Quantum Mechanica. Peter van der Straten Universiteit Utrecht. Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

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1 Quantum Mechanica Peter van der Straten Universiteit Utrecht Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

2 Matrix methode Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

3 Light pressure initial mv0 hk absorption mv0 hk spontaneous emission mv0 hk + hki = mv0 hk Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

4 Light pressure initial mv0 hk recoil kick v r = k m 3 cm/s (Na) absorption mv0 hk spontaneous emission mv0 hk + hki = mv0 hk Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

5 Light pressure initial absorption mv0 mv0 hk hk recoil kick v r = k m 3 cm/s (Na) thermal v 1000 m/s N stop fotons spontaneous emission mv0 hk + hki = mv0 hk Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

6 Light pressure initial absorption spontaneous emission mv0 mv0 hk hk mv0 hk + hki = mv0 hk recoil kick v r = k m 3 cm/s (Na) thermal v 1000 m/s N stop fotons lifetime τ = 16 ns T stop 1 msec l stop 0.5 m Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

7 Light pressure initial absorption spontaneous emission mv0 mv0 hk hk mv0 hk + hki = mv0 hk recoil kick v r = k m 3 cm/s (Na) thermal v 1000 m/s N stop fotons lifetime τ = 16 ns T stop 1 msec l stop 0.5 m acceleration a m/s 2 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

8 Excitation of Na with laser light 5 Na 4 5s 5p 4p 4d 3d 4f 3 4s Energy (ev) 2 3p Laser cooling 1 λ= nm 0 3s 2 S 2 P 2 D 2 F Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

9 Excitation of Na 62 MHz 36 MHz 16 MHz F=3 F=2 F=1 F=0 3 2 P 3/2 192 MHz F=2 F=1 3 2 P 1/2 D nm 1772 MHz 2 D nm F=2 F=1 3 2 S 1/2 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

10 Polarisation dependence Lineair gepolariseerd licht Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

11 Polarisation dependence Lineair gepolariseerd licht Circulair gepolariseerd licht Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

12 Doppler effect S D S D Doppler shift : Detector (D) moving towards source (S) and vice versa ν = ν ( 1 v ), c with ν = c/λ the frequency and c the velocity of light. Sodium (λ=590 nm) at 1000 m/s: ν = ν ν = 1700 MHz Γ= 10 MHz. D:/Upload/Phys2000/bec/lascool1.html D:/Upload/Phys2000/bec/lascool2.html D:/Upload/Phys2000/bec/lascool3.html Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

13 Simple picture Zeeman slowing SOLENOID LASER BEAM MOVING ATOM Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

14 Zeeman technique Na oven 600 K 1.25 m solenoid extraction coils cooling beam B z aom probe beam pump beam Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

15 Zeeman technique Na oven 600 K 1.25 m solenoid extraction coils cooling beam B z aom probe beam pump beam detect Pump Gate Probe Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

16 Zeeman shift of the states 2000 Zeeman shift [MHz] Magnetic field [Gauss] Shift of the ground state Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

17 Zeeman shift of the states Zeeman shift [MHz] Zeeman shift [MHz] Magnetic field [Gauss] Shift of the ground state Magnetic field [Gauss] Shift of the excited state Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

18 Excitation in a magnetic field 2500 Transition frequency [MHz] Cooling transition Magnetic field [Gauss] Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

19 Optical pumping with circular polarised light F = F =2 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

20 Laser cooling +hk mv -hk Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

21 Laser cooling +hk mv -hk ω 0 δ ω e +kv g Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

22 Laser cooling +hk mv -hk ω 0 δ ω e +kv F v g Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

23 Laser cooling +hk mv -hk ω 0 δ ω e +kv F v g δ < 0 F βv with β max = k2 4 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

24 Laser cooling +hk mv -hk ω 0 δ ω e +kv F v g δ < 0 F βv with β max = k2 4 m v = βv v = v 0 exp( t/t 0 ) Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

25 Laser cooling +hk mv -hk ω 0 δ ω e +kv F v g δ < 0 F βv with β max = k2 4 m v = βv v = v 0 exp( t/t 0 ) t 0 = m β max = 12.8µsec Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

26 Laser cooling +hk mv -hk ω 0 δ ω e +kv F v g δ < 0 F βv with β max = k2 4 m v = βv v = v 0 exp( t/t 0 ) t 0 = m β max = 12.8µsec Cooling limit: Damping by Doppler tuning vs. heating by random recoil Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

27 Laser cooling +hk mv -hk ω 0 δ ω e +kv F v g δ < 0 F βv with β max = k2 4 m v = βv v = v 0 exp( t/t 0 ) t 0 = m β max = 12.8µsec Cooling limit: Damping by Doppler tuning vs. heating by random recoil kt D = Γ 2 [Na : 240µK] Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

28 Principle MOT (Magneto-Optical Trap) M = 1 M =0 M = σ σ J =0 J =1 M =0 σ + : right handed circular polarized light σ : left handed circular polarized light Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

29 Principle of the magneto-optical trap Energy M e =+1 δ δ + δ M e =0 M e = 1 σ + beam ω l σ beam z M g =0 Position Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

30 Cold Atoms D:/upload/Phys2000/bec/lascool4.html Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

31 Bose-Einstein condensation Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

32 What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

33 What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

34 What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

35 What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

36 Bose-Einstein condensation ρ = nλ deb 3 = with Λ deb = h 2πmkB T Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

37 Magnetic trapping Zeeman structure of the ground state of Na: Energy [GHz] 0 F=2-2 F= Magnetic field [T] Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

38 Magnetic Trap Cloverleaf trap: Trap frequency 8 Hz 88 Hz Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

39 Magnetic Trap Cloverleaf trap: Trap frequency 8 Hz 88 Hz No spin polarization: 1 / 3 loaded in trap Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

40 Magnetic Trap Cloverleaf trap: Trap frequency 8 Hz 88 Hz No spin polarization: 1 / 3 loaded in trap 360 optical access Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22

41 Background pressure: < mbar Lifetime: 256 sec! Peter van der Straten (Atom Optics) Quantum Mechanica January 15, / 22 Lifetime in MT Remaining fraction % Time s