=C, exp( xa) B exp( xa) = B + Cx exp(xa), B B+Cx 31
x=1, A=- a + + *a,,b=a a +, γ a + γ * a e ae e + + γa γ* a γ a + γ * a + γ a γ * a + a e + + = a + γ = a + γ * (coherent state) 3 A=N=a+a, [N,a]=-a, [N,[N,a]]=a, xn xn BH xn e ae = ae x + xn + e a e = a e x, (squeezed state) A,B, [A,[A,B]]=[B,[A,B]]=0 exp( A + B) = exp( A)exp( B)exp( [ A, B]/ ) = exp( B)exp( A)exp([ A, B]/ ) 3