Solid metallic hydrogen, predicted by Wigner and Huntington in 1935 and by Ashcroft to be a high-temperature superconductor, has never been produced: static compression of molecular hydrogen requires pressures above roughly 400 GPa, beyond reliable diamond-anvil-cell operation. Shibata and Kodama (High Energy Density Physics 7, 288, 2011) proposed an alternative route: compress molecular hydrogen to only about 106 GPa in a diamond anvil cell and dissociate it in place with an ultrafast, intense ~250 nm short-pulse laser via three-photon absorption into dissociative excited states. In the authors' isolated-molecule calculations for 10 fs pulses at peak intensities of order ~6×10^13 W/cm^2, a near-transform-limited Lorentzian temporal profile is reported to be the only one of eight tested pulse shapes that dissociates close to 50% of the molecules while heating the sample by no more than ~750 K, below the ~1050 K melting point at that pressure. The proposal has never been tested: whether the photodissociation scheme can actually produce a persistent solid atomic (metallic) hydrogen phase at diamond-anvil-cell-accessible pressures, once the solid-state, ionization, and recombination physics neglected in the isolated-molecule treatment are accounted for, remains the open problem.

Background

Metallic hydrogen is the hypothesized conducting phase of the element hydrogen, first analyzed by Wigner and Huntington (1935), who showed that under sufficient compression the H2 molecules should dissociate into a lattice of protons with a delocalized electron gas. Ashcroft (1968) argued that such an atomic metallic phase would be a high-temperature superconductor, which has made it a long-standing goal of high-pressure physics. The standard tool is the diamond anvil cell (DAC), a device that compresses a micron-scale sample between two diamond culets; diamond is used because it is the hardest known material and is transparent over a wide spectral range (its band gap is 5.47 eV, so photons below that energy pass through it). Decades of DAC experiments have mapped the phase diagram of molecular hydrogen: the solid remains molecular, with the intramolecular vibrational mode (the vibron, an infrared- and Raman-active H–H stretching transition) serving as the main structural diagnostic, and calculations indicate that metallization of solid molecular hydrogen by band-gap closure requires pressures above roughly 400 GPa, near or beyond the limit of diamond anvil cells. By contrast, prior calculations — including the authors' own dynamical mean-field theory study of the metallization density of solid atomic hydrogen (dynamical mean-field theory, DMFT, is a method for treating strongly correlated electrons by embedding each lattice site in a self-consistently determined effective medium) — indicated that already-dissociated, atomic hydrogen becomes metallic at a substantially lower density, within reach of conventional DAC pressures around 100 GPa. This motivated the question of how one might dissociate molecular hydrogen inside a DAC without destroying the solid. Shibata and Kodama (2011) proposed photodissociation: excite H2 by three-photon absorption (the simultaneous absorption of three photons whose energies sum to an electronic transition) into the dissociative excited singlet states B¹Σu⁺, C¹Πu, and B'¹Σu⁺, whose combined asymptote H(1s)+H(2l) lies 14.677 eV above the molecular ground vibrational level. Single photons of 5 eV are chosen because they pass through the diamond windows (band gap 5.47 eV) while three of them exceed the dissociation threshold; the optimum photon energy is 4.9–4.95 eV (wavelength about 250 nm). Using isolated-molecule potential curves and cross sections, they computed the dissociation ratio and the temperature increase for eight pulse shapes of 10 fs duration, finding that the dissociation yield rises and the heating falls as the time-bandwidth product (the product of pulse duration and spectral width, minimal for a given shape in a transform-limited pulse) decreases: a Gaussian pulse (time-bandwidth product 2.773) gives a 48.2% dissociation ratio with ΔT = 780 K at peak intensity 6.18×10^13 W/cm^2, a square pulse gives 36.0% with ΔT = 1000 K, and only the Lorentzian waveform (time-bandwidth product 0.892) keeps the heating within the solid-state budget ΔT ≤ 750 K — the margin below the ~1050 K melting point of molecular hydrogen at 106 GPa measured by Eremets and Trojan (2009) — while dissociating about half of the molecules.

Problem Statement

Can the photodissociation route of Shibata and Kodama (2011) actually produce a solid atomic — and metallic — hydrogen phase at diamond-anvil-cell-accessible pressure (~100 GPa, versus >400 GPa for pure compression)? Concretely: (i) can ~10 fs, ~250 nm laser pulses at the peak intensities of the proposed design (of order ~6×10^13 W/cm^2) with the near-transform-limited (Lorentzian-class) temporal profile identified in the source's isolated-molecule calculations as the waveform that keeps heating within budget be generated and delivered through diamond anvils onto solid molecular hydrogen at ~106 GPa without damaging the diamonds or driving the sample above the ~750 K solid-state heating budget; (ii) does ultrafast three-photon dissociation then yield a substantial atomic fraction (the isolated-molecule calculation predicts ~50%) that persists as a solid rather than recombining, melting, or ionizing into a plasma; and (iii) is the resulting atomic solid metallic, as prior metallization-density calculations predict? What remains open is whether the predicted dissociation yield and heating budget survive once the solid-state physics neglected in the isolated-molecule treatment is included — intermolecular and band-structure effects on the H2 electronic levels, competing multiphoton-ionization channels, plasma formation, and the recombination, diffusion, and metastability of the hydrogen atoms — and whether the resulting atomic phase is stable long enough to be characterized by structural, optical, or electrical diagnostics.

References

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