Quantum Mechanica Peter van der Straten Universiteit Utrecht Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 1 / 22
Matrix methode Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 2 / 22
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, 2013 3 / 22
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, 2013 3 / 22
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 33.000 fotons spontaneous emission mv0 hk + hki = mv0 hk Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 3 / 22
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 33.000 fotons lifetime τ = 16 ns T stop 1 msec l stop 0.5 m Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 3 / 22
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 33.000 fotons lifetime τ = 16 ns T stop 1 msec l stop 0.5 m acceleration a 9 10 5 m/s 2 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 3 / 22
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= 589.1583 nm 0 3s 2 S 2 P 2 D 2 F Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 4 / 22
Excitation of Na 62 MHz 36 MHz 16 MHz 3 2 1 0 +1 +2 +3 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 2 589.0 nm 1772 MHz 2 D 1 589.6 nm 1 0 +1 +2 F=2 F=1 3 2 S 1/2 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 5 / 22
Polarisation dependence Lineair gepolariseerd licht Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 6 / 22
Polarisation dependence Lineair gepolariseerd licht Circulair gepolariseerd licht Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 6 / 22
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, 2013 7 / 22
Simple picture Zeeman slowing SOLENOID LASER BEAM MOVING ATOM Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 8 / 22
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, 2013 9 / 22
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, 2013 9 / 22
Zeeman shift of the states 2000 Zeeman shift [MHz] 1000 0-1000 -2000 0 200 400 600 800 1000 1200 Magnetic field [Gauss] Shift of the ground state Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 10 / 22
Zeeman shift of the states 2000 2000 Zeeman shift [MHz] 1000 0-1000 Zeeman shift [MHz] 1000 0-1000 -2000 0 200 400 600 800 1000 1200 Magnetic field [Gauss] Shift of the ground state -2000 0 200 400 600 800 1000 1200 Magnetic field [Gauss] Shift of the excited state Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 10 / 22
Excitation in a magnetic field 2500 Transition frequency [MHz] 2000 1500 1000 500 0 Cooling transition -500 0 200 400 600 800 1000 1200 Magnetic field [Gauss] Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 11 / 22
Optical pumping with circular polarised light 3 2 1 0 +1 +2 +3 F =3 2 1 0 +1 +2 F =2 Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 12 / 22
Laser cooling +hk mv -hk Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 13 / 22
Laser cooling +hk mv -hk ω 0 δ ω e +kv g Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 13 / 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, 2013 13 / 22
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, 2013 13 / 22
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, 2013 13 / 22
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, 2013 13 / 22
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, 2013 13 / 22
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, 2013 13 / 22
Principle MOT (Magneto-Optical Trap) M = 1 M =0 M =+1 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 0000000000 111111111 000000000 111111111 01 01 00 11 00 00 11 00 00 0 11 11 111 00 11 0 00 11 00 000 11 1 00 11 1 00 11 00 11 00 00 00 11 11 00 11 11 00 11 00 00 00 00 11 11 11 00 11 00 11 00 11 00 11 11 11 00 11 00 σ 00 11 00 11 σ + 11 00 11 00 11 00 11 00 00 00 11 11 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 1100 00 110 1 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 0000000000 111111111 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, 2013 14 / 22
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, 2013 15 / 22
Cold Atoms D:/upload/Phys2000/bec/lascool4.html Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 16 / 22
Bose-Einstein condensation Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 17 / 22
What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 18 / 22
What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 18 / 22
What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 18 / 22
What is Bose-Einstein condensation (BEC)? Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 18 / 22
Bose-Einstein condensation ρ = nλ deb 3 = 2.612375349... with Λ deb = h 2πmkB T Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 19 / 22
Magnetic trapping Zeeman structure of the ground state of Na: 2 2 1 0-1 Energy [GHz] 0 F=2-2 F=1-2 0-1 1-4 0.00 0.05 0.10 0.15 0.20 0.25 Magnetic field [T] Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 20 / 22
Magnetic Trap Cloverleaf trap: Trap frequency 8 Hz 88 Hz Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 21 / 22
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, 2013 21 / 22
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, 2013 21 / 22
Background pressure: < 10 12 mbar Lifetime: 256 sec! Peter van der Straten (Atom Optics) Quantum Mechanica January 15, 2013 22 / 22 Lifetime in MT Remaining fraction % 100 80 60 40 20 0 100 200 300 400 500 600 Time s