Fragmentation Dynamics of H2+ / D2+ Kansas State University in Intense Ultrashort Laser Pulses Kansas State AMO PHYSICS U. Thumm B. Feuerstein T. Niederhausen Kansas State University Introduction Method of Calculation Results: initial vibrational state dependence intensity dependence pump-probe study of coherent vibrational motion

Laser pulse (Ti:sapphire) INTRODUCTION Laser pulse (Ti:sapphire) H2+ (D2+) Time scales Tcycle = 2.7 fs Tpulse = 5 -150 fs Tv=0 = 14 (20) fs Telectr = 0.01 fs Energies  = 1.5 eV Ip = 30 eV De = 2.8 eV Length scales l = 16000 a.u. (800 nm) R0 = 2 a.u.

enhanced ionization (CREI) H0 + H+ dissociation 2 dissociation 1 single ionization H2 H2+ 3 enhanced ionization (CREI) 4 fast Coulomb explosion H+ + H+ Coulomb explosion

Dissociation and Ionization paths g u Charge resonance enhanced ionization 1w 2(3)w CE p + p H2+ R [a.u.] E [a.u.] Dressed potential curves (schematic) 3w 1w 2w 0w weak field strong field Adiabatic dressed states (Floquet theory, CW laser) -> distinguish 1w, 2w [effective (3-1)w – dipole selection], etc. dissociation paths via avoided crossings (tunneling and over barrier) E.g.: 1w has threshold at v=5 (Saendig/Haensch et al. 2000 did vibrationally resolved fragment momentum spectroscopy, level shift due to potential widening observed as function of intensity. trapping in 2w well = “bond hardening”) Avoided crossings: mixing of g and u states -> localization ->CREI

2D Crank-Nicholson split-operator propagation METHOD OF CALCULATION 2x1D model R z Laser field p e- 2D Crank-Nicholson split-operator propagation

Improved soft-core Coulomb potential R-dep. softening function a(R) + fixed shape parameter b = 5 (Kulander et al PRA 53 (1996) 2562) Fixed softening parameter a = 1 a(R) adjusted to (exact) 3D pot. curve present result

Dipole oscillator strength for sg – su transitions } Kulander et al PRA 53 (1996) 2562 This work (1D)

“virtual detector” method Array for 2x1D collinear non-BO wave packet propagation “virtual detector” method z: electron coordinate R: internuclear distance Grid: z = 0.2 a.u.; R = 0.05 a.u.

“virtual detector”: data analysis Integration over z and binning  fragment momentum distribution Dissociation Coulomb explosion Integration over R and binning  fragment momentum distribution

RESULTS Time evolution of wave function and norm (on numerical grid) Evolution of nuclear probability density r(R,t ) dissociation probability ionization rate jz(R,t) CE probability Kinetic energy spectra of the fragments Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs): vibrational state and intensity dependence B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs): CE-imaging of dissociating wave packets C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs): CE-imaging of bound and dissociating wave packets

total fragment energy [eV] 0.2 PW/cm2 25 fs PCE(t) Dissociation Coulomb explosion - - - - - (Coulomb energy) PD (t) Laser a Norm(t) b c d 1  2(3)  V 0 V 5 19 total fragment energy [eV] log scale Contours: jz(R,t)

- - - - - (Coulomb energy) Norm(t) v = 0 0.2 PW/cm2 25 fs Dissociation Coulomb explosion 1  2(3)  V 0 V 5 19 - - - - - (Coulomb energy) Laser PD (t) PCE(t) log scale

- - - - - (Coulomb energy) v = 2 0.2 PW/cm2 25 fs PCE(t) PD (t) Norm(t) Dissociation Coulomb explosion 1  2(3)  V 0 V 5 19 - - - - - (Coulomb energy) Laser log scale Contours: jz(R,t)

- - - - - (Coulomb energy) v = 4 0.2 PW/cm2 25 fs PCE(t) Dissociation Coulomb explosion - - - - - (Coulomb energy) PD (t) Laser a Norm(t) b c d 1  2(3)  V 0 V 5 19 log scale Contours: jz(R,t)

- - - - - (Coulomb energy) PCE(t) v = 6 0.2 PW/cm2 25 fs Dissociation Coulomb explosion 1  2(3)  V 0 V 5 19 - - - - - (Coulomb energy) PD (t) Laser Norm(t) log scale Contours: jz(R,t)

- - - - - (Coulomb energy) PCE(t) v = 8 0.2 PW/cm2 25 fs Dissociation Coulomb explosion 1  2(3)  V 0 V 5 19 - - - - - (Coulomb energy) Laser Norm(t) PD (t) log scale Contours: jz(R,t)

Branching ratio : Dissociation vs. Coulomb explosion

RESULTS II Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs): vibrational state and intensity dependence B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs): CE-imaging of dissociating wave packets C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs): CE-imaging of bound and dissociating wave packets

Pump-probe experiment 2(3)  CE D2 target 0.1 PW/cm2 2 x 80 fs variable delay 0 - 300 fs 1  Trump, Rottke and Sandner PRA 59 (1999) 2858

Pump-probe (D2+) v = 0 0.3 PW/cm2 2 x 25 fs delay 30 fs Norm(t) PCE(t) Dissociation Coulomb explosion Laser PD (t) - - - - - (Coulomb only) b c a log scale Contours: jz(R,t)

Pump-probe (D2+) v = 0 0.3 PW/cm2 2 x 25 fs delay 50 fs Norm(t) PCE(t) Dissociation Coulomb explosion PD (t) Laser - - - - - (Coulomb only) b c a log scale Contours: jz(R,t) c b a

Pump-probe (D2+) v = 0 0.3 PW/cm2 2 x 25 fs delay 70 fs Norm(t) PCE(t) Dissociation Coulomb explosion Laser PD (t) - - - - - (Coulomb only) b c a log scale Contours: jz(R,t) c b a

RESULTS III Single pulse (I = 0.05 – 0.5 PW/cm2, 25 fs): vibrational state and intensity dependence B) Pump-probe pulses (I = 0.3 PW/cm2, 25 fs): CE-imaging of dissociating wave packets C) Ultrashort pump-probe pulses (I = 1 PW/cm2, 5 fs): CE-imaging of bound and dissociating wave packets

Time evolution of a coherent superposition of states Time dependent density matrix: Time average: Incoherent mixture Preparation of coherent states of molecular ions. How ? Ion source: T  ms  incoherent ensemble Ultrashort laser pulse: T  5 fs  coherence effects expected H2+ (wkm-1 = 3 … 30 fs): produced by:

t autocorrelation pump 1 PW/cm2 5 fs probe 2 PW/cm2 5 fs D2+ D0 + D+ Model: vertical FC transition of D2 (v=0) -> D2+ potential curve. Calculation shows complete ioinization within < 1fs (cf. extra plot). Survivals in remaining half pulse, we calculated: H2+ ( period(v=0) = 14fs ) : 11% Diss., 4% CREI D2+ 20 2 1.7 Explanation D2+ vibr. wave packet doesn’t reach avoided croissings within pulse duration. WF collapse & partial revival in <R> and autocorrelation. t probe 2 PW/cm2 5 fs D0 + D+ D+ + D+ D2+ pump 1 PW/cm2 5 fs D2

Coulomb explosion imaging of nuclear wave packets Fragment yield Y at Ekin : Y(Ekin) dEkin = |(R)|2 dR  Y(Ekin) = R 2 |(R)|2 Kinetic energy Ekin (R) 1/R d + d Probe |(R,t)|2 R D2+ Pump D2 initial |(R)|2

|(R)|2 reconstruction from CE fragment kin. energy spectra  = 10 fs |(R)|2 reconstructed |(R)|2 original |(R)|2 incoherent FC distr. moving wave packet relatively fast outward motion => noticable kinetic energy shift in reconstructed wp

|(R)|2 reconstruction from CE fragment kin. energy spectra  = 20 fs |(R)|2 reconstructed |(R)|2 original |(R)|2 incoherent FC distr. turning point Turning point => NO kin. energy shift and good agreement

|(R)|2 reconstruction from CE fragment kin. energy spectra  = 40 fs reconstructed |(R)|2 original |(R)|2 incoherent FC distr. |(R)|2 wp moving back out again, but increasing broadening due to beginning collapse

|(R)|2 reconstruction from CE fragment kin. energy spectra  = 580 fs |(R)|2 reconstructed |(R)|2 original |(R)|2 incoherent FC distr. ‘revival’ Revival after about 20 oscillation periods => good reconstruction of initial wp