Bond hardening

If it is too small, the system can undergo a diabatic transition to the lower branch of the anticrossing and dissociate via bond softening.

This means that bound bond-hardened states can exist only in relatively narrow range of laser intensities, which makes them difficult to observe.

[7][8] Only at the end of the decade, the reality of bond hardening was established in an experiment[9] where the laser pulse duration was varied by chirping.

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 vertical axis gives grating position of the compressor in a chirped pulse amplifier of the Ti:Sapphire laser used in the experiment.

The proton TOF spectra allow one to measure the kinetic energy release (KER) in the dissociation process.

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.

The lowest energy protons are produced by the bond hardening process, which also starts at the 3-photon gap but proceeds to the 1ω limit (the lower red trough in Fig.

Since the initial and the final energies are also fixed here, the KER should also be constant but clearly it is not, as the round shape of the central "crater" demonstrates it in Fig.

Since the equilibrium internuclear separation for the neutral molecule is smaller than for the ionized one, the ionic nuclear wave packet finds itself on the repulsive side of the ground state potential well and starts to cross it (see Fig.

When the laser intensity falls, the bond-hardened energy curve returns to the original shape, flexing up, lifting the wave packet and releasing about a half of it to the 1ω limit (Fig.

The faster intensity falls, the higher the wave packet is lifted and more energy it gains, which explains why the KER of the "crater" in Fig.

One can say[citation needed] that the photon is not a particle but as a mere quantum of energy that is usually exchanged in integer multiples of ħω, but not always, as it is the case in the above experiment.

And since the pulse is short, it has sufficiently wide bandwidth to accommodate absorption of photons that are more energetic than the re-emitted ones, giving the net result of a fraction of ħω.

In increasing laser intensity the anticrossing gap was getting wider, lifting the wave packet to the 0ω limit and dissociating the molecule with very small KER.

Figure 1: Energy curves of the H 2 + ion dressed in photons for a few laser intensities. Bond hardening creates a new bound state on the upper branch of anticrossings. Bond softening dissociates the molecule along the lower branches.
Figure 2: Signature of bond hardening in proton time-of-flight spectra with varying laser pulse duration. The kinetic energy release (KER) varies with pulse duration for bond hardening, unlike in bond softening where it is constant.
Figure 3: Evolution of bond hardening in laser field. An H 2 + wave packet is created by absorption of n photons on the leading edge of the laser pulse (a). Trapping occurs near peak intensity (b). The wave packet is lifted up and released with some kinetic energy by the trailing edge of the pulse (c). A fraction of the photon energy is absorbed from the field.
Figure 4: Zero-photon dissociation. The 3rd harmonic of the Ti:Sapphire laser can lift the trapped wave packet all the way to the 0ω limit. The molecule is dissociated without absorption of a net number of photons.