Bond hardening is a process of creating a new chemical bond by strong laser fields—an effect opposite to bond softening. However, it is not opposite in the sense that the bond becomes stronger, but in the sense that the molecule enters a state that is diametrically opposite to the bond-softened state. Such states require laser pulses of high intensity, in the range of 1013–1015 W/cm2, and they disappear once the pulse is gone.
Theory
Bond hardening and bond softening share the same theoretical basis, which is described under the latter entry. Briefly, the ground and the first excited energy curves of the H2+ ion are dressed in photons. The laser field perturbs the curves and turns their crossings into anticrossings. Bond softening occurs on the lower branches of the anticrossings and bond hardening happens if the molecule is excited to the upper branches – see Fig. 1.
To trap the molecule in the bond-hardened state, the anticrossing gap cannot be too small or too large. If it is too small, the system can undergo a diabatic transition to the lower branch of the anticrossing and dissociate via bond softening. If the gap is too large, the upper branch becomes shallow or even repulsive, and the system can also dissociate. This means that bound bond-hardened states can exist only in relatively narrow range of laser intensities, which makes them difficult to observe.
Experimental search for bond hardening
When the existence of bond softening was experimentally verified in 1990, the attention turned to bond hardening. Rather noisy photoelectron spectra reported in the early 1990s implied bond hardening occurring at the 1-photon and 3-photon anticrossings. These reports were received with great interest because bond hardening could explain apparent stabilization of the molecular bond in strong laser fields accompanied by a collective ejection of several electrons. However, instead of more convincing evidence, new negative results relegated bond hardening to a remote theoretical possibility. Only at the end of the decade, the reality of bond hardening was established in an experiment where the laser pulse duration was varied by chirping.
Conclusive evidence
The results of the chirp experiment are shown in Fig. 2 in the form of a map. The central "crater" of the map is a signature of bond hardening. To appreciate the uniqueness of this signature requires explaining other features on the map.
The horizontal axis of the map gives the time-of-flight (TOF) of ions produced in ionization and fragmentation of molecular hydrogen exposed to intense laser pulses. The left panel reveals several proton peaks; the right panel shows relatively uninteresting, single peak of molecular hydrogen ion.
The vertical axis gives grating position of the compressor in a chirped pulse amplifier of the Ti:Sapphire laser used in the experiment. The grating position controls the pulse duration, which is shortest (42 fs) for the zero position and increases in both directions. While the stretched pulses are also chirped, it is not the chirp but the pulse duration that matters in this experiment, as corroborated by the symmetry of the map in respect to the zero position line. The pulse energy is kept constant, therefore the shortest pulses are also most intense producing most ions at the zero position.
Kinetic energy variation
The proton TOF spectra allow one to measure the kinetic energy release (KER) in the dissociation process. Protons ejected towards the detector have shorter TOFs than protons ejected away from the detector because the latter have to be turned back by an external electric field applied to the interaction region. This forward-backward symmetry is reflected in the symmetry of the proton map in respect to zero KER (1.27 µs TOF).
The most energetic protons come from the Coulomb explosion of the molecule, where laser field completely strips H2 from electrons and the two bare protons repel each other with strong Coulombic force, unimpeded by any chemical bond. The stripping process it not instantaneous but occurs in a stepwise fashion, on the rising edge of the laser pulse. The shorter the laser pulse, the quicker the stripping process and there is less time for the molecule to dissociate before the Coulomb force attains its full strength. Therefore, the KER is highest for the shortest pulses, as demonstrated by the outer curving "lobes" in Fig. 2.