Misha Ivanov

1. Surprising strong field dynamics in laser filaments MishaIvanov • Lasing without inversion in the air (N2) • Bound states of a free electron

2. Lasing without inversion in the air D.Kartashov, S. Haessler, G. Andriukaitis, A. Pugžlys, A. Baltuška A. Zheltikov J. Möhring, M. Motzkus M. Richter, F. Morales, O. Smirnova M. Spanner

3. Kerr effect and Kerr lens Laser filamentation: the bare basics • Self-guided beam, can move very far • Interplay of self-focusing and defocusing

4. Laser filamentation: the bare basics • Looks pretty • Broad spectrum: UV- IR

5. F coswt • Induced dipole: • d(E)= axE coswt • - oscillates with the field • Cycle-averaged interaction energy: • U(q)=- ¼ [Da] E2cos2q Q Strong field molecular alignment: the bare basics N2 Field-free alignment after a short pulse

6. Key facts for today • Air is made of molecules, mostly N2

7. Key facts for today • Air is made of molecules, mostly N2 • Filamentation by-product I: • They rotate

8. Key facts for today • Air is made of molecules, mostly N2 • Filamentation by-product I: • They rotate • Filamentation by-product II: molecular ions N2+ N2+ Energy, eV R, Å

9. Key facts for today • Air is made of molecules, mostly N2 • Filamentation by-product I: • They rotate • Filamentation by-product II: molecular ions N2+ • Filamentation by-product III : broad spectra, one-photon transitions can saturate N2+ B(v=0) -> X(v=0): 391 nm Energy, eV R, Å

10. Key facts for today • Air is made of molecules, mostly N2. Filamentation makes them rotate • You do not even need to saturate X-> B to make it lase ! N2+ B(v=0) -> X(v=0): 391 nm Energy, eV R, Å

11. Inversion without inversion B B • Inversion without inversion: • More X molecules than B molecules: PX>PB • But more aligned B molecules than X molecules: • PB (Q=0)>PX(Q=0) X X • B -> X is a parallel transition

12. Inversion without inversion B B • Inversion without inversion: Wup ~ <cos2Q>X PX X Wdown ~ <cos2Q>B PB X Gain: Wup - Wdown < 0

13. Transient inversion induced by rotations Wup - Wdown R=PB/PX=1/2 Almost transient inversion

14. Transient inversion induced by rotations Wup - Wdown R=PB/PX=1/2 R=PB/PX=3/4 Almost transient inversion Transient inversion • Lasing without inversion: transient inversion during rotational revivals • Better alignment – smaller R is needed for transient inversion

15. Experiment I: Bright emission 391 nm beam 391 emission in N2+ 9th 4 mm pump 11th • Forward, well collimated • Needs a seed: • Appears only when filamentation generates spectrum around 390 • Universal: has been observed for a single pump pulse @ • 400 nm, 800 nm, 1 mm, 2 mm, 4 mm

16. Another candidate ? • Emission due to coherent polarization • a.k.a. Wave mixing, Parametric emission,... DXB(t)= < YX(t)|d|YB(t) > DXB(W)= FT (DXB(t)) • General • only needs coherence between N2+ (X) and N2+(B) • all it needs is a seed around 390 nm • will happen for all pump wavelengths that make filaments • Will last after the filament is gone, as long as X-B coherence lasts • Natural sensitivity to rotations

17. Coherent polarization / Wave mixing: Effect of rotations • DXB(t)= <YX(t)|d| YB(t)> + c.c. • Requires overlap of YX(t) and YB(t) • Rotations with different period kill the overlap and DXB(t)

18. Opposite temporal patterns Inversion without inversion Wup - Wdown ‘Wave mixing’ • Need time-resolved measurements !

19. Experiment II: Time-resolved measurements • Experiment @ 1.03 mm, 240 fsec • Starts immediately, • Lasts ~ 15 psec • Follows revivals in N2+ B state

20. Time-resolved signal: Experiment vs Theory Experimental FROG Spectra ‘Wave mixing’ FROG (Theory)

21. Time-resolved signal: Experiment vs Theory Experimental FROG Spectra Excellent Disagreement !

22. Time-resolved signal: complementary patterns Experimental FROG Spectra Transient Inversion ‘Wave Mixing’ R=1

23. Experiment vs Theory Experimental FROG Spectra Transient Inversion ‘Wave Mixing’ R=3/4 • Lasing without inversion: • Threshold effect: better alignment – smaller R=PB/PX is needed • Let us optimize alignment!

24. Experiment III: Optimized alignment 3 bar N2+ emission: more than 104 brighter for optimal pulse sequence Optimal sequence x 10-4 delay,ps The smoking gun?

25. Bound states of a free electron NRC Canada Maria Richter Felipe Morales Olga Smirnova SergueiPatchkovskii

26. What is common between these? IlyaRepin: Barge haulers on Volga Laser filamentation in the air

27. Kerr effect and Kerr lens Laser filamentation: the bare basics

28. Is ionization needed for filamentation? n(I) Kerr effect, n(I), in air @ 800 nm Intensity 1013 W/cm2 • Is this really possible, and if possible – when, why, and how?

29. Acceleration of neutrals: ‘free’ electron pulling the parent ion He, 800 nm, ~1016 W/cm2 k Very strong laser field: Up=F2/4w2~ KeV e- + r ~ mm But how is the rope made?

30. How the rope is made: frustrated ionization What happens when the laser intensity is very high? -zFcoswt Oscillation amplitude a0=F/w2 >> Angstrom -zFcoswt Does above-barrier decay necessarily mean ionization? Again NO!

31. + Idea: W. Henneberger PRL, 1968 Bound electron Very strong laser field: nearly free oscillations How the rope is made: The Kramers-Henneberger atom Include both: Bound again! Bound states of the KH potential make the rope

32. -zFcoswt 6.1014 W/cm2 800 nm Bound states of the free electron The electron is placed at the exit from the barrier, simulating tunnel ionization. It refuses to behave ionized in 15-20% of cases.

33. Kr, Xe, Ar, O2, N2, @1013 W/cm2 Kerr response in strong low-frequency laser fields -zFcoswt - zFcoswt • Note: • at I~1013 W/cm2 all excited states are way above barrier, and ground state is well below • Oscillation amplitude a0> 6 a.u is large • Pertinent to all phenomena which include response of bound states in strong fields, e.g. Kerr effect around and above 1013 W/cm2

34. Energy Analysis In the KH regime for the excited states, En(F)=En+Up+DEn The ground state still goes down: Eg(F)=Eg-DEg En (F,w) – bound states of a ‘free’ electron Eg(F,w) ainst(I,w) Intensity ,>1013W/cm2 Intensity Can this be seen with everything else (ionization, real excitation) piling up on top?

35. Grid Spacing r Z Time step 1: 0.2 0-100 +/-200 0.005 2: 0.2 0-100 +/-400 0.005 2x: 0.2 0-200 +/-800 0.005 3: 0.1 0-100 +/-400 0.00125 Any signatures of this physics? TDSE for 3D Hydrogen 1600 a.u. 800 a.u. 2 1 r axis 2x 400 a.u. Field, z axis

36. Role of the box size: • Absorb more, or less, free electrons • See how this changes the Kerr response Role of box size 1600 a.u. 800 a.u. 2 1 r axis 2x 400 a.u. Field, z axis

37. Short pulse: sin2 with 4 cycles turn-on and turn-off, l=0.9 mm High order Kerr effect: TDSE for 3D Hydrogen

38. Short pulse: sin2 with 4 cycles turn-on and turn-off, l=1.8 mm High order Kerr effect: TDSE for 1D Hydrogen

39. Short pulse: Gaussian FWHM=4 cycles, l=1.8 mm High order Kerr effect: TDSE for 1D Hydrogen • Saturation of the Kerr response • Happens just before ionization kicks in • Once ionization kicks in, it takes over • HOKE is real, but is important in a very narrow intensity window • KH states are playing major role

40. Laser filamentation leads to • Very broad spectrum • -> Easy saturation of 1-photon transitions in the ion: IR-nearUV • Ionization • Molecular alignment • Rotational revivals naturally create time-windows with population inversion • Better alignment – better lasing ‘without inversion’ Conclusions: Lasing without inversion

41. In general, saturation of the Kerr effect comes from: • Ionization (major player) • Real excitations to ‘bound states of the free electron’ • Modification of the instantaneous response (i.e. virtual transitions) due to restructuring of the dressed atom. • Restructuring of the atom leads to saturation and – partly – to the onset of the reversal of the Kerr effect • This happens just before ionization kicks in • Ionization starts to dominate as soon as it kicks in • The interplay of the three effects is strongly pulse-shape dependent Conclusions: HOKE

42. Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. If we don’t sand the floor, we’ll get splinters into our bare feet! Proposal for HOKE Consensus

43. MishaIvanov and Bob Levis agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Proposal for HOKE Consensus Rabbi, who is right?

44. Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Proposal for HOKE Consensus Rabbi, who is right? You are both right!

45. Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Proposal for HOKE Consensus You are both right! We can’t both be right!

46. Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Proposal for HOKE Consensus We can’t both be right! Yes you can!

47. Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Proposal for HOKE Consensus OK, Rabbi, we can’t argue with you. But what shall we do with the floor? Shall we sand the floorboards or not? Yes you can!

48. Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Proposal for HOKE Consensus You should sand the floorboards, But put them sanded side down

49. Looking inside a dressed atom is not easy! Conclusions

50. Short pulse: Gaussian FWHM=4 cycles, l=0.9 mm • 5.6 1013 W/cm2 • Kerr is reversed • Box-size dependence High order Kerr effect: TDSE for 3D Hydrogen • 4.3 1013 W/cm2 • Kerr is saturated • No box size dependence! Field, a.u.