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arXiv:2511.16010

Quantum Reorientational Excitations in the Raman Spectrum of Hydrogen

Philip Dalladay-Simpson, Eric Edmund, Huixin Hu, Mario Santoro, Federico Aiace Gorelli

cond-mat.mtrl-scicond-mat.otherquant-phSubmitted Nov 20, 2025• Announced Nov 21, 2025
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Abstract

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.

Comments
8 pages, 6 figures

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Physical Review A•Feb 26, 2007•12 citations
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.
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.
In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H2 differ dramatically because atoms remain fixed in the H2 lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H2. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H2 molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x1019 cm-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.
We prepare an ensemble of isolated rovibrationally excited (v = 1, J = 2) H2 molecules in a phase-locked superposition of magnetic sublevels M using Stark-induced adiabatic Raman passage with linearly polarized single-mode pump (at 532 nm, ∼6 ns pulse duration, 200 mJ/pulse) and Stokes (699 nm, ∼4 ns pulse duration, 20 mJ/pulse) laser excitation. A biaxial superposition state, given by [line]ψ(t)⟩ = 1/√(2)[[line]ν = 1, J = 2, M = -2⟩ - [line]ν = 1, J = 2, M = +2⟩], is prepared with linearly but cross-polarized pump and Stokes laser pulses copropagating along the quantization z-axis. The degree of phase coherence is measured by using the O(2) line of the H2 E,F-X (0,1) band via 2 + 1 resonance enhanced multiphoton ionization (REMPI) at 210.8 nm by recording interference fringes in the REMPI signal in a time-of-flight mass spectrometer as the direction of the UV laser polarization is rotated using a half-wave plate. Nearly 60% population transfer from H2 (v = 0, J = 0) ground state to the superposition state in H2 (v = 1, J = 2) is measured from the depletion of the Q(0) line of the E,F-X (0,0) band as the Stokes frequency is tuned across the (v = 0, J = 0) → (v = 1, J = 2) Raman resonance.
In this work we report the results of calculation for quantum-mechanical rotational transitions in molecular hydrogen, H2{\mathrm{H}}_{2}H2​, induced by an ultracold ground-state antihydrogen atom H‾1s{\overline{\mathrm{H}}}_{1s}H1s​. The calculations are accomplished using a nonreactive close-coupling quantum-mechanical approach. The H2{\mathrm{H}}_{2}H2​ molecule is treated as a rigid rotor. The total elastic-scattering cross section ${\ensuremath{\sigma}}_{\mathrm{el}}(\ensuremath{\epsilon})$ at energy $\ensuremath{\epsilon}$, state-resolved rotational transition cross sections ${\ensuremath{\sigma}}_{{\mathit{jj}}^{'}}(\ensuremath{\epsilon})$ between states jjj and j′{j}^{'}j′, and corresponding thermal rate coefficients kjj′(T){k}_{{\mathit{jj}}^{'}}(T)kjj′​(T) are computed in the temperature range $0.004 \mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}$ 4 K. Satisfactory agreement with other calculations (variational) has been obtained for ${\ensuremath{\sigma}}_{\mathrm{el}}(\ensuremath{\epsilon})$.
The solid para-hydrogen film was prepared by depositing the para-hydrogen vapor onto a sapphire substrate. From the stimulated Raman scattering experiment using two ns-lasers whose laser-frequency difference is equal to the fundamental vibrational transition of the solid para-hydrogen, we observed the collinear generation of Raman sidebands. The high-order Raman sidebands were obtained under the strong pumping intensity (≥230 MW/cm 2 ). The generated five anti-Stokes(AS)-Raman sidebands extend from ultraviolet (292 nm for AS 5 band) to visible (565 nm for AS 1 band) region. Also, we found that the first AS-Raman signal shows weak rotational components as well as a strong vibrational line. From the experiment that makes the multimode probe beam beat with the prepared Raman coherence, we found that the prepared Raman coherence replicates the probe beam to its Raman sidebands. The frequency conversion efficiency from the probe beam to the first AS-Raman sideband rises to the maximum (4.7%) at 284 MW/cm 2 , and then falls with the increase of the pumping intensity. This is thought to be due to the fact that some molecules in the first vibrational level incline to go to the higher vibrational level under the higher pumping intensity. For the strong pumping intensity (290 MW/cm 2 ), four anti-Stokes and one Stokes Raman sidebands of the probe beam were generated.
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.