Strong-field physics revealed through time-domain spectroscopy Grad student: Dr. Li Fang – now at LCLS Hui Chen, Vincent Tagliamonti Funding : NSF-AMO November 7, 2011 Stony Brook University Stony Brook, New York George N. Gibson University of Connecticut Department of Physics

What can strong-field physics offer chemistry? Time resolution: femtosecond laser pulses can resolve nuclear motion, R Time resolution: femtosecond laser pulses can resolve nuclear motion, R Can control both R and  Can control both R and  Can look at processes as a function of both Can look at processes as a function of both Ultimate goal: Quantum tomography as a function of R – united atom to separated atom Ultimate goal: Quantum tomography as a function of R – united atom to separated atom Start with:End with:

Increasing internuclear separation: 2-D 1-electron double-well  g wavefunctions:

Back to Basics: Tunneling ionization of a double- well potential (All strong field experiments on molecules start here!) Ionization is dominated by an effect called “R-critical ”

Basic Tunneling Ionization: U1 j0  This separation is called “R critical ” (Bandrauk, Seideman, Corkum, Ivanov)

Dynamics of 1 electron in field: Dipole moment Unified atom limit

Separated atom limit.

Intermediate case. Strongly driven gerade  ungerade transition creates large dipole moments, compared to atoms or even-charged ground state molecules.

Data and calculations for H 2 + : End of story? This is from an ion. Also, not pump-probe, so a number of assumptions were made. Better: Zuo and Bandrauk, PRA (1995), Data: Gibson et al., PRL (1997)

Simple 1-D 1-e - calculation:

Simple model for R c For H 2 +, R c should be 3/(0.5) = 6, which is close. For H 2 +, R c should be 3/(0.5) = 6, which is close. Want to test in the neutral using pump-probe, since most experiments start in the neutral species. Want to test in the neutral using pump-probe, since most experiments start in the neutral species. Find condition where the inner barrier just equals the energy of the ground state:

Resonant excitation provides a mechanism for studying the neutral Using pump-probe techniques, we can control R. Resonant excitation follows a cos(  ) 2 pattern, producing a well-aligned and well-defined sample. This gives: = 0.6 at room temperature with one laser pulse. = 0.6 at room temperature with one laser pulse. [For unaligned samples = 0.33]

Laser System Ti:Sapphire 800 nm Oscillator with a Multipass Amplifier Ti:Sapphire 800 nm Oscillator with a Multipass Amplifier 750  J 1 KHz 750  J 1 KHz Transform Limited, 30 fs pulses Transform Limited, 30 fs pulses TOPAS Optical Parametric Amplifer: 490nm – 2000nm TOPAS Optical Parametric Amplifer: 490nm – 2000nm

Ion Time-of-Flight Spectrometer

Nitrogen TOF Spectrum

Wavepacket motion in the B-state of I 2 gives (t) Vibrational period (fs)‏ X-B coupling wavelength (nm)‏

Ionization vs. R We know from the motion on the B state. We know from the motion on the B state. Can convert from time to R(t). Can convert from time to R(t).

B-state wavepacket simulation

Wavelength check: I p R c = 3.01 Shorter wavelength: larger outer turning point longer vibrational period

Really want to study the ground state! Can we return the wavepacket to the X-state? Can we return the wavepacket to the X-state? Yes, with a pump-dump scheme: Yes, with a pump-dump scheme:

Returning wavefunction in X-state (2,0) (2,1)

Single ionization: I 2 +

Diatomic molecules in strong fields: N 2  N 2 1+  N 2 2+  N 1+ + N 1+  N 2 3+  N 1+ + N 2+  N 2 4+  N 2+ + N 2+  N 2 5+  N 3+ + N 2+  N 2 6+  N 3+ + N 3+  N 2 7+  N 4+ + N 3+ N 2  N 2 1+  N 2 2+  N 1+ + N 1+  N 2 3+  N 1+ + N 2+  N 2 4+  N 2+ + N 2+  N 2 5+  N 3+ + N 2+  N 2 6+  N 3+ + N 3+  N 2 7+  N 4+ + N 3+  N 2+ + N 0+ (15.1 eV)  N 3+ + N 1+ (17.8 eV)  N 4+ + N 2+ (30.1 eV)

Why is the observation of Charge- Asymmtric Dissociation so important? It represents direction excitation of states with energies in the VUV spectral region. (Up to 30eV in N 2 6+ ). It represents direction excitation of states with energies in the VUV spectral region. (Up to 30eV in N 2 6+ ). Excitation involves many photons. Excitation involves many photons. Have seen everything up to I  I 5+ + I 7+. Have seen everything up to I  I 5+ + I 7+. Optimizing excitation process may lead to amplifiers in the VUV as inversions are likely occurring. Optimizing excitation process may lead to amplifiers in the VUV as inversions are likely occurring. May be a new high-harmonic source. May be a new high-harmonic source. CAD is a ubiquitous and robust process: There must be something generic about the structure of homonuclear diatomic molecules. CAD is a ubiquitous and robust process: There must be something generic about the structure of homonuclear diatomic molecules.

What is so special about (even) charged diatomic molecules? Ground state is a far off- resonant covalent state. Above this is a pair of strongly coupled ionic states. Only a weak coupling between them.

3-Level Model System This system can be solved exactly for the n-photon Rabi frequency!

Three-level systems: “V”: “  ”: Now the “  ”:

Diatomic Dications How are asymmetric states populated? Is it through multiphoton transitions in the  -system? How are asymmetric states populated? Is it through multiphoton transitions in the  -system? (2,0) must have binding. In fact, it is an excimer- like system, bound in upper state, unbound in lower state. Can we trap population in this state? (2,0) must have binding. In fact, it is an excimer- like system, bound in upper state, unbound in lower state. Can we trap population in this state? Can we make a multiphoton pumped excimer laser? Can we make a multiphoton pumped excimer laser? We have evidence for bound population. We have evidence for bound population. Evidence for 3-  excitation – but is it due to the  structure??? Evidence for 3-  excitation – but is it due to the  structure???

Need spectroscopic information Namely, there should be (2,0) g and (2,0) u. Namely, there should be (2,0) g and (2,0) u. TOF spectroscopy not sensitive enough to distinguish them. TOF spectroscopy not sensitive enough to distinguish them. However, coherent 1  2  fields provide an interesting spectroscopic tool. However, coherent 1  2  fields provide an interesting spectroscopic tool.

What are 1  2  fields? If you add a fundamental laser frequency and its second harmonic, you can break spatial symmetry.

Molecular dissociation Charge-asymmetric dissociation is generally spatially symmetric (with a single frequency pulse). I.e., for I 2+ + I, the I 2+ goes to the left as much as to the right. Charge-asymmetric dissociation is generally spatially symmetric (with a single frequency pulse). I.e., for I 2+ + I, the I 2+ goes to the left as much as to the right. However, with a spatially-asymmetric laser field can break the spatial symmetry of the dissociation. However, with a spatially-asymmetric laser field can break the spatial symmetry of the dissociation.

Molecular dissociation, with a 1  2  field Phase = 0 Phase =  /2

Eigenstates vs. Observables Observable: I 2+ + I  (2,0) or (0,2) (left or right) Observable: I 2+ + I  (2,0) or (0,2) (left or right) Eigenstates:(2,0) g ~ (2,0) + (0,2) (2,0) u ~ (2,0) – (0,2) Eigenstates:(2,0) g ~ (2,0) + (0,2) (2,0) u ~ (2,0) – (0,2) Eigenstates must dissociate spatially symmetric. Eigenstates must dissociate spatially symmetric.  Therefore, a spatial asymmetry requires a coherent superposition of g and u states, which is only possible in a spatially asymmetric field.

Simple tunneling model g and u states strongly coupled – diagonalize in a dc field. g and u states strongly coupled – diagonalize in a dc field. Assuming ionization into the lowest lying (down field) level. Assuming ionization into the lowest lying (down field) level. Project back onto field-free states and calculate spatial asymmetry. Project back onto field-free states and calculate spatial asymmetry.

Spatial asymmetry as a function of R We can measure the spatial asymmetry of the (2,0) dissociation channel by populating the B-state of I 2. We can measure the spatial asymmetry of the (2,0) dissociation channel by populating the B-state of I 2.

What do we learn from 1  2  fields? In strong-field ionization, it appears that the field induced states are populated directly through tunneling ionization. In strong-field ionization, it appears that the field induced states are populated directly through tunneling ionization. It is not the case that ionization populates the ground state and the asymmetric states are then populated through the  -system. (Very difficult to reproduce the spatial asymmetry dependence.) It is not the case that ionization populates the ground state and the asymmetric states are then populated through the  -system. (Very difficult to reproduce the spatial asymmetry dependence.) Really must consider the field-induced molecular structure to understand strong-field ionization. Really must consider the field-induced molecular structure to understand strong-field ionization. Also, raises interesting questions about decoherence and dephasing. Also, raises interesting questions about decoherence and dephasing.

Conclusions Strong fields offer unprecedented control over t, R, and . Strong fields offer unprecedented control over t, R, and . We also have considerable control over nuclear wavepackets. We also have considerable control over nuclear wavepackets. Can measure strong field processes as a function of these variables. Can measure strong field processes as a function of these variables. Can investigate the structure of unusual (highly ionized) molecules. Can investigate the structure of unusual (highly ionized) molecules.