1. Exploration of the Ultracold World Ying-Cheng Chen( 陳應誠 ), Institute of Atomic & Molecular Sciences, Academia Sinica 12 October, 2009, NDHU IAMS

2. Outline Overview of Ultracold Atoms Introduction to Ultracold Molecules Exploration I: Molecular cooling Exploration II: Nonlinear optics with ultracold atoms

3. Studying, Research and Life: Adventure & Exploration

4. Temperature Landmark 10 6 10 3 110 -3 10 -6 10 -9 0 (K) Core of sun surface of sun Room temperature L N 2 L He 3 He superfluidity 2003 MIT Na BEC Typical T C of BEC Rb MOT Sub-Doppler cooling

5. 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 Matter wave interference, MIT Fermi pressure, Rice Vortex Lattice, JILA &MIT Superfluid-Mott insulator t Ransition, Max-Planck

6. Laser Cooling & Trapping Cooling, velocity-dependent force: Doppler effect Trapping, position-dependent force: Zeeman effect Laser fvfv Atom v

7. Magnetic Trapping & Evaporative Cooling Microwave transition

8. Modern Atomic Physics : Science & Technology Precision measurement Atomic clock Test of particle physics (EDM) Test of nuclear physics (parity violation) Test of general relativity Variation of physical constants Quantum information science Quantum control Quantum teleportation Quantum network Quantum cryptography Quantum computing Quantum simulation of condensed-matter physics BEC/Degenerate Fermi gas Superfluidity/superconductivity Quantum phase transition BEC/BCS crossover Antiferromagnetism/ high Tc superconductivity Opto-mechanics & Nano-photonics Laser cooling of mirror /mechanical oscillator Coupling of cold atom with mesoscopic(nano) object Quantum limit of detection Near field optics Extreme nonlinear optics Atom/molecule under intense short pulse High harmonic generation X-ray laser Attosecond laser Atom manipulation Core technology Laser advancement Weakness: Molecule manipulation

9. Double Helix of Science & Technology Science TechnologyBetter understanding of science helps technology moving forward Better technology helps to explore new science It is a tradition in AMO physics to extend new technology to explore physics at new regime.

10. Core Technology Atom cooling Laser technology Lasers Ultra-intense Ultra-short Ultra-stable Ultra-narrow -linewidth Non-classical (single photon, entangled photon pairs) Laser cooling 100TW Sub-Hz 250 as Sub-Hz atom trapping /optical lattice evaporative cooling Microwave transition Magnetic-tuned Feshbach resonance

11. Cold Molecules: Why ? Test of fundamental Physics. –Search for electron dipole moment… Quantum Dipolar Gases –Add new possibility in quantum simulation. Cold Chemistry –Chemistry with clear appearance of quantum effects –Controlled reaction Quantum Computation –Long coherence time and short gate operation time T S d P + - - + + -

12. Cold molecules : How ? Buffer gas cooling Electric, magnetic, optical deceleration Enhanced PA? Laser cooling? Sympathetic cooling? Evaporative cooling? Photo- association Coherent transfer from Feshbach molecule Direct approach Indirect approach ＋

13. Breakthrough in Indirect Approach The door to study quantum degenerate dipolar gases and quantum information with polar molecules is opened by JILA’s recent experiment with indirect approach. K.-K. Ni et al Science, 18,1(2008)

14. Laser Cooling of Molecule ? Not so cool ! Its impractical to implement laser cooling in molecules due to the lack of closed transition with their complicated internal structures. See, however, Di Rosa, Eur.Phys. J. D 31,395 (2004) for molecules with nearly closed transition. The ying and yang (dark/bright) sides of molecules. You have to pay the price !

15. Our approach ? General considerations Choose the direct approach to make cold molecules in order to have more impacts in other fields as well. Generate a large number of molecules in the first stage. Build an AC trap in order to avoid the inelastic collision loss. Use sympathetic cooling with laser-cooled atoms in the ac trap to overcome mK barrier for direct cooling. What advantages to take? What disadvantages to live with? Molecules precooling loading Trapping Laser-cooled atoms loading sympathetic cooling Inelastic collision? Reaction? Ultracold Molecules

16. Routes Towards Ultracold Molecules Buffer gas cooling plus magnetic guiding Sympathetic cooling in a microwave trap by ultracold cesium atoms. 1 K 1 mK 1 μ K Evaporative cooling in a microwave trap. hotter molecules colder molecules Cs atom SrF molecule Radiative damping & trap loading

17. Recent Ideas Buffer gas cooling plus magnetic guiding Direct laser cooling 1 K 1 mK 1 μ K Evaporative cooling in an optical dipole trap. hotter molecules colder molecules A 2 Π 1/2 X 2 Σ 1/2 v’’ 0 1 2 v’ 0 ω 00 A 00 A 01 A 02

18. What molecule? SrF, Why? Alkali-like electronic structure with strong transitions at visible wavelengths. Easy to be detected by convenient diode lasers. Large electric dipole moment, 3.47 D and many bosonic and fermionic isotopes. More possibilities in the future. Microwave trapping consideration. Available microwave high power amplifier at its rotational transition (2B~ 15 GHz). With nearly diagonal Frank-Condon array that allow direct laser cooling with reasonable number of lasers. Suitable for test of fundamental physics and quantum information science. Radical molecules. Disadvantages in molecule generation. What advantages to take? What disadvantages to live with ?

19. Buffer Gas Cooling P 11 (8.5) P 11 (7.5) P 11 (6.5) P 11 (5.5) Q 12 (7.5) Q 12 (6.5) Q 12 (5.5) Q 12 (4.5) X 2 Σ,v=1→A 2 Π 1/2,v’=1 SrF molecules generated by laser ablation of SrF 2 solid.

20. Development of an intense SrF Molecular Beam 2B+3 SrF 2 (high-temperature~1500K)→BF 3 +Sr+2SrF+BF SrF + Sr + BF + 2 (neutral BF 3 ) BF + N+2N+2 CO + 2 RGA Trace If one want to work with (cold) molecules then he need to learn some chemistry ! Electron-bombardment heating

21. SrF Beam Characterization Brewster window Light baffle Residual gas analyzer Turbo pump skimmer Laser beam PMT ψ3mmψ2mm 5cm 13cm 10cm chopper oven ECDL laser New Focus 6009/6300 Toptica WS-7 Wavelength meter Setup for laser-induced fluorescence

22. Even near the congested band edge, all hyperfine lines are well resolved ! Typical Spectrum (0,0) vibrational band of A 2 Π 1/2 - X 2 Σ + transition of 88 SrF Laser intensity ~5 00mW/cm 2 FWHM linewidth ~ 130MHz S/N ratio >200 Laser intensity ~ 5mW/cm 2 FWHM linewidth ~ 15 MHz S/N ratio > 50 Hyperfine lines resolved (I=1/2 for 19 F)

23. Beam Characterization Flux v.s. oven temperature Flux stability ~ 20% / one hour Highest flux of 2.1×10 15 /(steradian ． sec)! Even stronger and more stable beam is possible by resistive heating and is under development! “An intense SrF radical beam for molecule cooling experiment” submitted to Phys. Rev. A.

24. Better Spectroscopy of SrF The rotational/hyperfine lines of (0,0) A 2 Π 1/2 - X 2 Σ+ band 88 SrF have been recorded to 10 -4 cm -1 precision with a fitting accuracy of ±10 -3 cm -1 to the effective Hamiltonian.

25. Theoretical Modeling Effective Molecular Hamiltonian Better molecular constants have been determined ! parameterT 00 BDApq Value(cm -1 )15216.33978(19)0.2528325(12)2.5274(28)x10 -7 281.46333(34)-0.13353(9)9.32(3.8)x10 -5 “High-resolution laser spectroscopy of the (0,0) band of A 2 Π 1/2 - X 2 Σ + transition of 88 SrF ” submitted to J. of Mol. Spec.

26. Buffer-Gas-Cooled Molecular Beam & Guiding On-going work oven Dewar cryostat Magnetic guide UHV Chamber Spectroscopy or laser cooling Helium SrF Estimation of Flux (6.6×10 15 /s) × (9×10 -4 )x(2.9×10 -3 )=1.7×10 10 /s @ ~5K Already very intense for a radical beam! Higher flux is possible with modified oven. Turbo pump

27. Routes Towards Ultracold Molecules Buffer gas cooling plus ac electric guiding Sympathetic cooling in a microwave trap by ultracold cesium atoms. 1 K 1 mK 1 μ K Evaporative cooling in a microwave trap. hotter molecules colder molecules Cs atom SrF molecule Radiative damping & trap loading

28. Development of the Microwave Trap Rotational transition Red-detuned microwave AC Stark shift J=0 J=1 Trapping state Advantages of microwave trap 1.High trap depth ( ~ 1K) 2.Large trap volume (~ 1cm 3 ) 3.Good optical access. Allow overlap of MOT with trap for sympathetic cooling. 4.It can trap molecules in the absolute ground states and thus immune to inelastic collisions loss at low enough temperature. U(x) x DeMille, Eur.Phys.J D 31,375(2004)

29. Observation of standing wave pattern by thermal-sensitive LCD sheet Q=11000 η=0.87 P in =1060W R=0.217m D=0.2m E 0 =0.45 MV/m Trap depth ~ 0.1 K for SrF ground state “ A high-power microwave Fabry-Perot resonator for molecule trapping experiment” Rev. Sci. Inst. In preparation.

30. Routes Towards Ultracold Molecules Buffer gas cooling plus ac electric guiding Sympathetic cooling in a microwave trap by ultracold cesium atoms. 1 K 1 mK 1 μ K Evaporative cooling in a microwave trap. hotter molecules colder molecules Cs atom SrF molecule Radiative damping & trap loading

31. Sympathetic Cooling of Molecules by Ultracold Atoms Conceptually easy but depends on unknown collision properties. time T M ( t) TmTm TaTa T eq Tempature τ th Equilibrium temperature Thermalization time Collision rate c: a geometry factor and Larger number of cold atoms, colder atom temperature and higher atom density implies lower molecular temperature and shorter thermalization time.

32. Large-number Ultracold Atom System Initially developed for molecule sympathetic cooling (with N~ 10 10 ). Found its application in low-light-level nonlinear optics based on electromagnetic-induced transparency (EIT). “An elongated MOT with high optical density” Optics Express 16,3754(2008) 7cm Absorption Spectrum Optical density=105 for Cs D 2 line F=4 →F’=5 trapping beam trapping Coils&cell trapping Atom cloud probe

33. Quest of Second Stage Cooling to overcome the mK Barrier for Direct Approach Sympathetic cooling with ultracold atoms –Not so promising due to strong inelastic loss –AC trap is necessary Cavity laser cooling –Haven’t been demonstrated. Direct laser cooling –Being demonstrated –Limited to a few species Single-photon (information) cooling –In combination with magnetic trapping –May be demonstrated soon... A 2 Π 1/2 X 2 Σ 1/2 v’’ 0 1 2 v’ 0 ω 00 A 00 A 01 A 02 M.Raizen Scattering rate atomic linewidthΓ cavity linewidthκ cavity-enhanced Rayleigh scattering

34. Laser Cooling of SrF : to overcome the mK barrier! Di Rosa, Eur.Phys. J. D, 31,395 (2004) state X 2 Σ,v=0 v=1v=2v=3 A 2 Π, v=0 0.98950.01031.33x10 -4 1.57x10 -6 A 2 Π 1/2 X 2 Σ 1/2 v’’ 0 1 2 v’ 0 ω 00 A 00 A 01 A 02 J Phy Chem A, 102,9482,1998 0.999867 3600 =62% By repumping the v=1 population back to v=0, the transition is closed to 10 -4 level

35. A 2 Π 1/2,v’=0 X 2 Σ 1/2 (v’’=0) 663.1nm X 2 Σ 1/2 (v’’=1) 685.1nm N’’ 0 1 2 J’ J’’ parity 2.5 1.5 0.5 2.5 1.5 0.5 ＋ － ＋ ＋ － － － － ＋ ＋ ＋ main repumping nearest interference (0,0)Q 11 (0.5) (0,0)P 12 (1.5) (0,1)Q 11 (0.5) (0,1)P 12 (1.5) (0,0)R 12 (1.5)(0,0)Q 12 (1.5) Nearest>14GHz away ~45GHz A 2 Π 1/2, v’=0 X 2 Σ 1/2 (v’’=0) 663.1nm N’’ 0 2 J’ J’’ parity 0.5 1.5 ＋ ＋ － (0,0)Q 11 (0.5) (0,0)P 12 (1.5) 0.5 F’’ 1 0 26.79MHz 80.38MHz 112.19M Hz 1 2 N’ 0 21.75MHz 29.72MHz F’ 1 0 Small ~ few MHz Considering to rotational states, four lasers (two @ 663nm and two @685nm ) required to close the transition to 10 -4 level. Considering to hyperfine states, it is necessary to generate two frequencies differed by ~50 or 107 MHz by acousto-optical modulator for each laser.

36. Nonlinear optics with ultracold atoms - Detour of my planned journey but back to my old track !

37. Electromagnetically-induced Transparency Coupling laser Probe laser Transparent! |1> |3> 2> probe coupling ＝ ＋＋ ＋…＋… Path i Path iii Path ii |1> |2> |3> Physical origin: destruction interference between different transition pathways!

38. EIT, Propagation Effect Large optical density and small ground-state decoherence rate are two crucial factors in EIT-based application, e.g. optical delay line. Slow light ! V g <17m/s, Hau et.al. Nature397,594,1999

39. Nonlinear Optics with Ultracold Atoms With on-resonance signal, one can control the absorption/transmission of probe photon by signal photon. Photon switching. With off-resonant signal, one can control the phase of probe photon by signal photon. Cross phase modulation. coupling probe signal Without signal With signal beam Schmidt & Imamoglu Opt. Lett. 21,1936,1996 γ

40. XPM Application: Controlled-NOT gate for Quantum Computation CNOT and single qubit gates can be used to implement an arbitrary unitary operation on n qubits and therefore are universal for quantum computation. Single photon XPM can be used to implement the quantum phase gate and CNOT gate For a good introductory article, see 陳易馨 & 余怡德 CPS Physics Bimonthly, 524, Oct. 2008 Truth table for CNOT gate Signal Probe PBS Atoms Control qubit Target qubit

41. Reduction of Ground-state decoherence rate Coupling ECDL VCSEL Probe DL λ/2 PBS frequency coupling VCSEL probe ~9GHz Bias-Tee I dc RF Reduction of mutual laser linewidth ~10Hz Beatnote between coupling & probe laser Reduction of inhomogeneity of stray magnetic field Faraday rotation as diagnosis tool. Three pairs of coils for compensation. 350kHz/Gauss for Cs FFT δB<2mG limited by 60Hz AC magnetic field! Without compensation With compensation

42. Good EIT Spectrum Obtained EIT with ~50% transmission at 200kHz width for OD~ 60 for Cs D 2 F=3 →F’=3 transition.

43. The Slow Light 10μs for ~2cm atomic sample ! V g ~2000m/s

44. XPM with Group-Velocity-Matched Double Slow Light Pulses Both probe & signal pulses becoming group-velocity-match slow light in a high OD gas for longer interaction time. M. Lukin Phys. Rev. Lett. 84, 1419 (2000). coupling probe signal Atom A Atom B medium probe signal

45. Double EIT Spectrum Photon-switching with on-resonance signal field has been observed. XPM work is underway ! mF=mF=01234 F=4, g F =4/15 F=3, g F =0 F=4, g F =1/4 F=3, g F =-1/4 C1C1 P1P1 C2C2 P2P2 P2P2 P1P1 (a) Cs 6S 1/2 -6P 3/2 (D 2 -line)

46. Matching the Group Velocity T d (P 1 ) T d (P 2 ) Group velocity matched ! Probe 1Probe 2 No atoms I C1 fixed decrease I C2

47. Future Work : Cavity Enhanced Cross Phase Modulation A “holy grail” in nonlinear optics is to realize a mutual phase shift of πradian with two light pulses containing a single photon. It can be applied to the implement of controlled- NOT gate for quantum computation and to generate quantum entangled state. Few-photon-level XPM is challenging ! –Large Kerr Nonlinearity –Low loss –Strong focusing to increase the atom-laser interaction strength –Long atom-laser interaction time We are working on cavity-enhanced XPM. The technology may also be applied to cavity laser cooling of molecules in the future. cold atom Signal beam Coupling& probe

48. The Setup

49. Acknowledgement Financial support from NSC, IAMS. Helps from many colleagues, WY Cheng, KJ Song, J Lin, K Liu, SY Chen… Current member: –Chih-Chiang Hsieh –Ming-Feng Tu –Jia-Jung Ho –Wen-Chung Wang Former member –S. -R. Pan (now in Colorado state University) –H.-S. Ku (now in Univ. of Colorado/JILA) –T.-S. Ku (now in Univ. of Colorado/JILA) –Prashant Dwivedi (now in Germany’s Univ.) –P.- H. Sun (now in industry)

50. Keep walking ! Molecule cooling Nonlinear optics with ultrcold atoms Welcome to join us ! Ultracold Atom and Molecule Lab IAMS, Academia Sinica

51. Slow Light : Dark-State Polariton coupling 1> |2> |3> coupling 1> |2> |3> probe coupling 1> |2> |3> probe Lukin&Fleischhauer, PRL 84,5094,2000 Light component Matter component: atomic spin coherence

52. EIT and the Photon Storage By adiabatically turn off the coupling light, the probe pulse can completely transfer to atomic spin coherence and stored in the medium and can be retrieved back to light pulse later on when adiabatically turn on the coupling. This effect can be used as a quantum memory for photons. The photon storage and retrieved process has been proved to be a phase coherent process by Yu’s team. coupling probe Hau et.al. Nature, 409,490,2001Y.F. Chen et.al. PRA 72, 033812, 2005

53. Q-Value Measurement Under High-Power Operation microwave OFF Quality-factor Coupling efficiency P Locked P Unlocked

54. Cavity Frequency Locking Pound-Drever-Hall Scheme to obtain error signal Feedback by vacuum linear translation stage Locked to better than 50 kHz (linewidth ~ 700kHz) Locked

55. Fabry-Perot Cavity Coupling Coupling by a circular horn through mirror with mesh. Obtained optimum coupling through systematic study by varying mesh parameters. Reflection signal

56. Observed Line narrowing effect for large OD gas Increasing the OD of atom cloud