1. Attosecond Optical Science V R

2. The key idea; F=ma Classically an atom’s own electron, driven by a strong electric field can interact with its parent within a cycle. Attoseconds arise first here Mapped by classical physics to here

3. 30 Å gg  c =a(k)e ikx-i  t The key idea

4. F=ma 3.17U osc ~200 eV  0 ~ 31 Å 10 15 W/cm 2, 800 nm 2020 Last or next 1/2 optical cycle

5. Collision Perspective -- 10 11 amp/cm 2 -- Attosecond precision -- ~ 1 Å wavelength -- Time dependent field is present Coherent Collision physics and optics converge Nature, 417, 917, (2002)

6. Optical interferometer Molecular interferometer Interferometers measure everything about the waves involved bound electron re-collision electron Attosecond and High Harmonic Generation; an Interferometer

7. High Harmonics/Attoseconds pulses d(t)={  ra(k)e ikx d 3 r} e i{(IP+KE)t +  }  d(t) is essentially the Fourier transform of the wave function Amplitude, energy and phase of the re-collision electron are transferred to light

8. A second interferometer If one: Single attosecond pulse If more than one: Train of attosecond pulse Optical interference --- but it is as if it were an electron interference!

9. Producing High Harmonics Fundamental and XUV emission Jet, cell or fibre Up to 1,200 eV photons, ~ 1000 th harmonics Not single atom -- Conversion efficiency ~10 -5

10. 30 Å gg  c =a(k)e ikx-i  t Ways to manipulate the interferometer Move the tunnel Move the arm Move the wave function --- Rotate the molecule Give the electron a push

11. Time dependence of the oscillating dipole Making single attosecond pulses --- controlling the laser field

12. High Harmonics

13. 020406080100120140 -0.5 0.0 0.5 1.0 electric field phase Making single attosecond optical pulses control the laser field

14. Producing Attosecond Pulses XUV emission Jet, cell or fibre 250 attoseconds Nature 427 817 (2004) Filter

15. 020406080100120140 -0.5 0.0 0.5 1.0 electric field phase Attosecond Pulse Generation with no Filter State-of-the-art 130 attoseconds

16. Attosecond generation and measurement system Constructed under contract to ALLS

17. Measuring attosecond photon pulses (MAKE A PHOTOELECTRON REPLICA AND MEASURE IT) Streak Camera: PRL 74, 2933 (1995); Science 291, 1923 (2001); PRL 88, 173903 (2002) SPIDER: PRL 90, 073902 (2003)

18. Atomic ionization produces a replica photoelectron pulse V 1/2 mV 2 =   x - IP Measurement of the photo-electron replica is a measurement of the pulse

19. Attosecond Streak Camera

20. F=ma once again linear polarization initial velocity (V 0x, V 0y, V 0Z ) V drift, x = V 0x - {V d = qE 0 (t)/m  Sin (  t I +  )} V drift, y = V 0y V drift, z = V 0z Drift velocity distribution Polarization

21. A single sub-cycle X-ray pulse VxVx VyVy --- photoelectron replica is streaked (attosecond streak camera)

22. Streaked photoelectron of 100 eV pulse -- parallel observation 70 attosecond I = 6x10 14 W/cm 2

23. 30 Å gg  c =a(k)e ikx-i  t Ways to manipulate the interferometer

24. Moving the arms --- a phase gate A (weak) 2 2  field breaks symmetry, generating even harmonics Each moment of birth (re-collision) has an optimum phase difference (  ) between  and 2 

25. 60  BBO /2 Wave plate Supersonic gas jet Experimental Set-Up calcite glass Ti:sapphire amplifier 1mJ, 27 fs @ 50 Hz grating MCP

26. 16 18 20 22 24 26 Harmonic order Delay [fs] What Phase difference moves the interferometer arms optimally?

27. Re-collision time [rad]  (t) Harmonic number  (N  ) Attosecond Temporal Phase Gate d ,2  (t) ~ d  (t) e i  (t) SFA  : two color delay which maximizes the even harmonic signal

28. Electron Wave-Packet Reconstruction Re-collision time [rad] Short trajectories Long trajectories Harmonic order SFA Electron wave packet measurement is equivalent to a xuv pulse measurement up to the transition dipole.

29. Interferometers also allow control Larger phases or

30. Using Interferometry for everything: Tomographic Imaging of electronic orbitals Nature 432, 867 (2004)

31. High Harmonics/Attoseconds pulses d(t)={  ra(k)e ikx d 3 r} e i{(IP+KE)t +  }  d(t) is essentially the Fourier transform of the wave function

32. Transient alignment of molecules time

33. The Experiment “Pump” Alignment pulse “Probe” HHG pulse (60fs, 5 x 10 13 W/cm 2 ) (30fs, 1.5 x 10 14 W/cm 2 ) H15 23.3eV H21 32.6eV H27 41.9eV H33 51.2eV H39 60.5eV Space Ti:sapphire CPA 1 TW, 27 fs @ 50 Hz

34. Angle Dependent High Harmonic Spectrum

35. Harmonics from N 2 and Ar  2 d(  )=  2 a(k)  g re ikx dx Note the relation to Photoelectron spectroscopy

36. Normalized Harmonic Intensities Harmonic intensities from N2 at different molecular angles ELEL

37. Reconstructed N 2  g Orbital Reconstructed from 19 angular projections wave function, not its square We see electrons! Amplitude and Phase!

38. Review: Measure orbitals Measure attosecond pulses Control high harmonics Probe atomic or molecular dynamics

39. The Attogroup (2007) Scientists: Paul Corkum, David Villeneuve, Eli Simova, Andrei Naumov and David Rayner Technologists: Bert Avery, John Parsons Postdoctoral Fellows: Nirit Dudovitch, Rajeev Pattathil, Domagoj Pavicic and Yann Mairesse. Visitors: Hiromichi Niikura, Gennady Yudin and Andre Staudte Ph. D. Students: Kevin Lee (McMaster), Julien Bertrand and Marina Gertsvolf (Ottawa).