Laser Cooling and Trapping of Atom

1. Laser Cooling and Trapping of Atom Ying-Cheng Chen, 陳應誠 Institute of Atomic and Molecular Science, Academic Sinica, 中研院原分所

2. Outline • Basic idea & concept • Overview of laser cooling and cold atom study • The light force • Doppler cooling for a two-level atom • Sub-Doppler Cooling • Others cooling scheme • Practical issues about a Magneto-Optical Trap (MOT) • Atomic species • Lasers • Vacuum • Magnetic field • Imaging

3. sub-Doppler cooling L He 2003 MIT Na BEC core of sun surface of sun L N2 3He superfluidity 0 (K) 103 106 1 10-3 10-6 10-9 MOT room temperature typical TC of BEC Temperature Landmark To appreciate something is a good motivation to learn something! Laser cooling and trapping of atom is a breakthrough to the exploration of the ultracold world. A 12 orders of magnitude of exploration toward absolute zero temperature from room temperature !!!

4. What is special in the ultracold world? • A bizarre zoo where Quantum Mechanics governs • Wave nature of matter, interference, tunneling, resonance • Quantum statistics • Uncertainty principle, zero-point energy • System must be in an ordered state • Quantum phase transition ~1μm for Na @ 100nk

5. Trends in Ultracold Research Cold Molecule From atomic to condensed-matter physics From Physics to Chemistry Many-body Physics Cold Plasma & Rydberg Gas Cold Atom From ground to highly-excited states From fundamental to application From isotropic to anisotropic interaction Dipolar Gas Quantum Computation Atom Chips…

6. Useful References • Books, • H. J. Metcalf & P. van der Straten, “Laser cooling and trapping” • C. J. Pethick & H. Smith ,“Bose-Einstein condensation in dilute gases” • P. Meystre, “Atom optics” • C. Cohen-Tannoudji, J. Dupont-Roc & G. Grynberg “Atom-Photon interaction” • Review articles • V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms” , Rep. Prog. Phys.63 No 9 (September 2000) 1429-1510. • V S Letokhov, M A Ol'shanii and Yu B OvchinnikovQuantum Semiclass. Opt. 7 No 1 (February 1995) 5-40 “Laser cooling of atoms: a review” • Journal of Opt. Soc. Am. B, Issue 11,1989, special issue on laser cooling

7. The Light Force: Concept absorption emission An exchange of momentum & energy between photon and atom ! Photon posses energy and momentum ! Net momentum exchange from the photon to atom Force on atom

8. Energy and Momentum Exchange between Atom and Photon • Atom absorbs a photon and re-emit another photon. always positive, recoil heating Criteria of laser cooling If the momentum decrease, and if then＜ΔK ＞avg <0 or ＜ωi＞ >＜ωs＞ , where avg stands for averaging over photon scattering events. A laser cooling scheme is thus an arrangement of an atom-photo interaction scheme in which atoms absorb lower energy photon and emit higher energy photon on average!

9. The Light force : quantum mechanical • Ehrenfest theorem, the quantum-mechanical analogue of Newton’s second law, where V(r,t) is the interaction potential. • Interaction potential: for an atom interacting with the laser field, , where d is atomic dipole moment operator. • Semi-classical treatmentof atomic dynamics: • Atomic motion is described by the averaged velocity • EM field is treat as a classical field • Atomic internal state can be described by a density matrix which is determined by the optical Bloch equation

10. Discussion on semi-classical treatment • Momentum width pis large compared with photon momentum k. • Considering slow atoms only simplify the formalism. (Internal variables are fast components and variation of atomic motion is slow components in density matrix of atom ρ(r,v,t)) • Two conditions are compatible only if • If the above conditions is not fullified, full quantum-mechanical treatment is needed. e.g. Sr narrow-line cooling, =27.5kHz ~ ωr=2k/2m=24.7kHz an lower bound on v an upper bound on v or J. Dalibard & C. Cohen-Tannoudhi, J. Phys. B. 18,1661,1985 T.H. Loftus et.al. PRL 93, 073001,2004

11. Why Density Matrix Not Wavefunction? • Pure versus Mixed ensemble. • The system that we are studied are usually not in the same state (described by the same wavefunction) but in a statistical mixture, e.g. atomic population follows Boltzman distribution both in internal states as well as in external states. Atomic system under preparation (like optical pumping) can be in the same internal state. Bose-Einstein condensate is a system in the same state both in internally and externally . • When dealing with atom-photon interaction, we usually interest in partial system (e.g. atomic system). Spontaneous emission caused by the coupling of atom with infinite degree of freedom of radiation results in a transition from an initial to a final state and can convert a pure state to a statistical mixture since phase information are lost ! • Density matrix formalism establishes a more direct connection with observables! • Density matrix is a more powerful method for doing calculations.

12. Density Matrix • Probablity density to find particle in state |i> is • The complete basis for state vector • Diagonal elements are probabilities |cm|2 and off-diagonal terms are coherences cmcn* since they are depend on phase difference. • Expectation value of operator • Considering mixed ensemble instead of just pure ensemble, where Pm is classical statistical weight. • If we are only interested in part of the system, the density matrix has to be average over the other part of the system.

13. The light force for a two-level atom Remark: dipole moment contain in phase and in quadrature components with incident field. Note! A general form, can be plane wave,Gaussian beam… Where d12=d21 are assumed to be real and we have introduced the Bloch vectors u,v, and w. ρij (or σij)can be determined by the optical Bloch equation of atomic density matrix.

14. Optical Bloch equation Incoherent part due to spontaneous emission or others relaxation processes. The loss of quantum coherence is a big Issue in quantum computation. Rabi frequency Ω characterize the magnitude of atom-photon interaction. steady state solution Isat ~1-10 mW/cm2 for alkali atom

15. Two types of forces Without loss of generality, choose At r =0, Take average over one optical cycle dipole force or gradient force a reactive force related to u vector radiation pressure or spontaneous emission force a dissipative force Related to v vector Origin of optical trapping Origin of optical cooling

16. Light force for a Gaussian beam Frp F Fdip k z

17. Optical Tweezers and Dipole Trap • Laser is far off-resonance, the dipole force dominates and trapping of small • particles occurs. • For atom, it is called a optical dipole trap. Usually it has a trap depth around • 1~1000 μK.

18. Spontaneous emission force for steady-state From Decay rate, For a plane wave ,where Rsp is the flourescence rate. Its maximum value is . Max deceleration for Na D2 line !

19. Dipole Force in a standing wave • A standing wave has an amplitude gradient, but not a phase gradient. So only the dipole force exists. Where s0is the saturation parameter for each of the two beams that form the standing wave. For δ<0 (red detuning), the force attracts atom toward high intensity regions. For δ>0 (blue detuning), the force repels atom away from high intensity regions.

20. Velocity dependent force Atom with velocity v experiences a Doppler shift kv. The velocity range of the force is significant for atoms with velocity such that their Doppler detunings keeps them within one linewidth considering the power broadening factor.

21. δ/ Doppler Cooling For δ<0, the force slows down the velocity. [/k]

22. Doppler Cooling, Energy Point of View • Red-detune laser photons are absorbed by atoms, spontaneously emitted photons have average energy on the resonance frequency. • On average, atoms absorb lower energy photons and emit higher energy photon. • Photons from laser are coherent, photons spontaneously emitted are quite random. Entropy of atoms are carried away by spontaneously emitted photons. Atom VAL, excite the atom VAR, Radiation vacuum de-excite atom, Entropy flow Laser Radiation Reservior Coherent photon Incoherent photon Finite degree of freedom infinite degree of freedom

23. Doppler Cooling limit • Doppler cooling : cooling mechanism; Recoil heating : heating mechanism • Temperature limit is determined by the relation that cooling rate is equal to heating rate. • Recoil heating can be treat as a random walk with momentum step size k. Minimum temperature TD ~ 100-1000K for alkali atom For low intensity s0<<1

24. Magneto-optical trap (MOT) • Cooling, velocity-dependent force: Doppler effect • Trapping, position-dependent force: Zeeman effect 3-D case 1-D case

25. Position-dependent Force in a MOT Considering v=0,

26. Sub-Doppler cooling • Many laser cooling schemes allow one to cool atoms below the Doppler limit, or even down to the recoil limit. • Polarization gradient cooling (Sisyphus cooling) • Already exist in the MOT • Raman sideband cooling • Velocity-selective-coherent-population-trapping (VSCPT) cooling …

27. Sisyphus Cooling • Polarization gradient cause a periodic modulation with period of λ/2 for the ac Stark shift of the ground states. • Atom climbs up the Stark potential and tends to be optically pumped to excited state and then spontaneously emit to the other ground state. It then repeat the same process • On average, atoms absorb lower energy photons but emit higher energy photon.

28. Polarization Gradient Cooling • A new friction force mechanism for the low velocity atom (vτp~λ/4 where τp is the optical pumping time ). • Equiliurium temperature Cs

29. Optical Pumping

30. Angular Momentum of Photon

31. Raman Sideband Cooling • Atoms are confined in a tight optical dipole trap and prepared in polarized states. • Cooling cycle : |3,3;v> →Stimulated Raman transition → |3,1;v-1> →optical pumping →|3,3;v=0> or |3,3;v> • |3,3;v=0> is dark both to Stimulated Raman transition and to optical pumping light so population will accumulate here. • Since atoms are tightly trapped, recoil heating is negligible. σ+ π PRL81,5768(1998)

32. VSCPT Cooling • Atoms are in the CPT dark states when their velocities are almost zero. • Atomic velocity distribution are non-thermal (Levy flight). • Longer atom-photon interaction time cause narrower momentum width. PRL 61,826(1988)

33. Microwave transition Beyond Laser Cooling • Evaporative cooling • Sympathetic cooling • Demagnetization cooling • Stochastic cooling • Feedback cooling • ….???

34. Part II: Practical Issues about a magneto-optical trap

35. Laser cooling : demonstrated species

36. Atomic species • Different atomic species has its unique feature ! (5s5p)1P1 32MHz 2 3P2 1.6MHz F=5 6 2P3/2 5.2MHz 4 (5s5p)3P1 4.7kHz 3 1083nm 2 cooling 2 3S1 metastable 460.73nm Broad-line cooling 689.26nm Narrow-line cooling 852.35nm repumping ~20eV by discharge 4 3 6 2S1/2 (5s2)1S0 1 0S1 88Sr, alkali earth, I=0 4He, nobel gas, I=0 133Cs, alkali metal, I=7/2

37. Lasers • Diode lasers are extensive use in laser cooling community due to inexpensive cost and frequency tunability. • Diode lasers in external cavity configuration are used to reduce the laser linewidth. • Master oscillator power amplifier (MOPA) configuration is used to increase the available laser power. ECDL in Littrow configuration master Diode laser ECDL in Littman-Metcalf configuration Tampered amplifiier MOPA

38. Laser frequency stabilization • Frequency-modulated saturation spectroscopy is the standard setup to generate the error signal for frequency stabilization. • Feedback circuits are usually built to lock the laser frequency. laser Background subtracted saturation spectrometer spectrometer Error signal Feedback circuit

39. Frequency Modulation Spectroscopy • Frequency modulation and lock-in detection obtain dispersive error signal for frequency stabilization.

40. Vacuum • Two different kinds of vacuum setup are mainly used, one is glass vapor cell, the other is stainless chamber. • Ion pump and titanium sublimation pump are standard setup to achieve ultrahigh vacuum. Vapor-cell MOT Chamber MOT

41. Magnetic field • Anti-Helmholtz coils for the MOT • Magnetic field reach maximum if the distance between two coils equal to the radius of the coil • Arial field gradient is twice the radial field gradient. • Helmholtz coils for earth-compensation • Magnetic field is most uniform ~ x4 when the distance between two coils equal to the radius of the coil • Earth compensation is critical to get good polarization gradient cooling. • The magnitude of magnetic field scales ~  for different atomic species.

42. MOT Alignment • Counterpropagating lasers are with the same polarizations (handness or helicity) but the configuration is referred as σ+σ- configuration in laser cooling. • Be careful the specifications from vendors on the quarter might be wrong or inconsistent. • A thumb rule ! E slow axis Fast axis B laser

43. Imaging and Number of Atoms I0(x,y) Itransmitted(x,y) From experiment From theory Considering the dark count of CCD 3* = 0~3, depends on laser polarization and population distribution around Zeeman sublevels

44. How to determine the temperature? MOT laser t=3 ms Magnetic field t Image beam Size(mm) t=7ms t=15 ms TOF(ms)

45. Our Exploration, Cold Molecules 1 μK 1 mK 1 K Buffer-gas cooling to prepare 4K large sample of molecules. Evaporative cooling of molecules to μK in a microwave trap. Sympathetic cooling of molecules to mK in a microwave trap by ultracold atoms. Stark-guiding and optical pumping to load molecules into a microwave trap.

46. Why Cold Molecules ? • High-resolution spectroscopy • Better understanding of molecular structure • Molecular clock • Cold molecular collision and reaction • Precise determination of molecular potential energy • Controlled reaction by electromagnetic field • Test of fundamental physics, • e.g. searching for electron dipole moment • Study of quantum degenerate dipolar gases • Dipolar effect on Bose condensate • Cooper pairing by dipolar interaction • Quantum computation

47. Welcome to join us to explore the ultracold world ! Ying-Cheng Chen, 陳應誠 Institute of Atomic and Molecular Science, Academic Sinica, Ultracold Atom and Molecule Labortory 中研院原分所 超低溫原子與分子實驗室