Attosecond technology - quantum control of high harmonic generation for phase matching Xiaoshi Zhang, Amy Lytle, Oren Cohen, Ivan P. Christov, Margaret M. Murnane, Henry C. Kapteyn JILA, University of Colorado, Boulder, Colorado 80309-0440, USA
Objective: Many critical questions important to scientific and technological progress can be addressed using ultrafast coherent short wavelength sources Nanoscale electron dynamics (e.g. heat transport) Nano imaging Control and manipulation of atoms and electrons in molecules x-ray beam Barrier to overcome - increasing the flux and wavelength range
Coherent x-ray generation using HHG Coherent EUV is generated by focusing an intense laser into a gas Origin of HHG work: 3HG, 5HG, FWM work using nanosecond lasers S.E. Harris et al, J. Reintjes P(3!)" # (3) EEE etc. Nonperturbative nature of HHG using ps, fs pulses was a discovery L Huillier Rhodes CO 2 laser HHG Frequency
The birth of Nonlinear Optics P.A. Franken et al, Physical Review Letters 7, p. 118 (1961) Ruby laser Lens Quartz crystal Prism Photographic plate
NLO technology has seen widespread use NLO Crystal Second Harmonic generation!! 2! Need phase-matching for good efficiency v phase (!) = v phase (2!) Problem in case of HHG: crystal based phase-matching does not apply Neither do methods based on resonant dispersion!
Waveguides for high harmonic generation laser x-ray Rundquist et al, Science 280, 1412, 1998 Durfee et al, PRL 83, 2187, 1999 " k = qk f! kq = 0 2!' - u 00 = q& + 2!%, 43a * - ( 23. P + (1. 1) / 2. 1 N atm r e ), 00 *! $ [ ]( #!" / k 11 0 0 ( ) Waveguide Neutrals Plasma Use structure surrounding NLO medium to control phase matching!
Limitation: HHG is coupled to ionization Ionization 1.0 0.8 0.6 0.4 0.2 0.0-0.2-0.4-0.6-0.8-1.0 Phase mismatch "k (a.u) 0 ionization E field 0 5 10 15 20 25 Time (periods) Phase matching Since higher harmonics are generated at higher laser intensities and ionization levels, impossible to phase match above # c! 0.5-5% or E < 100eV 2!' - u 0 * 0 - & + ( 23 = q. +. /. 11 P (1 1) 2 1 N 2 (!%, 43 0 atm r e a ), 00 ) Waveguide Neutrals Plasma *! $ [ ]( #!" / k 0 0 5 10 15 20 25 Time (periods)
Beating ionization using shorter pulses 5fs, 10fs, 20fs, 30fs Impossible to phase match above 150eV Need phase corrective technique to compensate for ionization
The quantum phase-- HHG depends on phase of recolliding electron A non-instantaneous, but still purely electronic, NLO response!!! " EUV = 2# h t' $ * & % t o p 2 2m + I p ' ) dt ( + 2# h U p(t',t o ) = 2# h U p-. 2# h I p/ 2 - M. Lewenstein, et al., Physical Review A 49 (3), 2117 (1994). Z. Chang et al., Physical Review A 58 (1), R30 (1998).
Experimental evidence of quantum phase Propagation, spatial gradients P. Saliéres et al PRL 74, 3776 (1995) P. Balcou et al, PRA 55, 3204 (1997) Chirp dependence of spectrum Single atom, time-domain Z. Chang, et al., PRA 58 (1), R30 (1998)
Quantum picture (2D) of electron in strong field Phase shift $~1 rad / harmonic order laser time Electron wavefunction Physics Today, Kapteyn et al. March 2005
EUV photonics : Quasi Phase matching Modulate the driving field by modulating a waveguide HHG is modulated because it is sensitive to phase and amplitude of driving laser # k QPM = qk f " k 2 $ + = 0! %= Periodicity of nonlinear medium q Intensity!k=0 QPM!k!" + - + - + - + L coh ="/!k
QPM using modulated waveguides straight fiber modulated fiber (0.25mm) carbon K-edge Nature 421, 51 (2003) Science 302, 95 (2003) First quasi phase matching technique to work in highly-ionized gas Pathway for more efficient higher harmonics (up to kev) BUT: Limited (~10-100x) enhancement because of varying coherence length To design the modulation, need to know coherence length Periodicity limited to ~diameter Plasma and waveguide help with quasi random QPM
Counterpropagating pulses waveguide counter propagating laser beam Ti: Sapphire laser beam EUV beam coherent zones Counterpropagating beam can probe coherence Pulse train can implement QPM
Counterpropagating beams in a gas cell Presence of counterpropagating field disrupts HHG Observe suppression of HHG Peatross et al. PRL 84, 2370 (2000); Opt. Exp. 12, 4430 (2004) Should work better in hollow waveguide long, uniform, interaction length pressure-controlled phase matching
Single counterpropagating pulse in waveguide Driving pulse waveguide coherent zones counter propagating pulse EUV beam Use low pressure, non-phase matched regime standard phase matching in waveguide is ~30 torr for H23-31 General method for mapping coherence coherence length corresponds to 1/2 fringe period
Single counterpropagating pulse in waveguide 0.65mJ 25fs Ar gas inlet (5 torr) 0.6mJ 1.6ps Use low pressure, non-phase matched regime standard phase matching in waveguide is ~30 torr for H23-31 General method for mapping coherence coherence length corresponds to 1/2 fringe period
Single counterpropagating pulse 37 0 2 4 6 8 z [mm] 10 45 43 41 39 Harmonic Order
Colliding pulses
Coherence length vs order, position Coherence Length [mm] 1.5 1.0 0.5 20 25 30 35 Harmonic Order Experimental data Calculated,! = 0.18 Calculated,! = 0.22 Calculated,! = 0.26 40 45 Threshold Photon Energy (ev) 70 60 50 40 30 20 25th 31st 37th 43rd -15-10 -5 0 5 10 15 Time [fs] 0.4 0.3 0.2 0.1 0.0 Ionization Fraction L c decreases with increasing harmonic order At high ionization, near cutoff, L c ~1/q 2 ADK and L c can be used to identify at which ionization levels different harmonics are generated
Coherence length in waveguide Cutoff region Coherence Length [mm] 1.5 1.0 25th 29th 31st 33rd 0.5 2 4 6 z [mm] 8 10 Loss in waveguide decreases ionization, increases L c toward exit Varying L c limits number of fringes observed for fixed counterpropagating pulse duration Evidence of mode beating?
Quantum path control Observe HHG from long and short trajectories Long trajectories strongly modulated, while short trajectories need higher energies! (rad) 8 6 4 2 THEORY Long trajectory Short trajectory 0 0 400 800 Z [nm] Normalized Int. [19th order] EXPT. Long trajectory Short trajectory 0 5 10 15 20 Collision point (mm)
QPM using a TWO pulse train N pulses give (N+1)2 enhancement (expect factor of 9) Glass plate in stretcher splits pulse, allows independent control Intensity Lc + - + - + - + 2 Lc 4 Lc
Modulation due to each pulse, separately Ti: Sapphire laser beam waveguide coherent zones counter propagating train EUV beam Intensity (Arb Unit) 1600 1400 1200 1000 800 600 0.55 mm 1st pulse 2nd pulse) 400 200 0-4 -2 0 2 4 6 8 Collision Point (mm) Pulse sequence adjusted so each counter propagating pulse causes modulation Can measure and adjust the pulse separation - in this case! 1.1mm
QPM using two pulses Intensity [A.U.] 1000 100 10 Double pulse Single Pulse W/O Counter Pulse 35 37 39 41 43 45 47 49 High Harmonic Order Enhancement Factor 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 Double pulse Single pulse Coherence length 0.6 0.5 0.4 0.3 0.2 0.1 0.0-0.1 37 39 41 43 45 47 High Harmonic Order Coherence Length [mm] Use 1.1 mm pulse separation When L c = 1/4 pulse separation, largest enhancement H43 is closest to QPM period => shows largest (x14) enhancement!!
Intensity [A.U.] 1000 100 Higher-order QPM Double Pulse Single Pulse 12 Double pulse Single pulse W/O Counter Pulse 10 Coherence length 10 35 37 39 41 43 45 47 49 High Harmonic Order Enhancement Factor 8 6 4 2 37 39 41 43 45 47 High Harmonic Order 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00-0.05-0.10 Coherence Length (mm) Pulse separation 2.2 mm Intensity + - + - + - + m=2 QPM is obtained at H43 with 7x enhancement 4 Lc
Directly observe pressure-tuned phase matching 15 105 torr Intensity [A.U] 10 5 85 torr 65 torr 45 torr 25 torr 6 0 5 torr Intensity [A.U] 4 2 5 10 z [mm] 15 20 0 20 40 60 Pressure [torr] 80 100 H29 (in standard phase-matching regime!) For phase matching (~40 torr) L c is longer than counterpulse For lower and higher pressures, observe finite coherence length
Excellent p-m in WG reveals atto dynamics Phase matching: signal from all emitters adds in phase & signal reflects single atom dynamics 1st demonstration of learning control on a very high-order quantum nonlinear system Learning algorithm discovered new science! Bartels et al., Nature 406,164 (2000)
Controlling interfering pathways Christov et al, PRL 86, 5458 (2001) Bartels et al. Chem. Phys. 267, 277 (2001) Bartels et al. PRA 70, 112409 (2004)
Attosecond control Delay (attoseconds) 100 50 0-50 -100 optimized pulse gaussian 9 10 11 12 13 14 15 Time (periods) Use algorithm to optimize theory For optimized laser pulse, all harmonics in phase within 25 attoseconds! Experiment feasible using fewcycle pulses
How far can we go? HHG in Helium in the water window 5 torr L c ~100 "m Absorption depth @ 300 ev: 10 meters Possible enhancement: # % $ 10 10 "4 & ( ' 2 ~ 10 10 Neon L c ~ 100 "m Abs depth ~0.5 meters Limitations: defocusing, waveguide propagation, group velocity slip
Future plans for HHG sources Better quasi phase matching techniques pre-formed, tailored and modulated discharges counterpropagating pulsetrains chirped, tapered, waveguides 1-D waveguide to increase flexibility of structures quasi phase matching using twocolor laser fields HHG from molecules 2 L coh1 2 L coh2 More-extensive modeling to understand laser propagation in plasma-filled waveguides Multi khz repetition rate lasers
Ultrafast Coherent Spectroscopy and Imaging Lensless Imaging Optics Lett. submitted High Order X-Ray Raman Probes of Molecules PNAS Sept 2006 Dynamic Holography APL 2006 Attosecond solid state dynamics PRL Sept 2006
Generating Bright Ultrafast X-Ray Pulses Quasi Phase Matching using Light Postdeadline, Ultrafast Phenomena, Aug. 2006 HHG from ions (plasma discharge) PRL, May 2006 High harmonic order Bright, sub-cycle, EUV pulses PRL submitted COLTRIMS - attosecond reaction microscope
Conclusion HHG does not simply happen -- it can be manipulated and optimized in sophisticated ways (!!) It involves the fastest coherent, controllable dynamics yet encountered by man Complex, yet decipherable, spatial-spectraltemporal couplings The attosecond quantum dynamics of rescattering provides the basis for a new technology of extreme nonlinear-optics, with many possibilities Shaped pulse optimization Engineered waveguide structures Counterpropagating fields???