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arXiv:2601.04549

Observation of ΔJ=0 Rotational Excitation in Dense Hydrogens

Jie Feng, XiaoDi Liu, Haian Xu, Pu Wang, Graeme J. Ackland, Eugene Gregoryanz

quant-phSubmitted Jan 8, 2026• Announced Jan 9, 2026
arXivHTMLPDF

Abstract

Raman measurements performed on dense H2, D2 and H2+D2 in a wide pressure-temperature range reveal the presence of the ΔJ=0 rotational excitation. In the gas/fluid state this excitation has zero Raman shift, but in the solid, the crystal field drive s it away from the zero value e.g. 75 cm-1 at around 50 GPa and 10 K for both isotopes and their mixture. In the case of deuterium, the ΔJ=0 mode splits upon entering phase II suggesting a very complex molecular environment of the broken symmetry phase (BSP). In the fluid state and phases I and II the frequencies (energies) of the ΔJ=0 transition for H2 and D2 do not scale either as rotational (by factor of 2) nor vibrational (by square 2) modes and appear to be completely isotope independent. This independence on mass marks this transition as unique and a fundamentally different type of excitation from the commonly considered harmonic oscillator and quantum rotor.

Journal reference
Physical Review Letters 136, 016101 (2026)
DOI
10.1103/7m51-n6w7

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Raman measurements performed on dense H2, D2 and H2+D2 in a wide pressure-temperature range reveal the presence of the ΔJ=0 rotational excitation. In the gas/fluid state this excitation has zero Raman shift, but in the solid, the crystal field drive s it away from the zero value e.g. 75 cm-1 at around 50 GPa and 10 K for both isotopes and their mixture. In the case of deuterium, the ΔJ=0 mode splits upon entering phase II suggesting a very complex molecular environment of the broken symmetry phase (BSP). In the fluid state and phases I and II the frequencies (energies) of the ΔJ=0 transition for H2 and D2 do not scale either as rotational (by factor of 2) nor vibrational (by square 2) modes and appear to be completely isotope independent. This independence on mass marks this transition as unique and a fundamentally different type of excitation from the commonly considered harmonic oscillator and quantum rotor.
Low-frequency Raman peaks, below 250 cm-1, are observed in hydrogen between 2-174 GPa and 13-300 K. The origin of these features is attributed to reorientational transitions (DeltaJ = 0; Q0-branch), which shift from the Rayleigh line as anisotropic intermolecular interactions lift the mJ degeneracy. This family of excitations closely follows the behavior of the S0-branches, sharing their dependence on pressure, temperature, and ortho-H2 concentration. Above 65 K, spectra corrected by the Bose-Einstein population factor reveal a broad continuum arising from populated higher J-states and increased ortho-para disorder. Upon entering phase III, where molecular rotation is inhibited, this continuum is quenched, giving way to well-established optical phonons. Below 25 K, equilibrated samples demonstrate a fine structure from isolated and pair excitations from impurity ortho-H2 molecules in a parahydrogen lattice, the latter a sensitive probe to anisotropic intermolecular interactions relevant to the quantum modeling of solid H2.
We report an experimental observation of simultaneous rotational and vibrational collinear Raman generation in low pressure cooled deuterium gas, with only two narrow-band laser pulses applied at the input of the molecular cell. Only the fundamental vibrational transition Q1{Q}_{1}Q1​ (0) is driven strongly in this experiment. However, in addition to efficient vibrational Raman generation we observe generation of a large number of rotational sidebands (more than 100) corresponding to S0{S}_{0}S0​ (0) transition. We notice that fine-tuning of the frequency difference of the driving fields near the vibrational Raman resonance changes dramatically the aspects of the generated spectrum and the efficiency of rotational generation: from complete suppression of a self-starting stimulated rotational Raman generation to a strong enhancement of two orders of magnitude. We conduct a numerical analysis that allows us to attribute this behavior to quantum interference among the probability amplitudes of the three molecular states involved.
Precision vibrational spectroscopy of the molecular hydrogen ions is of significant interest for determining fundamental constants, for searching for new forces, and for testing quantum electrodynamics calculations. Future experiments can profit from the ability of preparing molecular hydrogen ions at ultralow kinetic energy and in preselected internal states, with respect to vibration, rotation, and spin degrees of freedom. For the homonuclear ions (H2+,D2+{\mathrm{H}}_{2}{}^{+}, {\mathrm{D}}_{2}{}^{+}H2​+,D2​+), direct laser cooling of the rotational degree of freedom is not feasible. We show by quantum calculations that rotational cooling by cold He buffer gas is an effective approach. For this purpose we have computed the energy-dependent cross sections for rotationally elastic and inelastic collisions, ${\mathrm{h}}_{2}{}^{+}(v=0,\phantom{\rule{0.16em}{0ex}}N)+\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow} {\mathrm{h}}_{2}{}^{+}(v=0,\phantom{\rule{0.16em}{0ex}}{N}^{\ensuremath{'}})+\mathrm{He}$ (where h=H,D)\mathrm{h}=\mathrm{H},\phantom{\rule{0.16em}{0ex}}\mathrm{D})h=H,D), using ab initio coupled-channel calculations. We find that rotational cooling to the lowest rotational state is possible within tens of seconds under experimentally realistic conditions. We furthermore describe possible protocols for the preparation of a single quantum state, where also the spin state is well defined.
Isotope shifts have been measured in the velocity-dependent total cross sections of the m1{m}_{1}m1​=1 magnetic substate of He(3 3^{3}3P) formed in low keV He+{\mathrm{He}}^{+}He++H2{\mathrm{H}}_{2}H2​ or D2{\mathrm{D}}_{2}D2​ collisions. Similar isotope shifts have been predicted on theoretical grounds and observed in ion-atom collision experiments, where united-atom rotational coupling is the primary excitation mechanism. By extending the basic theoretical ideas to ion-molecule collisions, we can interpret our measured shifts as resulting from rotational coupling within the triatomic HeH2+{\mathrm{HeH}}_{2}^{+}HeH2+​ complex.
We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.
Uniaxial stress perturbations establish the 1.257 eV 'H2' zero-phonon line as an electric-dipole allowed transition at the centre of a C 2v point group. Taken in conjunction with a simple one-electron model, the magnitudes of the perturbations support recent suggestions that the H2 centre is a negative charge state of the well-known nitrogen-vacancy-nitrogen 'H3' centre. The H2 zero-phonon line is 0.9 meV higher in energy in 13 C diamond than in 12 C diamond. The shift is consistent, within large uncertainties, with the shift expected from the temperature dependence of the line. A local vibrational mode involving predominantly carbon atoms is identified.