When the Environment Writes the Rules of Quantum Dynamics
In quantum physics, we often learn that the rules governing a system are set by its symmetry. These rules—known as selection rules—determine which transitions between quantum states are allowed and which are forbidden. For example, rotational symmetry constrains how an atom’s angular momentum can change. But what if those rules are not fixed? A recent study of hydrogen (H2)—one of the simplest molecules in nature—showed that the allowed pathways between quantum states are determined not solely by the molecule’s internal symmetry but also by its surroundings. By embedding hydrogen molecules in different crystalline environments, Nathan McLane and colleagues from the University of Maryland, College Park, have demonstrated that the symmetry of the host material can selectively enable or suppress nuclear-spin transitions [1]. In doing so, the team revealed that quantum dynamics is not just an intrinsic property—it can be shaped by the environment.
H2 is one of the simplest systems for exploring quantum behavior. Its two identical protons can align their spins in two different ways: In so-called orthohydrogen the nuclear spins are parallel, whereas in parahydrogen they are antiparallel. Although this difference is subtle, it leads to markedly different physical properties for the two forms. Crucially, transitions between them are highly constrained: In an isolated hydrogen molecule, the overall wave function is symmetric under exchange of the two protons, and this exchange symmetry forbids direct conversion between ortho and para states [2]. This restriction makes H2 a textbook example of how symmetry governs quantum dynamics.
However, most molecules are not isolated—they interact with their environment. When H2 is confined within a solid, its behavior changes. The surrounding atoms generate an anisotropic potential that modifies the molecule’s rotational motion and splits apart overlapping (or degenerate) energy levels. In nearly isotropic environments, such as fullerene cages, H2 behaves almost as a free quantum rotor with characteristic rotational excitations [3]. In more complex environments, including porous materials and adsorption sites, anisotropy reshapes the molecule’s quantum states and dynamics [4, 5]. In strongly interacting systems, such as hydrogen hydrates (high-pressure hydrogen–water compounds), host–guest coupling becomes so strong that the dynamics of hydrogen and water molecules are no longer independent but intertwined [6, 7].
Despite these observed phenomena, a key question has remained open: How does the environment influence not just the energy levels of a molecule but the transitions between them? In other words, can the surroundings determine which quantum pathways are dynamically accessible?
To address this question, McLane and colleagues examined hydrogen molecules trapped inside a crystalline matrix of solid carbon dioxide (CO2) at cryogenic temperatures. By monitoring the hydrogen rovibrational absorption lines with high-resolution infrared spectroscopy, the researchers tracked how the populations of specific quantum states evolve over time. This approach provides direct insight into nuclear-spin conversion processes. The measurements reveal that the crystal enables some transitions between ortho and para states, but not all pathways are equally accessible. Specifically, transitions that conserve the magnetic quantum number m—which labels the projection of angular momentum along a chosen axis—are active. By contrast, those requiring a change in m are spectroscopically observed, but they remain frozen in time, with no population flowing through them. These forbidden pathways are not energetically inaccessible—in fact, thermodynamics strongly favors conversion to the para state at cryogenic temperatures, with an equilibrium ortho-to-para ratio of roughly 10–7 at 10 K. And yet the team observes a long-lived persistence of the ortho population, providing a direct signature of the blocked conversion channels.
The origin of this behavior lies in the symmetry of the electric field created by the surrounding crystal (Fig. 1). In simplified terms, the crystal field of CO2 has a highly symmetric pattern, which is dominated by quadrupolar terms (rank-2 tensor components), with negligible dipolar contributions (rank-1 tensor components). The dipolar components are the ones that mediate m-changing transitions, so the CO2 environment enforces a strict selection rule: Only transitions that do not change the magnetic quantum number are allowed.
What makes this result particularly compelling is that the selection rules can be tuned experimentally. In the study, the researchers replaced CO2 with nitrous oxide (N2O)—a molecule carrying a small dipole moment that slightly breaks the quadrupole symmetry of the local environment. This change relaxes the selection rules and allows additional transitions. Going further with this relaxation, the researchers added a small amount of nitrogen dioxide (NO2)—a paramagnetic molecule—to a CO2 crystal. In this case, magnetic interactions lifted the remaining constraints, opening all possible pathways and dramatically accelerating nuclear-spin conversion. The environment, in effect, acts as a filter that selects which quantum transitions are permitted.
This ability to tailor selection rules has implications that extend well beyond hydrogen. In recent years, there has been growing interest in using molecules as platforms for quantum technologies. Molecular systems offer remarkable flexibility: Their structure, symmetry, and interactions can be tuned through chemical design [8]. As a result, they are being explored as candidates for quantum bits (qubits), where spin states encode information. Nuclear-spin states, in particular, are attractive because they can be long-lived and well-defined.
However, a central challenge in this field is balancing isolation and control. Quantum states must be protected from environmental noise to preserve coherence, yet they must also be coupled in controlled ways to perform useful operations [9, 10]. The work by McLane and colleagues suggests a new way to navigate this balance. Instead of viewing the environment solely as a source of decoherence, it can be treated as a design parameter. By selecting host materials with different molecular shapes, dipole moments, or magnetic properties, one can selectively enable or suppress transitions between states, effectively programming how a quantum system evolves, without relying on strong external fields or complex pulse sequences.
Looking ahead, several questions remain. The microscopic mechanisms underlying nuclear-spin conversion in solids are still not fully understood, and extending these ideas to more complex or strongly interacting systems will be an important next step. It will also be interesting to explore whether similar environmental sensitivities apply to other quantum degrees of freedom, such as electronic spins or vibrational states.
More broadly, this work challenges a familiar assumption. Selection rules are often presented as fundamental and immutable. Yet here, they emerge as properties of a coupled system—a molecule embedded in an environment. The rules are not rewritten but recontextualized: Symmetry still governs quantum behavior, but that symmetry can now be designed.
References
- N. McLane et al., “Environment-imposed selection rules for nuclear-spin conversion of H2 in molecular crystals,” Phys. Rev. Lett. 136, 178002 (2026).
- G. Herzberg, Molecular Spectra and Molecular Structure, Spectra of Diatomic Molecules, Vol. I (Van Nostrand, Princeton, 1950), p. 194–204[Amazon][WorldCat].
- S. Mamone et al., “Rotor in a cage: Infrared spectroscopy of an endohedral hydrogen-fullerene complex,” J. Chem. Phys. 130, 081103 (2009).
- T. Yildirim and A. B. Harris, “Rotational and vibrational dynamics of interstitial molecular hydrogen,” Phys. Rev. B 66, 214301 (2002).
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- L. Renaud et al., “Dual quantum locking: Dynamic coupling of H2 and H2O sublattices in hydrogen-filled ice,” Proc. Natl. Acad. Sci. U.S.A. 123, e2526369123 (2026).
- S. Di Cataldo et al., “Giant splitting of the hydrogen rotational eigenenergies in the C2 filled ice,” Phys. Rev. Lett. 133, 236101 (2024).
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